Hướng dẫn how do you count digits in python? - làm thế nào để bạn đếm các chữ số trong python?

Ví dụ 1: Số lượng chữ số trong một số nguyên sử dụng trong khi vòng lặp

num = 3452
count = 0

while num != 0:
    num //= 10
    count += 1

print("Number of digits: " + str(count))

Đầu ra

Show
Number of digits: 4

Trong chương trình này, vòng lặp trong khi được lặp lại cho đến khi biểu thức kiểm tra

Number of digits: 4
0 được đánh giá thành 0 (sai).

  1. Sau lần lặp đầu tiên,
    Number of digits: 4
    1 sẽ được chia cho 10 và giá trị của nó sẽ là 345. Sau đó,
    Number of digits: 4
    2 được tăng lên 1.
  2. Sau lần lặp thứ hai, giá trị của
    Number of digits: 4
    1 sẽ là 34 và
    Number of digits: 4
    2 được tăng lên 2.
  3. Sau lần lặp thứ ba, giá trị của
    Number of digits: 4
    1 sẽ là 3 và
    Number of digits: 4
    2 được tăng lên 3.
  4. Sau lần lặp thứ tư, giá trị của
    Number of digits: 4
    1 sẽ là 0 và
    Number of digits: 4
    2 được tăng lên 4.
  5. Sau đó, biểu thức kiểm tra được đánh giá là sai và vòng lặp chấm dứt.

Ví dụ 2: Sử dụng các phương thức sẵn có

num = 123456
print(len(str(num)))

Đầu ra

6

Trong chương trình này, vòng lặp trong khi được lặp lại cho đến khi biểu thức kiểm tra

Number of digits: 4
0 được đánh giá thành 0 (sai).

Như được hiển thị bởi các câu trả lời khác, việc sử dụng

num = 123456
print(len(str(num)))
1 dẫn đến kết quả không chính xác cho
num = 123456
print(len(str(num)))
2 lớn trong khi sử dụng
num = 123456
print(len(str(num)))
3 hoặc vòng lặp thủ công dẫn đến hiệu suất chậm cho
num = 123456
print(len(str(num)))
2 lớn. Câu trả lời của Jodag cung cấp một sự thay thế thực sự tốt mà chỉ thất bại đối với các số nguyên có thể sẽ làm hỏng máy tính của bạn, nhưng chúng tôi có thể làm tốt hơn một chút và thậm chí nhanh hơn (đối với
num = 123456
print(len(str(num)))
2 đủ nhỏ để
num = 123456
print(len(str(num)))
6 được đảm bảo là chính xác) bằng cách tránh logarit hoàn toàn và sử dụng nhị phân thay thế :and even faster (for
num = 123456
print(len(str(num)))
2 small enough that
num = 123456
print(len(str(num)))
6 is guaranteed to be accurate) by avoid logarithms altogether and using binary instead:

def num_digits(n: int) -> int:
    assert n > 0
    i = int(0.30102999566398114 * (n.bit_length() - 1)) + 1
    return (10 ** i <= n) + i

Hãy phá vỡ điều này. Đầu tiên, có

num = 123456
print(len(str(num)))
7 kỳ lạ. Điều này tính toán độ dài trong nhị phân:

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()

Không giống như logarit, đây là cả nhanh chóng và chính xác cho các số nguyên. Hóa ra, điều này dẫn đến chính xác

num = 123456
print(len(str(num)))
8. Để tự mình có được
num = 123456
print(len(str(num)))
9, chúng tôi trừ
6
0, do đó
6
1.

Tiếp theo, chúng tôi nhân với

6
2. Điều này tương đương với
6
3 hơi tròn xuống. Điều này tận dụng các quy tắc logarit để tính toán ước tính
6
4 từ
num = 123456
print(len(str(num)))
9.

Bây giờ, bạn có thể tự hỏi làm thế nào chúng ta có thể ở thời điểm này, bởi vì mặc dù

6
6, điều tương tự cũng không đúng với
6
7. Hãy nhớ lại rằng
6
8 để chúng ta có thể thực hiện một số toán học nhanh:

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))

Lưu ý rằng

6
9 ít nhất là
def num_digits(n: int) -> int:
    assert n > 0
    i = int(0.30102999566398114 * (n.bit_length() - 1)) + 1
    return (10 ** i <= n) + i
0, có nghĩa là chúng ta sẽ giảm nhiều nhất so với kết quả của chúng ta. Đây là nơi mà sự điều chỉnh cuối cùng xuất hiện, nơi chúng tôi kiểm tra
def num_digits(n: int) -> int:
    assert n > 0
    i = int(0.30102999566398114 * (n.bit_length() - 1)) + 1
    return (10 ** i <= n) + i
2, dẫn đến một
def num_digits(n: int) -> int:
    assert n > 0
    i = int(0.30102999566398114 * (n.bit_length() - 1)) + 1
    return (10 ** i <= n) + i
3 khi kết quả quá nhỏ hoặc
def num_digits(n: int) -> int:
    assert n > 0
    i = int(0.30102999566398114 * (n.bit_length() - 1)) + 1
    return (10 ** i <= n) + i
4 khi kết quả vừa phải.

Tương tự như câu trả lời của Jodag, cách tiếp cận này thực sự thất bại với

num = 123456
print(len(str(num)))
2 rất lớn, ở đâu đó vào khoảng
def num_digits(n: int) -> int:
    assert n > 0
    i = int(0.30102999566398114 * (n.bit_length() - 1)) + 1
    return (10 ** i <= n) + i
6 trong đó
def num_digits(n: int) -> int:
    assert n > 0
    i = int(0.30102999566398114 * (n.bit_length() - 1)) + 1
    return (10 ** i <= n) + i
7 bị tắt nhiều hơn
def num_digits(n: int) -> int:
    assert n > 0
    i = int(0.30102999566398114 * (n.bit_length() - 1)) + 1
    return (10 ** i <= n) + i
8. Tuy nhiên, các số nguyên có kích thước đó có thể sẽ làm hỏng máy tính của bạn, vì vậy điều này đủ.

Bài viết này được đóng góp bởi Suruchi Kumari. Nếu bạn thích GeekSforGeeks và muốn đóng góp, bạn cũng có thể viết một bài viết bằng cách sử dụng PROPTENT.GeekSforGeeks.org hoặc gửi bài viết của bạn đến. Xem bài viết của bạn xuất hiện trên trang chính của GeekSforGeek và giúp các chuyên viên máy tính khác. & NBSP; Vui lòng viết nhận xét nếu bạn tìm thấy bất cứ điều gì không chính xác hoặc bạn muốn chia sẻ thêm thông tin về chủ đề được thảo luận ở trên.

Example:

Hướng dẫn how do you count digits in python? - làm thế nào để bạn đếm các chữ số trong python?

Làm thế nào để bạn đếm các chữ số và chữ cái trong Python?

Đầu tiên chúng tôi tìm thấy tất cả các chữ số trong chuỗi với sự trợ giúp của RE. Findall () đưa ra danh sách các mẫu phù hợp với sự trợ giúp của LEN, chúng tôi tính toán độ dài của danh sách và tương tự chúng tôi tìm thấy tổng số chữ cái trong chuỗi với sự trợ giúp của RE. Phương thức Findall () và tính độ dài của danh sách bằng LEN.

Làm thế nào để bạn đếm số chữ số trong một số?

  1. Công thức sẽ là số nguyên của (log10 (số) + 1). Ví dụ, nếu số là 1245, thì nó trên 1000 và dưới 10000, do đó giá trị nhật ký sẽ nằm trong phạm vi 3
  2. Làm thế nào để bạn tính toán số trong Python?
  3. Đối với các tính toán toán học đơn giản trong Python, bạn có thể sử dụng các toán tử toán học tích hợp, chẳng hạn như bổ sung ( +), phép trừ ( -), chia ( /) và nhân ( *). Nhưng các hoạt động nâng cao hơn, chẳng hạn như các hàm theo cấp số nhân, logarit, lượng giác hoặc năng lượng, không được xây dựng.
  4. Các chữ số được tính như thế nào?
  5. 0, 1, 2, 3, 4, 5, 6, 7, 8 và 9 là mười chữ số chúng ta sử dụng trong các chữ số hàng ngày. Ví dụ: Số 153 được tạo thành từ 3 chữ số ("1", "5" và "3"). Ví dụ: Số 46 được tạo thành từ 2 chữ số ("4" và "6"). Chúng ta cũng có thể sử dụng các biểu tượng khác, ví dụ HexAdeCimal cũng sử dụng một số chữ cái!

Đưa ra một số N, nhiệm vụ là trả về số lượng các chữ số trong số này.

C++

def num_digits(n: int) -> int:
    assert n > 0
    i = int(0.30102999566398114 * (n.bit_length() - 1)) + 1
    return (10 ** i <= n) + i
9

Chương trình để đếm các chữ số trong một số nguyên

Giải pháp lặp đơn giản để đếm các chữ số trong một số nguyên

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

Số nguyên được nhập bởi người dùng được lưu trữ trong biến n. Sau đó, vòng lặp trong khi được lặp lại cho đến khi biểu thức kiểm tra n! = 0 được đánh giá thành 0 (sai). & nbsp; Chúng tôi sẽ coi 3456 là số nguyên đầu vào. & nbsp;

Sau lần lặp đầu tiên, giá trị của N sẽ được cập nhật lên 345 và số lượng được tăng lên 1.

Sau lần lặp thứ hai, giá trị của N sẽ được cập nhật lên 34 và số lượng được tăng lên 2.

Sau lần lặp thứ ba, giá trị của N sẽ được cập nhật lên 3 và số lượng được tăng lên 3.

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
Number of digits : 9
2

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
Number of digits : 9
4

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits : 9
6

Trong lần lặp thứ tư, giá trị của N sẽ được cập nhật về 0 và số lượng sẽ được tăng lên 4. & nbsp;

Number of digits : 9
6

Sau đó, biểu thức kiểm tra được đánh giá (n! = 0) là sai và vòng lặp chấm dứt với số lượng cuối cùng là 4.

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

Dưới đây là việc thực hiện phương pháp trên:

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
0
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
1
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
2

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
Number of digits : 9
6

Number of digits : 9
6

assert 4 == (0b1111).bit_length() assert 8 == (0b1011_1000).bit_length() assert 9 == (0b1_1011_1000).bit_length() 3 assert 4 == (0b1111).bit_length() assert 8 == (0b1011_1000).bit_length() assert 9 == (0b1_1011_1000).bit_length() 4assert 4 == (0b1111).bit_length() assert 8 == (0b1011_1000).bit_length() assert 9 == (0b1_1011_1000).bit_length() 5 assert 4 == (0b1111).bit_length() assert 8 == (0b1011_1000).bit_length() assert 9 == (0b1_1011_1000).bit_length() 5 assert 4 == (0b1111).bit_length() assert 8 == (0b1011_1000).bit_length() assert 9 == (0b1_1011_1000).bit_length() 7

Number of digits : 9
8

Giải pháp lặp đơn giản để đếm các chữ số trong một số nguyên

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
0
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
1

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
4

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
3
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
7

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
9
Number of digits : 9
0

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
Number of digits : 9
2

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
Number of digits : 9
4

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits : 9
6

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
Number of digits : 9
9

Number of digits : 9
6

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
3
Number of digits :9
2
Number of digits :9
3
Number of digits :9
4

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
5
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
5
Number of digits :9
9

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits: 4
37
Number of digits: 4
38
Number of digits: 4
39
Number of digits: 4
40

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
Number of digits : 9
6

Number of digits : 9
6

Java

Number of digits: 4
45
Number of digits: 4
46

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits: 4
48
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
3
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
4
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
5
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
7

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
3
Number of digits: 4
57
Number of digits: 4
58
Number of digits: 4
59

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
9
Number of digits: 4
62
Number of digits: 4
58
Number of digits: 4
64

Number of digits: 4
65
Number of digits: 4
66
Number of digits: 4
67
Number of digits: 4
59

Number of digits: 4
65
Number of digits : 9
4

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
Number of digits : 9
6

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
Number of digits : 9
9

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits : 9
6

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits: 4
79
Number of digits: 4
48
Number of digits :9
3
Number of digits: 4
82

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
5
Number of digits: 4
87
Number of digits: 4
88
Number of digits: 4
59

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
Number of digits: 4
91
Number of digits : 9
2

Number of digits: 4
93
Number of digits: 4
94

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits : 9
6

Number of digits : 9
6

Python3

Number of digits: 4
98
Number of digits: 4
99

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
num = 123456
print(len(str(num)))
01
num = 123456
print(len(str(num)))
02
Number of digits: 4
58

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
9
num = 123456
print(len(str(num)))
06
num = 123456
print(len(str(num)))
02
Number of digits: 4
58
num = 123456
print(len(str(num)))
09

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
num = 123456
print(len(str(num)))
11
num = 123456
print(len(str(num)))
1212121212
num = 123456
print(len(str(num)))
02
Number of digits: 4
67

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
num = 123456
print(len(str(num)))
01__218
num = 123456
print(len(str(num)))
02
6
0

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
Number of digits: 4
2

num = 123456
print(len(str(num)))
11
num = 123456
print(len(str(num)))
02
Number of digits: 4
88

num = 123456
print(len(str(num)))
27
Number of digits: 4
38
num = 123456
print(len(str(num)))
29
num = 123456
print(len(str(num)))
30
num = 123456
print(len(str(num)))
31

C#

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
0
num = 123456
print(len(str(num)))
33

Number of digits: 4
45
Number of digits: 4
46

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits: 4
48
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
3
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
4
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
5
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
7

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
3
Number of digits: 4
57
Number of digits: 4
58
Number of digits: 4
59

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
9
Number of digits: 4
62
Number of digits: 4
58
Number of digits: 4
64

Number of digits: 4
65
Number of digits : 9
2

Number of digits: 4
65
Number of digits : 9
4

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
Number of digits : 9
6

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
Number of digits : 9
9

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits : 9
6

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits: 4
79
Number of digits: 4
48
Number of digits :9
3
Number of digits: 4
82

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
5
Number of digits: 4
87
Number of digits: 4
88
Number of digits: 4
59

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
num = 123456
print(len(str(num)))
72
num = 123456
print(len(str(num)))
73

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits : 9
6

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits : 9
6

Number of digits : 9
6

Number of digits: 498 Number of digits: 499

num = 123456
print(len(str(num)))
81

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
num = 123456
print(len(str(num)))
01
num = 123456
print(len(str(num)))
02
Number of digits: 4
58

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
9
num = 123456
print(len(str(num)))
06
num = 123456
print(len(str(num)))
02
Number of digits: 4
58
num = 123456
print(len(str(num)))
09

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
num = 123456
print(len(str(num)))
11
num = 123456
print(len(str(num)))
1212121212
num = 123456
print(len(str(num)))
02
Number of digits: 4
67

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
num = 123456
print(len(str(num)))
01__218
num = 123456
print(len(str(num)))
02
6
0

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
6
05
num = 123456
print(len(str(num)))
88
Number of digits: 4
59

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits : 9
6

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
Number of digits: 4
2

Number of digits : 9
6

num = 123456
print(len(str(num)))
11
num = 123456
print(len(str(num)))
02
Number of digits: 4
88

num = 123456
print(len(str(num)))
27
Number of digits: 4
38
num = 123456
print(len(str(num)))
29
num = 123456
print(len(str(num)))
30
num = 123456
print(len(str(num)))
31

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
6
20
num = 123456
print(len(str(num)))
84
6
22

6
23

assert 4 == (0b1111).bit_length() assert 8 == (0b1011_1000).bit_length() assert 9 == (0b1_1011_1000).bit_length() 0 num = 123456 print(len(str(num)))33

6
24

Number of digits: 4
45
Number of digits: 4
46

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
6
29

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
3
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
7

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
6
36

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
Number of digits : 9
4

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits : 9
6

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
Number of digits : 9
9

Number of digits : 9
6

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits :9
9

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
6
48
Number of digits : 9
2
Number of digits: 4
94

6
51

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
9
Number of digits : 9
0

Number of digits : 9

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits: 4
79
Number of digits: 4
48
Number of digits :9
3
num = 123456
print(len(str(num)))
65
O(log10(n)) or O(num digits)
Auxiliary Space: O(1) or constant

log2(n) - 1 < floor(log2(n)) <= log2(n) log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n) floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n)) 2assert 4 == (0b1111).bit_length() assert 8 == (0b1011_1000).bit_length() assert 9 == (0b1_1011_1000).bit_length() 5 Number of digits :99

num = 123456
print(len(str(num)))
74
num = 123456
print(len(str(num)))
75
num = 123456
print(len(str(num)))
76
Number of digits: 4
94

Algorithm:

  • PHP
  • num = 123456
    print(len(str(num)))
    82
    assert 4 == (0b1111).bit_length()
    assert 8 == (0b1011_1000).bit_length()
    assert 9 == (0b1_1011_1000).bit_length()
    
    4
    num = 123456
    print(len(str(num)))
    84
    Number of digits :9
    4

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
num = 123456
print(len(str(num)))
88
num = 123456
print(len(str(num)))
89

C++

def num_digits(n: int) -> int:
    assert n > 0
    i = int(0.30102999566398114 * (n.bit_length() - 1)) + 1
    return (10 ** i <= n) + i
9

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
9
Number of digits: 4
38
num = 123456
print(len(str(num)))
84
num = 123456
print(len(str(num)))
94

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
num = 123456
print(len(str(num)))
84
num = 123456
print(len(str(num)))
99
6
00
Number of digits: 4
38
num = 123456
print(len(str(num)))
84
6
03

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
num = 123456
print(len(str(num)))
88
Number of digits: 4
59

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
4

num = 123456
print(len(str(num)))
84
6
16

Number of digits : 9
6

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
3
Number of digits :9
2
Number of digits :9
3
Number of digits :9
4

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
5
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
5
Number of digits :9
9

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
Number of digits : 9
6

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
Number of digits : 9
6

Number of digits : 9
6

Java

Number of digits : 9
8

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
num = 123456
print(len(str(num)))
84
num = 123456
print(len(str(num)))
99
6
00
Number of digits: 4
38
num = 123456
print(len(str(num)))
84
6
03

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
num = 123456
print(len(str(num)))
88
Number of digits: 4
59

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
4

num = 123456
print(len(str(num)))
84
6
16

Number of digits : 9
6

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
3
Number of digits :9
2
Number of digits :9
3
Number of digits :9
4

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
5
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
5
Number of digits :9
9

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits: 4
37
Number of digits: 4
38
Number of digits: 4
39
Number of digits: 4
40

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
Number of digits : 9
6

Number of digits : 9
6

Java

Number of digits: 4
45
Number of digits: 4
46

Number of digits: 4
45
Number of digits: 4
46

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits: 4
48
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
3
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
4
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
5
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
7

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
3
Number of digits: 4
57
Number of digits: 4
58
Number of digits: 4
59

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
9
Number of digits: 4
62
Number of digits: 4
58
Number of digits: 4
64

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
Number of digits : 9
9

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits : 9
6

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits: 4
79
Number of digits: 4
48
Number of digits :9
3
Number of digits: 4
82

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
5
Number of digits: 4
87
Number of digits: 4
88
Number of digits: 4
59

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
Number of digits: 4
91
Number of digits : 9
2

Number of digits: 4
93
Number of digits: 4
94

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits : 9
6

Number of digits : 9
6

Python3

Number of digits: 4
98
Number of digits: 4
99

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
0
num = 123456
print(len(str(num)))
22__21212

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
6
0

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
6
0
num = 123456
print(len(str(num)))
18
def num_digits(n: int) -> int:
    assert n > 0
    i = int(0.30102999566398114 * (n.bit_length() - 1)) + 1
    return (10 ** i <= n) + i
94
num = 123456
print(len(str(num)))
1212

num = 123456
print(len(str(num)))
11
num = 123456
print(len(str(num)))
02
Number of digits: 4
88

num = 123456
print(len(str(num)))
27
Number of digits: 4
38
num = 123456
print(len(str(num)))
29
num = 123456
print(len(str(num)))
30
num = 123456
print(len(str(num)))
31

C#

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
0
num = 123456
print(len(str(num)))
33

Number of digits: 4
45
Number of digits: 4
46

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits: 4
48
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
3
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
4
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
5
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
7

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
0
6
64

Number of digits: 4
65
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
4

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
6
70

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits : 9
6

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits: 4
79
Number of digits: 4
48
Number of digits :9
3
num = 123456
print(len(str(num)))
65

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
5
Number of digits :9
9

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
num = 123456
print(len(str(num)))
72
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
42

num = 123456
print(len(str(num)))
74
num = 123456
print(len(str(num)))
75
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
45

num = 123456
print(len(str(num)))
74
Number of digits: 4
94

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits : 9
6

Number of digits : 9
6

PHP

num = 123456
print(len(str(num)))
81

num = 123456
print(len(str(num)))
82
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
4
num = 123456
print(len(str(num)))
84
Number of digits :9
4

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
0
Number of digits: 4
38
num = 123456
print(len(str(num)))
84
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
61

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
4

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
67
num = 123456
print(len(str(num)))
84
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
69

Number of digits : 9
6

num = 123456
print(len(str(num)))
84
6
16

num = 123456
print(len(str(num)))
27
Number of digits: 4
38
Number of digits : 9
2
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
76

Number of digits: 4
65
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
78
num = 123456
print(len(str(num)))
84
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
80

6
23

JavaScript

6
24

num = 123456
print(len(str(num)))
82
6
26

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
0
6
64

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
4

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
67
num = 123456
print(len(str(num)))
84
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
69

Number of digits : 9
6

num = 123456
print(len(str(num)))
84
6
16

num = 123456
print(len(str(num)))
27
Number of digits: 4
38
Number of digits : 9
2
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
76

6
51

JavaScript

Number of digits :9

num = 123456
print(len(str(num)))
82
6
26
O(log(n)) 
Auxiliary Space : O(log(n))

assert 4 == (0b1111).bit_length() assert 8 == (0b1011_1000).bit_length() assert 9 == (0b1_1011_1000).bit_length() 9log2(n) - 1 < floor(log2(n)) <= log2(n) log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n) floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n)) 0 664

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
94
Digit count of N = upper bound of log10(N)

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
96
Number of digits :9
9

C++

def num_digits(n: int) -> int:
    assert n > 0
    i = int(0.30102999566398114 * (n.bit_length() - 1)) + 1
    return (10 ** i <= n) + i
9

6
48
6
83
Number of digits: 4
94

Đầu ra

Độ phức tạp về thời gian: O (log (n)) & nbsp; không gian phụ trợ: O (log (n))

Number of digits : 9
6

Giải pháp dựa trên log để đếm các chữ số trong một số nguyên

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

Chúng ta có thể sử dụng log10 (logarit của cơ sở 10) để đếm số chữ số của các số dương (logarit không được xác định cho các số âm). Số lượng số lượng của N = giới hạn trên của log10 (n). & Nbsp;

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits : 9
1
Number of digits : 9
2

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
30
Number of digits : 9
3

Dưới đây là việc thực hiện ý tưởng trên:

Number of digits : 9
6

assert 4 == (0b1111).bit_length() assert 8 == (0b1011_1000).bit_length() assert 9 == (0b1_1011_1000).bit_length() 0 assert 4 == (0b1111).bit_length() assert 8 == (0b1011_1000).bit_length() assert 9 == (0b1_1011_1000).bit_length() 1 assert 4 == (0b1111).bit_length() assert 8 == (0b1011_1000).bit_length() assert 9 == (0b1_1011_1000).bit_length() 2

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
36

Number of digits : 9
8

Đầu ra

Độ phức tạp về thời gian: O (log (n)) & nbsp; không gian phụ trợ: O (log (n))

Number of digits : 9
6

Giải pháp dựa trên log để đếm các chữ số trong một số nguyên

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

Chúng ta có thể sử dụng log10 (logarit của cơ sở 10) để đếm số chữ số của các số dương (logarit không được xác định cho các số âm). Số lượng số lượng của N = giới hạn trên của log10 (n). & Nbsp;

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits: 4
37
Number of digits: 4
38
Number of digits: 4
39
Number of digits: 4
40

Dưới đây là việc thực hiện ý tưởng trên:

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
0
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
1
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
2

assert 4 == (0b1111).bit_length() assert 8 == (0b1011_1000).bit_length() assert 9 == (0b1_1011_1000).bit_length() 3 assert 4 == (0b1111).bit_length() assert 8 == (0b1011_1000).bit_length() assert 9 == (0b1_1011_1000).bit_length() 4assert 4 == (0b1111).bit_length() assert 8 == (0b1011_1000).bit_length() assert 9 == (0b1_1011_1000).bit_length() 5 assert 4 == (0b1111).bit_length() assert 8 == (0b1011_1000).bit_length() assert 9 == (0b1_1011_1000).bit_length() 5 log2(n) - 1 < floor(log2(n)) <= log2(n) log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n) floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n)) 10

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
11
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
13
Number of digits: 4
38
num = 123456
print(len(str(num)))
1
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
16

Number of digits: 4
45
Number of digits: 4
46

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits: 4
48
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
3
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
4
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
5
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
7

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
0
6
64

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits : 9
6

Number of digits: 4
65
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
4

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
6
70

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
Number of digits: 4
91
Number of digits : 9
2

Number of digits: 4
93
Number of digits: 4
94

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits : 9
6

Number of digits : 9
6

Python3

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits: 4
79
Number of digits: 4
48
Number of digits :9
3
num = 123456
print(len(str(num)))
65

Number of digits: 4
98
Number of digits: 4
99

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
5
Number of digits :9
9

num = 123456
print(len(str(num)))
11
num = 123456
print(len(str(num)))
02
Number of digits: 4
88

num = 123456
print(len(str(num)))
27
Number of digits: 4
38
num = 123456
print(len(str(num)))
29
num = 123456
print(len(str(num)))
30
num = 123456
print(len(str(num)))
31

C#

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
0
num = 123456
print(len(str(num)))
33

Number of digits: 4
45
Number of digits: 4
46

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits: 4
48
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
3
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
4
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
5
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
7

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
0
6
64

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits : 9
6

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits: 4
79
Number of digits: 4
48
Number of digits :9
3
num = 123456
print(len(str(num)))
65

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
5
Number of digits :9
9

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
num = 123456
print(len(str(num)))
72
Number of digits : 9
2

num = 123456
print(len(str(num)))
74
Number of digits: 4
94

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits : 9
6

Number of digits : 9
6

PHP

num = 123456
print(len(str(num)))
81

num = 123456
print(len(str(num)))
82
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
4
num = 123456
print(len(str(num)))
84
Number of digits :9
4

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
0
Number of digits: 4
38
num = 123456
print(len(str(num)))
84
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
61

Number of digits : 9
6

num = 123456
print(len(str(num)))
84
6
16

num = 123456
print(len(str(num)))
27
Number of digits: 4
38
Number of digits : 9
2
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
76

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
4
num = 123456
print(len(str(num)))
84
6
22

6
23

JavaScript

6
24

num = 123456
print(len(str(num)))
82
6
26

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
0
6
64

Number of digits : 9
6

num = 123456
print(len(str(num)))
84
6
16

num = 123456
print(len(str(num)))
27
Number of digits: 4
38
Number of digits : 9
2
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
76

Number of digits :9
00
Number of digits :9
01

6
51

JavaScript

Number of digits : 9

num = 123456
print(len(str(num)))
82
6
26
O(1) or constant
Auxiliary Space: O(1) or constant

assert 4 == (0b1111).bit_length() assert 8 == (0b1011_1000).bit_length() assert 9 == (0b1_1011_1000).bit_length() 9log2(n) - 1 < floor(log2(n)) <= log2(n) log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n) floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n)) 0 664 to count digits in an integer

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
94

C++

def num_digits(n: int) -> int:
    assert n > 0
    i = int(0.30102999566398114 * (n.bit_length() - 1)) + 1
    return (10 ** i <= n) + i
9

6
48
6
83
Number of digits: 4
94

Đầu ra

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits :9
13

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits :9
15

Number of digits : 9
6

Độ phức tạp về thời gian: O (log (n)) & nbsp; không gian phụ trợ: O (log (n))

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

Giải pháp dựa trên log để đếm các chữ số trong một số nguyên

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits :9
24

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
Number of digits : 9
6

Number of digits : 9
6

Java

def num_digits(n: int) -> int:
    assert n > 0
    i = int(0.30102999566398114 * (n.bit_length() - 1)) + 1
    return (10 ** i <= n) + i
24
def num_digits(n: int) -> int:
    assert n > 0
    i = int(0.30102999566398114 * (n.bit_length() - 1)) + 1
    return (10 ** i <= n) + i
25

Number of digits: 4
79
Number of digits: 4
45
Number of digits: 4
46

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits: 4
48
Number of digits :9
3
Number of digits :9
08
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
3
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
7

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
Number of digits :9
43

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
Number of digits :9
45

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits : 9
6

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits: 4
79
Number of digits: 4
48
Number of digits :9
3
Number of digits :9
52

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
3
Number of digits: 4
87
Number of digits :9
58
Number of digits: 4
59

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
Number of digits :9
24

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits : 9
6

Number of digits : 9
6

Python3

Number of digits: 4
98
Number of digits :9
66

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
num = 123456
print(len(str(num)))
11
num = 123456
print(len(str(num)))
02
Number of digits :9
70
Number of digits :9
71

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
Number of digits :9
74
Number of digits :9
71

num = 123456
print(len(str(num)))
11
num = 123456
print(len(str(num)))
02
Number of digits :9
78

num = 123456
print(len(str(num)))
27
Number of digits :9
80

C#

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
0
num = 123456
print(len(str(num)))
33

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
0
Number of digits :9
84

Number of digits: 4
45
Number of digits: 4
46

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits: 4
48
Number of digits :9
3
Number of digits :9
08
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
3
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
7

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits: 4
79
Number of digits: 4
48
Number of digits :9
3
Number of digits :9
52

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
Number of digits :9
99

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits : 9
6

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
3
Number of digits: 4
87
Number of digits :9
58
Number of digits: 4
59

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

Number of digits: 4
98
Number of digits :9
66

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
Number of digits :9
24

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits : 9
6

Number of digits : 9
6

assert 4 == (0b1111).bit_length() assert 8 == (0b1011_1000).bit_length() assert 9 == (0b1_1011_1000).bit_length() 9num = 123456 print(len(str(num)))11num = 123456 print(len(str(num)))02 Number of digits :970Number of digits :971

6
24

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
3
Number of digits :9
74
Number of digits :9
71

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
8

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
Number of digits : 9
26

log2(n) - 1 < floor(log2(n)) <= log2(n)

log10(n) - 0.30102999566398114 < 0.30102999566398114 * floor(log2(n)) <= log10(n)

floor(log10(n) - 0.30102999566398114) < floor(0.30102999566398114 * floor(log2(n))) <= floor(log10(n))
2
Number of digits : 9
28

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits : 9
6

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits : 9
32

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
9
Number of digits :9
24

6
51

num = 123456
print(len(str(num)))
11
num = 123456
print(len(str(num)))
02
Number of digits :9
78
O(1) or constant
Auxiliary Space:  O(Number of digits in an integer)

assert 4 == (0b1111).bit_length()
assert 8 == (0b1011_1000).bit_length()
assert 9 == (0b1_1011_1000).bit_length()
0
num = 123456
print(len(str(num)))
33Suruchi Kumari . If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to . See your article appearing on the GeeksforGeeks main page and help other Geeks. 
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.


Làm thế nào để bạn đếm các chữ số và chữ cái trong Python?

Đầu tiên chúng tôi tìm thấy tất cả các chữ số trong chuỗi với sự trợ giúp của RE. Findall () đưa ra danh sách các mẫu phù hợp với sự trợ giúp của LEN, chúng tôi tính toán độ dài của danh sách và tương tự chúng tôi tìm thấy tổng số chữ cái trong chuỗi với sự trợ giúp của RE. Phương thức Findall () và tính độ dài của danh sách bằng LEN.

Làm thế nào để bạn đếm số chữ số trong một số?

Công thức sẽ là số nguyên của (log10 (số) + 1).Ví dụ, nếu số là 1245, thì nó trên 1000 và dưới 10000, do đó giá trị nhật ký sẽ nằm trong phạm vi 3 integer of (log10(number) + 1). For an example, if the number is 1245, then it is above 1000, and below 10000, so the log value will be in range 3 < log10(1245) < 4. Now taking the integer, it will be 3. Then add 1 with it to get number of digits.

Làm thế nào để bạn tính toán số trong Python?

Đối với các tính toán toán học đơn giản trong Python, bạn có thể sử dụng các toán tử toán học tích hợp, chẳng hạn như bổ sung ( +), phép trừ ( -), chia ( /) và nhân ( *).Nhưng các hoạt động nâng cao hơn, chẳng hạn như các hàm theo cấp số nhân, logarit, lượng giác hoặc năng lượng, không được xây dựng.use the built-in mathematical operators, such as addition ( + ), subtraction ( - ), division ( / ), and multiplication ( * ). But more advanced operations, such as exponential, logarithmic, trigonometric, or power functions, are not built in.

Các chữ số được tính như thế nào?

0, 1, 2, 3, 4, 5, 6, 7, 8 và 9 là mười chữ số chúng ta sử dụng trong các chữ số hàng ngày.Ví dụ: Số 153 được tạo thành từ 3 chữ số ("1", "5" và "3").Ví dụ: Số 46 được tạo thành từ 2 chữ số ("4" và "6").Chúng ta cũng có thể sử dụng các biểu tượng khác, ví dụ HexAdeCimal cũng sử dụng một số chữ cái!. Example: The numeral 153 is made up of 3 digits ("1", "5" and "3"). Example: The numeral 46 is made up of 2 digits ("4", and "6"). We can use other symbols too, for example hexadecimal also uses some letters!