Đưa ra một mảng các số N, tìm LCM của nó. & Nbsp; & nbsp;
Input : {1, 2, 8, 3} Output : 24 Input : {2, 7, 3, 9, 4} Output : 252
Chúng tôi biết, & nbsp; mối quan hệ trên chỉ giữ cho hai số, & nbsp; ý tưởng ở đây là mở rộng mối quan hệ của chúng tôi cho hơn 2 số. Hãy nói rằng chúng tôi có một mảng mảng [] chứa n các yếu tố có LCM cần được tính toán. Các bước chính của thuật toán của chúng tôi là: & nbsp; & nbsp;
The above relation only holds for two numbers,
The idea here is to extend our relation for more than 2 numbers. Let’s say we have an array arr[] that contains n elements whose LCM needed to be calculated.
The main steps of our algorithm are:
- Khởi tạo ANS = mảng [0].
- Lặp lại tất cả các phần tử của mảng, tức là từ i = 1 đến i = n-1 & nbsp; tại ith itation ans = lcm [mảng [0], mảng [1], . Điều này có thể được thực hiện dễ dàng như LCM [ARR [0], ARR [1], Mạnh., ARR [i]] = LCM [ANS, ARR [i]]. Do đó, tại I WIRT, chúng tôi chỉ cần làm ANS = LCM [ANS, ARR [i]] = Ans X Arr [i] / GCD [ANS, ARR [i]] & nbsp; & nbsp;
At the ith iteration ans = LCM[arr[0], arr[1], …….., arr[i-1]]. This can be done easily as LCM[arr[0], arr[1], …., arr[i]] = LCM[ans, arr[i]]. Thus at i’th iteration we just have to do ans = LCM[ans, arr[i]] = ans x arr[i] / gcd[ans, arr[i]]
Dưới đây là việc thực hiện thuật toán trên: & nbsp; & nbsp;
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Độ phức tạp về thời gian: O [n * log [min [a, b]]], trong đó n đại diện cho kích thước của mảng đã cho. Không gian .O[n * log[min[a, b]]], where n represents the size of the given array.
Auxiliary Space: O[n*log[min[a, b]]] due to recursive stack space.
Dưới đây là việc thực hiện thuật toán trên một cách đệ quy:
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