Consider Ø(n) as the Euler Totient Function for n. You will be given a positive integer N and you have to find the smallest positive integer n, n <= N for which the ratio n/Ø(n) is maximized.
Input: N = 6 Output: 6 Explanation: For n = 1, 2, 3, 4, 5 and 6 the values of the ratio are 1, 2, 1.5, 2, 1.25 and 3 respectively. The maximum is obtained at 6.
Input: N = 50 Output: 30 Explanation: For n = 1 to 50, the maximum value of the ratio is 3.75 which is obtained at n = 30.
You don't need to read input or print anything. Your task is to complete the function maximizeEulerRatio() which takes an Integer N as input and returns the smallest positive integer (<= N) which maximizes the ratio n/Ø(n) is maximized.
Expected Time Complexity: O(constant)
Expected Auxiliary Space: O(constant)
1 <= N <= 1012
We strongly recommend solving this problem on your own before viewing its editorial. Do you still want to view the editorial?Yes