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396. Rotate Function
Given an array of integers A
and let n to be its length.
Assume Bk
to be an array obtained by rotating the array A
k positions clock-wise, we define a "rotation function" F
on A
as follow:
F(k) = 0 * Bk[0] + 1 * Bk[1] + ... + (n-1) * Bk[n-1]
.
Calculate the maximum value of F(0), F(1), ..., F(n-1)
.
Note:
n is guaranteed to be less than 105.
Example:
A = [4, 3, 2, 6] F(0) = (0 * 4) + (1 * 3) + (2 * 2) + (3 * 6) = 0 + 3 + 4 + 18 = 25 F(1) = (0 * 6) + (1 * 4) + (2 * 3) + (3 * 2) = 0 + 4 + 6 + 6 = 16 F(2) = (0 * 2) + (1 * 6) + (2 * 4) + (3 * 3) = 0 + 6 + 8 + 9 = 23 F(3) = (0 * 3) + (1 * 2) + (2 * 6) + (3 * 4) = 0 + 2 + 12 + 12 = 26 So the maximum value of F(0), F(1), F(2), F(3) is F(3) = 26.
public class Solution { // Math way F[k+1] - F[k] = sum - n * Bk[n-1]; F[k+1] = F[k] + sum - n * Bk[n-1]; public int maxRotateFunction(int[] A) { if(A == null || A.length == 0) return 0; int sum = 0; int rotateSum = 0; for(int i = 0 ; i < A.length ; i++){ sum += A[i]; rotateSum += i * A[i]; } int max = rotateSum; for(int i = 1; i < A.length ; i++){ rotateSum += sum - A.length * A[A.length-i]; max = Math.max(max, rotateSum); } return max; } /** // brute way but TLE public int maxRotateFunction(int[] A) { if(A == null || A.length == 0) return 0; int len = A.length; int max = Integer.MIN_VALUE; for(int i = 0; i < A.length ; i++){ max = Math.max(max, getValue(A, i)); } return max; } public int getValue(int[] A, int k){ int res = 0; int len = A.length; for(int i = 0 ; i < A.length; i++){ res += i * A[(k+i) % len]; } return res; } */ }
396. Rotate Function
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