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.
Anlysis:
roateValue[i-1] = rotateValue[i] - (len-1)*A[i] + (sum-A[i])
Solution:
public class Solution { public int maxRotateFunction(int[] A) { if (A.length==0) return 0; if (A.length==1) return 0; int rotateValue = 0; int sum = 0; for (int i=0;i<A.length;i++){ sum += A[i]; rotateValue += i*A[i]; } int maxValue = rotateValue; for (int i=A.length-1;i>=1;i--){ rotateValue = rotateValue - (A.length-1)*A[i] + (sum-A[i]); maxValue = Math.max(maxValue,rotateValue); } return maxValue; } }