技術標籤：# 棧、佇列、串及其他資料結構leetcode演算法

題目地址：

https://leetcode.com/problems/sum-of-absolute-differences-in-a-sorted-array/

給定一個長 n n n的非降陣列 A A A，要求返回一個數組 B B B，使得 B [ i ] = ∑ j = 0 n − 1 ∣ A [ i ] − A [ j ] ∣ B[i]=\sum_{j=0}^{n-1}|A[i]-A[j]| B[i]=j=0∑n−1​∣A[i]−A[j]∣

思路是字首和。求出字首和陣列 p p p使得 p [ 0 ] = 0 , ∀ i > 0 , p [ i ] = ∑ j = 0 i − 1 A [ j ] p[0]=0,\forall i>0,p[i]=\sum_{j=0}^{i-1}A[j]

public class Solution {
    public int[] getSumAbsoluteDifferences(int[] nums) {
    	int n = nums.length;
        int[] preSum = new int[n + 1];
        for (int i = 0; i < n; i++) {
            preSum[i + 1] = preSum[i] + nums[i];
        }
    
        for (int
 
 i = 0; i < n; i++) {
            nums[i] = (2 * i + 1 - n) * nums[i] - preSum[i] + preSum[n] - preSum[i + 1];
        }
        
        return nums;
    }
}

時空複雜度 O ( n ) O(n) O(n)。