LeetCode-in-Java
1685. Sum of Absolute Differences in a Sorted Array
Medium
You are given an integer array nums sorted in non-decreasing order.
Build and return an integer array result with the same length as nums such that result[i] is equal to the summation of absolute differences between nums[i] and all the other elements in the array.
In other words, result[i] is equal to sum(|nums[i]-nums[j]|) where 0 <= j < nums.length and j != i (0-indexed).
Example 1:
Input: nums = [2,3,5]
Output: [4,3,5]
Explanation: Assuming the arrays are 0-indexed, then
result[0] = |2-2| + |2-3| + |2-5| = 0 + 1 + 3 = 4,
result[1] = |3-2| + |3-3| + |3-5| = 1 + 0 + 2 = 3,
result[2] = |5-2| + |5-3| + |5-5| = 3 + 2 + 0 = 5.
Example 2:
Input: nums = [1,4,6,8,10]
Output: [24,15,13,15,21]
Constraints:
2 <= nums.length <= 1051 <= nums[i] <= nums[i + 1] <= 104
Solution
public class Solution {
public int[] getSumAbsoluteDifferences(int[] nums) {
int len = nums.length;
int[] preSums = new int[len];
for (int i = 1; i < len; i++) {
preSums[i] = preSums[i - 1] + nums[i - 1];
}
int[] postSums = new int[len];
for (int i = len - 2; i >= 0; i--) {
postSums[i] = postSums[i + 1] + nums[i + 1];
}
int[] result = new int[len];
for (int i = 0; i < len; i++) {
result[i] = nums[i] * i - preSums[i] + postSums[i] - nums[i] * (len - i - 1);
}
return result;
}
}