1685. Sum of Absolute Differences in a Sorted Array LeetCode Solution

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Problem Statement
Complexity Analysis
Sum of Absolute Differences in a Sorted Array solution in C++
Sum of Absolute Differences in a Sorted Array solution in Java
Sum of Absolute Differences in a Sorted Array solution in Python
Additional Resources

1685. Sum of Absolute Differences in a Sorted Array LeetCode Solution image

Problem Statement of Sum of Absolute Differences in a Sorted Array

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 <= 105
1 <= nums[i] <= nums[i + 1] <= 104

Complexity Analysis

Time Complexity: O(n)
Space Complexity: O(n)

1685. Sum of Absolute Differences in a Sorted Array LeetCode Solution in C++

class Solution {
 public:
  vector<int> getSumAbsoluteDifferences(vector<int>& nums) {
    const int n = nums.size();
    vector<int> ans;
    // prefix[i] := sum(nums[0..i])
    vector<int> prefix(n);
    // suffix[i] := sum(nums[i..n - 1])
    vector<int> suffix(n);

    prefix[0] = nums[0];
    for (int i = 1; i < n; ++i)
      prefix[i] = prefix[i - 1] + nums[i];

    suffix[n - 1] = nums[n - 1];
    for (int i = n - 2; i >= 0; --i)
      suffix[i] = suffix[i + 1] + nums[i];

    for (int i = 0; i < nums.size(); ++i) {
      const int left = nums[i] * (i + 1) - prefix[i];
      const int right = suffix[i] - nums[i] * (n - i);
      ans.push_back(left + right);
    }

    return ans;
  }
};
/* code provided by PROGIEZ */

1685. Sum of Absolute Differences in a Sorted Array LeetCode Solution in Java

class Solution {
  public int[] getSumAbsoluteDifferences(int[] nums) {
    final int n = nums.length;
    int[] ans = new int[n];
    int[] prefix = new int[n];
    int[] suffix = new int[n];

    prefix[0] = nums[0];
    for (int i = 1; i < n; ++i)
      prefix[i] = prefix[i - 1] + nums[i];

    suffix[n - 1] = nums[n - 1];
    for (int i = n - 2; i >= 0; --i)
      suffix[i] = suffix[i + 1] + nums[i];

    for (int i = 0; i < nums.length; ++i) {
      final int left = nums[i] * (i + 1) - prefix[i];
      final int right = suffix[i] - nums[i] * (n - i);
      ans[i] = left + right;
    }

    return ans;
  }
}
// code provided by PROGIEZ

1685. Sum of Absolute Differences in a Sorted Array LeetCode Solution in Python

class Solution:
  def getSumAbsoluteDifferences(self, nums: list[int]) -> list[int]:
    prefix = list(itertools.accumulate(nums))
    suffix = list(itertools.accumulate(nums[::-1]))[::-1]
    return [num * (i + 1) - prefix[i] + suffix[i] - num * (len(nums) - i)
            for i, num in enumerate(nums)]
 # code by PROGIEZ