1600 - 1699
1685 - Sum of Absolute Differences in a Sorted Array (Medium)
Problem Link
https://leetcode.com/problems/sum-of-absolute-differences-in-a-sorted-array/
Problem Statement
You are given an integer array nums sorted in non-decreasing order.
Build and return an integer arrayresultwith the same length asnumssuch thatresult[i]is equal to the summation of absolute differences betweennums[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 <= 10 ^ 51 <= nums[i] <= nums[i + 1] <= 10 ^ 4
Approach 1: Prefix and Suffix Sum
// Prefix and suffix sum:
def getSumAbsoluteDifferences(nums: Array[Int]): Array[Int] = {
val n = nums.length
val pref = nums.scanLeft(0)(_ + _).tail
val suff = nums.scanRight(0)(_ + _).init
Array.tabulate(n)(i =>
suff(i) - pref(i) + nums(i) * (2 * i + 1 - n))
}static int fast_io = []() { std::ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); return 0; }();
class Solution {
public:
__attribute__((no_sanitize("address")))
static vector<int> getSumAbsoluteDifferences(vector<int>& nums) {
const int total = accumulate(begin(nums), end(nums), 0);
for (int i = 0, ps = 0; i < size(nums); ++i) {
const int num = nums[i];
const int before = num * (i - 1) - ps;
const int after = total - ps - num * (size(nums) - i - 1);
nums[i] = before + after;
ps += num;
}
return nums;
}
};