leetcode

Author: ayoubzulfiqar

SumOfAbsoluteDifferencesInASortedArray/sum_of_absolute_differences_in_a_sorted_array.dart

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+/*
+
+
+-* 1685. 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
+
+*/
+
+List<int> getSumAbsoluteDifferences(List<int> nums) {
+ int x = 0;
+ int y = 0;
+ final int len = nums.length;
+
+ for (int i = 0; i < len; i++) {
+ y += nums[i];
+ }
+
+ for (int i = 0; i < len; i++) {
+ x += nums[i];
+ int tmp = (nums[i] * (i + 1) - x) + (y - nums[i] * (len - i));
+
+ y -= nums[i];
+ nums[i] = tmp;
+ }
+
+ return nums;
+}

SumOfAbsoluteDifferencesInASortedArray/sum_of_absolute_differences_in_a_sorted_array.go

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+package main
+
+func getSumAbsoluteDifferences(nums []int) []int {
+var x, y int = 0, 0
+var len int = len(nums)
+
+for i := 0; i < len; i++ {
+y += nums[i]
+}
+
+for i := 0; i < len; i++ {
+x += nums[i]
+tmp := (nums[i]*(i+1) - x) + (y - nums[i]*(len-i))
+
+y -= nums[i]
+nums[i] = tmp
+}
+
+return nums
+}

SumOfAbsoluteDifferencesInASortedArray/sum_of_absolute_differences_in_a_sorted_array.md

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+# 🔥 Sum of Absolute Differences in a Sorted Array 🔥 || Simple Fast and Easy || with Explanation 😈
+
+## Intuition
+
+The goal is to find the sum of absolute differences between each element and all other elements in the array. The code uses a prefix and suffix sum approach to efficiently calculate these absolute differences.
+
+### Approach
+
+1. **Suffix Sum Calculation (Initialization):**
+ - Calculate the total sum of the array and store it in the variable `y`. This is done using a loop that iterates through each element of the array.
+
+2. **Absolute Difference Calculation:**
+ - Iterate through the array again.
+ - For each element, calculate the sum of absolute differences using the prefix sum (`x`) and the suffix sum (`y`). Update the element in the array with this calculated value.
+ - Update the prefix sum (`x`) and suffix sum (`y`) accordingly for the next iteration.
+
+### Time Complexity
+
+- The time complexity of this algorithm is O(n), where n is the length of the input array. This is because the code iterates through the array twice, and each iteration takes O(n) time.
+
+### Space Complexity
+
+- The space complexity is O(1) since the algorithm uses a constant amount of additional space, regardless of the size of the input array. The input array is modified in place.
+
+This approach efficiently calculates the sum of absolute differences without the need for nested loops, resulting in a linear time complexity solution.
+
+## Code
+
+```go
+func getSumAbsoluteDifferences(nums []int) []int {
+// Initialize variables
+var x, y int = 0, 0
+var len int = len(nums)
+
+// Calculate the total sum of the array (suffix sum)
+for i := 0; i < len; i++ {
+y += nums[i]
+}
+
+// Iterate through the array to calculate the absolute differences
+for i := 0; i < len; i++ {
+// Calculate the sum of absolute differences using prefix and suffix sums
+x += nums[i]
+tmp := (nums[i]*(i+1) - x) + (y - nums[i]*(len-i))
+
+// Update the suffix sum for the next iteration
+y -= nums[i]
+
+// Update the array with the calculated absolute difference
+nums[i] = tmp
+}
+
+// Return the array with updated absolute differences
+return nums
+}
+```
+
+## [GitHub](https://github.com/ayoubzulfiqar/leetcode)