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‎MinimumAverageDifference/minimum_average_difference.dart

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/*
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-* 2256. Minimum Average Difference *-
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You are given a 0-indexed integer array nums of length n.
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The average difference of the index i is the absolute difference between the average of the first i + 1 elements of nums and the average of the last n - i - 1 elements. Both averages should be rounded down to the nearest integer.
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Return the index with the minimum average difference. If there are multiple such indices, return the smallest one.
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Note:
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The absolute difference of two numbers is the absolute value of their difference.
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The average of n elements is the sum of the n elements divided (integer division) by n.
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The average of 0 elements is considered to be 0.
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Example 1:
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Input: nums = [2,5,3,9,5,3]
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Output: 3
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Explanation:
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- The average difference of index 0 is: |2 / 1 - (5 + 3 + 9 + 5 + 3) / 5| = |2 / 1 - 25 / 5| = |2 - 5| = 3.
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- The average difference of index 1 is: |(2 + 5) / 2 - (3 + 9 + 5 + 3) / 4| = |7 / 2 - 20 / 4| = |3 - 5| = 2.
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- The average difference of index 2 is: |(2 + 5 + 3) / 3 - (9 + 5 + 3) / 3| = |10 / 3 - 17 / 3| = |3 - 5| = 2.
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- The average difference of index 3 is: |(2 + 5 + 3 + 9) / 4 - (5 + 3) / 2| = |19 / 4 - 8 / 2| = |4 - 4| = 0.
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- The average difference of index 4 is: |(2 + 5 + 3 + 9 + 5) / 5 - 3 / 1| = |24 / 5 - 3 / 1| = |4 - 3| = 1.
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- The average difference of index 5 is: |(2 + 5 + 3 + 9 + 5 + 3) / 6 - 0| = |27 / 6 - 0| = |4 - 0| = 4.
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The average difference of index 3 is the minimum average difference so return 3.
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Example 2:
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Input: nums = [0]
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Output: 0
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Explanation:
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The only index is 0 so return 0.
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The average difference of index 0 is: |0 / 1 - 0| = |0 - 0| = 0.
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Constraints:
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1 <= nums.length <= 105
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0 <= nums[i] <= 105
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*/
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import 'dart:math';
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class A {
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int minimumAverageDifference(List<int> nums) {
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int ans = 0, n = nums.length, mi = double.maxFinite.toInt();
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// since we need the sum for first i + 1 and last n - i - 1 elements
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// we can pre-calculate it first
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// it is called prefix sum and suffix sum
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List<int> pref = List.filled(n, 0);
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// prev[0] is the first element
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pref[0] = nums[0];
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// starting from i = 1, pref[i] is the sum + the current element
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for (int i = 1; i < n; i++) pref[i] = pref[i - 1] + nums[i];
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// then we can iterate each number
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for (int i = 0; i < n; i++) {
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// now we know the prefix sum
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// the suffix sum is simply pref[n - 1] - pref[i]
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int k = ((pref[i] ~/ (i + 1)) -
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((pref[n - 1] - pref[i]) ~/ max(n - i - 1, 1)))
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.abs();
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// check the min and update ans
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if (k < mi) {
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mi = k;
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ans = i;
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}
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}
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return ans;
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}
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}
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class B {
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int minimumAverageDifference(List<int> nums) {
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int n = nums.length;
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int sum = 0;
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for (int num in nums) sum += num;
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int minDiff = double.maxFinite.toInt();
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int leftSum = 0;
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int rightSum = sum;
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int ans = 0;
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for (int i = 0; i < n; i++) {
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leftSum += nums[i];
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rightSum -= nums[i];
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int lAvg = leftSum ~/ (i + 1);
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int rAvg = (n - 1 - i) != 0 ? rightSum ~/ (n - 1 - i) : rightSum;
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int diff = (lAvg - rAvg).abs();
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if (diff == 0) return i;
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if (diff < minDiff) {
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minDiff = diff;
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ans = i;
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}
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}
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return ans;
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}
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}
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class C {
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int minimumAverageDifference(List<int> nums) {
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// if there is only one element then itself would be the ans (index 0).
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if (nums.length == 1) return 0;
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// finding total sum of vector (using int int to prevent overflow)
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int sum = 0;
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for (int a in nums) {
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sum += a;
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}
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//initially left side sum will be zero and right side sum will be total sum
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int leftSum = 0;
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int rightSum = sum;
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// this will be used to keep track of minimum
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int avgDiff;
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int mini = -1;
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int minIndex = -1;
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int n = nums.length;
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for (int i = 0; i < n - 1; i++) {
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// increasing left sum and decreasing right sum
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leftSum += nums[i];
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rightSum -= nums[i];
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// finding avgDiff , (here (n-i-1) represents element count in right part, ans (i+1) in left part)
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avgDiff = ((leftSum ~/ (i + 1)) - (rightSum ~/ (n - i - 1))).abs();
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//updating mini
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if (mini == -1) {
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mini = avgDiff;
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minIndex = i;
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} else if (mini > avgDiff) {
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mini = avgDiff;
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minIndex = i;
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}
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}
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// check for last element
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avgDiff = sum ~/ n;
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if (mini > avgDiff) {
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mini = avgDiff;
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minIndex = n - 1;
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}
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return minIndex;
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}
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}

‎MinimumAverageDifference/minimum_average_difference.go

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package main
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import "math"
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func ToFloat64(in int) float64 {
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return float64(in)
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}
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func minimumAverageDifference(nums []int) int {
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// if there is only one element then itself would be the ans (index 0).
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if len(nums) == 1 {
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return 0
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}
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// finding total sum of vector (using int int to prevent overflow)
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var sum int = 0
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for _, a := range nums {
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sum += a
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}
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//initially left side sum will be zero and right side sum will be total sum
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var leftSum int = 0
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var rightSum int = sum
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// this will be used to keep track of minimum
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var avgDiff float64
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var mini int = -1
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var minIndex int = -1
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var n = len(nums)
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for i := 0; i < n-1; i++ {
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// increasing left sum and decreasing right sum
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leftSum += nums[i]
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rightSum -= nums[i]
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// finding avgDiff , (here (n-i-1) represents element count in right part, ans (i+1) in left part)
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avgDiff = math.Abs(ToFloat64((leftSum / (i + 1)) - (rightSum / (n - i - 1))))
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//updating mini
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if mini == -1 {
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mini = int(avgDiff)
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minIndex = i
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} else if mini > int(avgDiff) {
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mini = int(avgDiff)
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minIndex = i
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}
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}
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// check for last element
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avgDiff = math.Round(ToFloat64(sum / n))
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if mini > int(avgDiff) {
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mini = int(avgDiff)
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minIndex = n - 1
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}
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return minIndex
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}

‎MinimumAverageDifference/minimum_average_difference.md

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# 🔥 Minimum Average Difference 🔥 || 3 Approaches || Simple Fast and Easy || with Explanation
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## Solution - 1 Greedy
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```dart
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class Solution {
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int minimumAverageDifference(List<int> nums) {
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// if there is only one element then itself would be the ans (index 0).
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if (nums.length == 1) return 0;
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// finding total sum of vector (using int int to prevent overflow)
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int sum = 0;
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for (int a in nums) {
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sum += a;
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}
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//initially left side sum will be zero and right side sum will be total sum
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int leftSum = 0;
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int rightSum = sum;
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// this will be used to keep track of minimum
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int avgDiff;
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int mini = -1;
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int minIndex = -1;
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int n = nums.length;
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for (int i = 0; i < n - 1; i++) {
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// increasing left sum and decreasing right sum
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leftSum += nums[i];
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rightSum -= nums[i];
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// finding avgDiff , (here (n-i-1) represents element count in right part, ans (i+1) in left part)
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avgDiff = ((leftSum ~/ (i + 1)) - (rightSum ~/ (n - i - 1))).abs();
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//updating mini
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if (mini == -1) {
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mini = avgDiff;
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minIndex = i;
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} else if (mini > avgDiff) {
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mini = avgDiff;
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minIndex = i;
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}
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}
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// check for last element
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avgDiff = sum ~/ n;
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if (mini > avgDiff) {
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mini = avgDiff;
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minIndex = n - 1;
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}
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return minIndex;
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}
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}
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```
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## Solution - 2
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```dart
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class Solution {
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int minimumAverageDifference(List<int> nums) {
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int n = nums.length;
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int sum = 0;
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for (int num in nums) sum += num;
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int minDiff = double.maxFinite.toInt();
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int leftSum = 0;
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int rightSum = sum;
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int ans = 0;
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for (int i = 0; i < n; i++) {
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leftSum += nums[i];
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rightSum -= nums[i];
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int lAvg = leftSum ~/ (i + 1);
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int rAvg = (n - 1 - i) != 0 ? rightSum ~/ (n - 1 - i) : rightSum;
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int diff = (lAvg - rAvg).abs();
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if (diff == 0) return i;
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if (diff < minDiff) {
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minDiff = diff;
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ans = i;
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}
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}
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return ans;
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}
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}
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```
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## Solution - 3
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```dart
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class Solution {
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int minimumAverageDifference(List<int> nums) {
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int ans = 0, n = nums.length, mi = double.maxFinite.toInt();
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// since we need the sum for first i + 1 and last n - i - 1 elements
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// we can pre-calculate it first
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// it is called prefix sum and suffix sum
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List<int> pref = List.filled(n, 0);
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// prev[0] is the first element
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pref[0] = nums[0];
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// starting from i = 1, pref[i] is the sum + the current element
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for (int i = 1; i < n; i++) pref[i] = pref[i - 1] + nums[i];
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// then we can iterate each number
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for (int i = 0; i < n; i++) {
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// now we know the prefix sum
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// the suffix sum is simply pref[n - 1] - pref[i]
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int k = ((pref[i] ~/ (i + 1)) -
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((pref[n - 1] - pref[i]) ~/ max(n - i - 1, 1)))
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.abs();
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// check the min and update ans
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if (k < mi) {
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mi = k;
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ans = i;
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}
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}
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return ans;
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}
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}
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```

‎README.md

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- [**1657.** Determine if Two Strings Are Close](DetermineIfTwoStringsAreClose/determine_if_two_strings_are_close.dart)
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- [**401.** Binary Watch](BinaryWatch/binary_watch.dart)
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- [**451.** Sort Characters By Frequency](SortCharactersByFrequency/sort_characters_by_frequency.dart)
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- [**2256.** Minimum Average Difference](MinimumAverageDifference/minimum_average_difference.dart)
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## Reach me via
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