Minimum Moves to Equal Array Elements II

Minimum Moves to Equal Array Elements II - Problem

Given an integer array nums of size n, return the minimum number of moves required to make all array elements equal.

In one move, you can increment or decrement an element of the array by 1.

Test cases are designed so that the answer will fit in a 32-bit integer.

Input & Output

Example 1 — Basic Case

$ Input: nums = [1,2,3]

› Output: 2

💡 Note: Only two moves are needed (remember that it is an array): [1,2,3] => [2,2,3] => [2,2,2]

Example 2 — Single Element

$ Input: nums = [1,10,2,9]

› Output: 16

💡 Note: Sort to [1,2,9,10]. Median is 2 or 9, both give same result. Using median approach: target could be any value between 2 and 9, let's use 5.5 rounded to 6: |1-6| + |2-6| + |9-6| + |10-6| = 5+4+3+4 = 16. Actually optimal is median 2: |1-2| + |2-2| + |9-2| + |10-2| = 1+0+7+8 = 16

Example 3 — All Equal

$ Input: nums = [5,5,5]

› Output: 0

💡 Note: All elements are already equal, so no moves needed

Constraints

n == nums.length
1 ≤ n ≤ 10⁵
-10⁹ ≤ nums[i] ≤ 10⁹

Visualization

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Asked in

G Google 15 f Facebook 12 M Microsoft 8 a Amazon 6

The key insight is that the median minimizes the sum of absolute deviations. Sort the array and use the median as target, or use two pointers to pair elements from ends. Best approach is median-based with Time: O(n log n), Space: O(1).

Common Approaches

✓ Sort and Find Median

⏱️ Time: O(n log n) Space: O(1)

The optimal target is the median of the array. After sorting, the median minimizes the sum of absolute deviations. Calculate moves by summing absolute differences from each element to the median.

Try All Target Values

⏱️ Time: O(range × n) Space: O(1)

For each possible target value between the minimum and maximum elements, calculate the total moves needed to make all elements equal to that target. Return the minimum moves found.

Two Pointers from Ends

⏱️ Time: O(n log n) Space: O(1)

After sorting, use two pointers starting from both ends. Each pair of elements at equal distance from median contributes to the total moves. The distance between paired elements gives the moves needed.

Sort and Find Median — Algorithm Steps

Sort the array
Find median (middle element)
Calculate sum of absolute differences from median

Visualization

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Step-by-Step Walkthrough

Sort Array

Arrange elements: [1,3,3,4]

Find Median

Middle element at index 2: value=3

Calculate Moves

Sum distances to median: 2+0+0+1=3

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

int compare(const void* a, const void* b) {
    return (*(int*)a - *(int*)b);
}

int abs_val(int x) {
    return x < 0 ? -x : x;
}

int solution(int* nums, int numsSize) {
    if (numsSize == 0) return 0;
    
    qsort(nums, numsSize, sizeof(int), compare);
    int median = nums[numsSize / 2];
    
    int moves = 0;
    for (int i = 0; i < numsSize; i++) {
        moves += abs_val(nums[i] - median);
    }
    
    return moves;
}

int main() {
    char line[10000];
    fgets(line, sizeof(line), stdin);
    
    int nums[1000];
    int numsSize = 0;
    
    char* token = strtok(line + 1, ",]");
    while (token != NULL) {
        nums[numsSize++] = atoi(token);
        token = strtok(NULL, ",]");
    }
    
    printf("%d\n", solution(nums, numsSize));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n log n)

Sorting takes O(n log n), calculating moves takes O(n)

✓ Linear Growth

Space Complexity

O(1)

Only using constant extra space for variables

✓ Linear Space

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Input & Output

Constraints

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Related Problems

Common Approaches

Sort and Find Median — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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