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Minimum Moves to Equal Array Elements

Difficulty: Medium

Problem Description

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 n - 1 elements of the array by 1.

Key Insights

  • To make all elements equal, it's beneficial to think in terms of reducing the number of moves needed rather than directly counting the moves.
  • Incrementing n - 1 elements is equivalent to decrementing one element, which suggests that we can focus on the minimum element of the array.
  • The total number of moves required is the sum of differences between each element and the minimum element.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

The algorithm involves finding the minimum element in the array and calculating the total number of moves by summing the differences between each element and this minimum. We use a single pass through the array to find the minimum and another pass to calculate the moves, resulting in an efficient solution.

Code Solutions

def minMoves(nums):
    min_num = min(nums)  # Find the minimum number in the array
    moves = 0  # Initialize the move counter
    for num in nums:
        moves += num - min_num  # Sum the differences from the minimum
    return moves  # Return the total moves required
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