algoadvance

Given an integer array nums of size n, return the minimum number of moves required to make all array elements equal, where a move is incrementing n - 1 elements by 1.

Clarifying Questions

  1. Constraints on the values within the array nums?
    • Typically, we would assume they can be any integer, but usually within the range of typical integer limits in Python.
  2. Can the array be empty or contain only one element?
    • Generally, the array will contain at least one element.
  3. Do we consider negative numbers?
    • Yes, the array can contain negative as well as positive numbers.

Strategy

To solve this problem, note that incrementing n-1 elements by 1 is equivalent to decrementing one element by 1 in reverse.

The crucial insight is that to equalize all elements, we need the target value that every element should match at the end:

The strategy involves:

  1. Calculate the sum of the array.
  2. Find the minimum element in the array.
  3. Compute the total number of moves required using the formula: ( \text{moves} = \text{sum(nums)} - n \times \text{min(nums)} )

This formula essentially is derived by considering reducing all elements to the smallest element (min(nums)) directly.

Time Complexity

Code

def minMoves(nums):
    total_sum = sum(nums)
    min_num = min(nums)
    return total_sum - len(nums) * min_num

# Example Usage
nums = [1, 2, 3]
print(minMoves(nums))  # Output: 3

Explanation

Each operation of reducing elements to the minimum gives us the optimal number of moves required in ( O(n) ) time.

Try our interview co-pilot at AlgoAdvance.com