Minimum Operations to Make Array Equal — LeetCode 1551 Python Solution

The problem

You have an array arr of length n where arr[i] = (2 * i) + 1 for all valid values of i (i.e., 0 <= i < n). In one operation, you can select two indices x and y where 0 <= x, y < n and subtract 1 from arr[x] and add 1 to arr[y] (i.e., perform arr[x] -=1 and arr[y] += 1).

Example

Input

n = 3

Output

2

Explanation

arr = [1, 3, 5]

Python solution

class Solution:
    def minOperations(self, n: int) -> int:
        return sum(n - (i << 1 | 1) for i in range(n >> 1))

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 1551. Minimum Operations to Make Array Equal is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

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