Count Operations to Obtain Zero

LeetCode 2288 | Difficulty: Easy

Easy

Problem Description

You are given two non-negative integers num1 and num2.

In one operation, if num1 >= num2, you must subtract num2 from num1, otherwise subtract num1 from num2.

- For example, if `num1 = 5` and `num2 = 4`, subtract `num2` from `num1`, thus obtaining `num1 = 1` and `num2 = 4`. However, if `num1 = 4` and `num2 = 5`, after one operation, `num1 = 4` and `num2 = 1`.

Return the number of operations required to make either num1 = 0 or num2 = 0.

Example 1:

Input: num1 = 2, num2 = 3
Output: 3
Explanation: 
- Operation 1: num1 = 2, num2 = 3. Since num1  num2, we subtract num2 from num1.
- Operation 3: num1 = 1, num2 = 1. Since num1 == num2, we subtract num2 from num1.
Now num1 = 0 and num2 = 1. Since num1 == 0, we do not need to perform any further operations.
So the total number of operations required is 3.

Example 2:

Input: num1 = 10, num2 = 10
Output: 1
Explanation: 
- Operation 1: num1 = 10, num2 = 10. Since num1 == num2, we subtract num2 from num1 and get num1 = 10 - 10 = 0.
Now num1 = 0 and num2 = 10. Since num1 == 0, we are done.
So the total number of operations required is 1.

Constraints:

- `0 <= num1, num2 <= 10^5`

Topics: Math, Simulation

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Approach

Mathematical

Look for mathematical patterns or formulas. Consider: modular arithmetic, GCD/LCM, prime factorization, combinatorics, or geometric properties.

When to use

Problems with clear mathematical structure, counting, number properties.

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Solutions

Solution 1: C# (Best: 37 ms)

Metric	Value
Runtime	37 ms
Memory	25.1 MB
Date	2022-02-13

Solution

public class Solution {
    public int CountOperations(int num1, int num2) {
        int moves = 0;
        while(num1!= 0 && num2 != 0)
        {
            if(num1>num2) num1 = num1 - num2;
            else num2 = num2-num1;
            moves++;
        }
        return moves;
    }
}

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Complexity Analysis

Approach	Time	Space
Solution	$O(n)$	$O(1) to O(n)$

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Interview Tips

Key Points

• Start by clarifying edge cases: empty input, single element, all duplicates.
• LeetCode provides 2 hint(s) for this problem — try solving without them first.

💡 Hints

Hint 1: Try simulating the process until either of the two integers is zero.

Hint 2: Count the number of operations done.