Leetcode #2169: Count Operations to Obtain Zero
In this guide, we solve Leetcode #2169 Count Operations to Obtain Zero in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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.
Quick Facts
- Difficulty: Easy
- Premium: No
- Tags: Math, Simulation
Intuition
There is a mathematical invariant or formula that directly leads to the result.
Using math avoids unnecessary loops and reduces complexity.
Approach
Derive the formula or update rule, then compute the answer directly.
Handle edge cases like overflow or zero carefully.
Steps:
- Identify the math relationship.
- Compute the result with a loop or formula.
- Handle edge cases.
Example
Input: num1 = 2, num2 = 3
Output: 3
Explanation:
- Operation 1: num1 = 2, num2 = 3. Since num1 < num2, we subtract num1 from num2 and get num1 = 2, num2 = 3 - 2 = 1.
- Operation 2: num1 = 2, num2 = 1. 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.
Python Solution
class Solution:
def countOperations(self, num1: int, num2: int) -> int:
ans = 0
while num1 and num2:
if num1 >= num2:
num1 -= num2
else:
num2 -= num1
ans += 1
return ans
Complexity
The time complexity is , where is the maximum of and . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.