Leetcode #2749: Minimum Operations to Make the Integer Zero
In this guide, we solve Leetcode #2749 Minimum Operations to Make the Integer 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 integers num1 and num2. In one operation, you can choose integer i in the range [0, 60] and subtract 2i + num2 from num1.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Bit Manipulation, Brainteaser, Enumeration
Intuition
The problem structure lets us track state with bitwise operations.
Bit operations are constant time and avoid extra memory.
Approach
Apply XOR/AND/OR and shifts to maintain the required invariant.
Aggregate the result in a single pass.
Steps:
- Identify a bitwise invariant.
- Combine values with bit operations.
- Return the aggregated result.
Example
Input: num1 = 3, num2 = -2
Output: 3
Explanation: We can make 3 equal to 0 with the following operations:
- We choose i = 2 and subtract 22 + (-2) from 3, 3 - (4 + (-2)) = 1.
- We choose i = 2 and subtract 22 + (-2) from 1, 1 - (4 + (-2)) = -1.
- We choose i = 0 and subtract 20 + (-2) from -1, (-1) - (1 + (-2)) = 0.
It can be proven, that 3 is the minimum number of operations that we need to perform.
Python Solution
class Solution:
def makeTheIntegerZero(self, num1: int, num2: int) -> int:
for k in count(1):
x = num1 - k * num2
if x < 0:
break
if x.bit_count() <= k <= x:
return k
return -1
Complexity
The time complexity is , and the space complexity is . 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.