Leetcode #2571: Minimum Operations to Reduce an Integer to 0
In this guide, we solve Leetcode #2571 Minimum Operations to Reduce an Integer to 0 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 a positive integer n, you can do the following operation any number of times: Add or subtract a power of 2 from n. Return the minimum number of operations to make n equal to 0.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Greedy, Bit Manipulation, Dynamic Programming
Intuition
The problem breaks into overlapping subproblems, so caching results prevents exponential repetition.
A carefully chosen DP state captures exactly what we need to build the final answer.
Approach
Define the DP state and recurrence, then compute states in the correct order.
Optionally compress space once the recurrence is clear.
Steps:
- Choose a DP state definition.
- Write the recurrence and base cases.
- Compute states in the correct order.
Example
Input: n = 39
Output: 3
Explanation: We can do the following operations:
- Add 20 = 1 to n, so now n = 40.
- Subtract 23 = 8 from n, so now n = 32.
- Subtract 25 = 32 from n, so now n = 0.
It can be shown that 3 is the minimum number of operations we need to make n equal to 0.
Python Solution
class Solution:
def minOperations(self, n: int) -> int:
ans = cnt = 0
while n:
if n & 1:
cnt += 1
elif cnt:
ans += 1
cnt = 0 if cnt == 1 else 1
n >>= 1
if cnt == 1:
ans += 1
elif cnt > 1:
ans += 2
return ans
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.