Leetcode #29: Divide Two Integers
In this guide, we solve Leetcode #29 Divide Two Integers 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
Given two integers dividend and divisor, divide two integers without using multiplication, division, and mod operator. The integer division should truncate toward zero, which means losing its fractional part.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Bit Manipulation, Math
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: dividend = 10, divisor = 3
Output: 3
Explanation: 10/3 = 3.33333.. which is truncated to 3.
Python Solution
class Solution:
def divide(self, a: int, b: int) -> int:
if b == 1:
return a
if a == -(2**31) and b == -1:
return 2**31 - 1
sign = (a > 0 and b > 0) or (a < 0 and b < 0)
a = -a if a > 0 else a
b = -b if b > 0 else b
ans = 0
while a <= b:
x = b
cnt = 1
while x >= (-(2**30)) and a <= (x << 1):
x <<= 1
cnt <<= 1
a -= x
ans += cnt
return ans if sign else -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.