Leetcode #1404: Number of Steps to Reduce a Number in Binary Representation to One
In this guide, we solve Leetcode #1404 Number of Steps to Reduce a Number in Binary Representation to One 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 the binary representation of an integer as a string s, return the number of steps to reduce it to 1 under the following rules: If the current number is even, you have to divide it by 2. If the current number is odd, you have to add 1 to it.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Bit Manipulation, String, Simulation
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: s = "1101"
Output: 6
Explanation: "1101" corressponds to number 13 in their decimal representation.
Step 1) 13 is odd, add 1 and obtain 14.
Step 2) 14 is even, divide by 2 and obtain 7.
Step 3) 7 is odd, add 1 and obtain 8.
Step 4) 8 is even, divide by 2 and obtain 4.
Step 5) 4 is even, divide by 2 and obtain 2.
Step 6) 2 is even, divide by 2 and obtain 1.
Python Solution
class Solution:
def numSteps(self, s: str) -> int:
carry = False
ans = 0
for c in s[:0:-1]:
if carry:
if c == '0':
c = '1'
carry = False
else:
c = '0'
if c == '1':
ans += 1
carry = True
ans += 1
if carry:
ans += 1
return ans
Complexity
The time complexity is , where is the length of the string . 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.