1404

1404. Number of Steps to Reduce a Number in Binary Representation to One (Medium)

Given a number s in their binary representation. 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.

It's guaranteed that you can always reach to one for all testcases.

 

Example 1:

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.  

Example 2:

Input: s = "10"
Output: 1
Explanation: "10" corressponds to number 2 in their decimal representation.
Step 1) 2 is even, divide by 2 and obtain 1.  

Example 3:

Input: s = "1"
Output: 0

 

Constraints:

• 1 <= s.length <= 500
• s consists of characters '0' or '1'
• s[0] == '1'

Related Topics:
String, Bit Manipulation

Solution 1.

// OJ: https://leetcode.com/problems/number-of-steps-to-reduce-a-number-in-binary-representation-to-one/
// Author: github.com/lzl124631x
// Time: O(N)
// Space: O(1)
class Solution {
public:
    int numSteps(string s) {
        int ans = 0;
        while (s != "1") {
            if (s.back() == '1') {
                int i = s.size() - 1;
                while (i >= 0 && s[i] == '1') {
                    s[i] = '0';
                    --i;
                }
                if (i == -1) s.insert(s.begin(), '1');
                else s[i] = '1';
            } else s.pop_back();
            ++ans;
        }
        return ans;
    }
};