1404. Number of Steps to Reduce a Number in Binary Representation to One
Description
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.
It is guaranteed that you can always reach one for all test cases.
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" corresponds 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'
Solutions
Solution 1: Simulation
We simulate operations $1$ and $2$, while using carry
to record the carry-over.
The time complexity is $O(n)$, where $n$ is the length of the string $s$. The space complexity is $O(1)$.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 |
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 |
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 |
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 |
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