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.
Question
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.
Solution
Sure, let's break down the steps to solve the problem:
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Initialize a counter: This will keep track of the number of steps taken to reduce the number to 1.
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Loop until the number is 1: We will repeatedly apply the given rules until the number becomes 1.
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Check if the number is even or odd:
- If the number is even, divide it by 2.
- If the number is odd, add 1 to it.
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Increment the counter: Each time a rule is applied, increment the counter.
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Return the counter: Once the number is reduced to 1, return the counter as the result.
Here is the step-by-step implementation:
def numSteps(s: str) -> int:
steps = 0
while s != "1":
if s[-1] == '0': # If the number is even
s = s[:-1] # Divide by 2 (remove the last character)
else: # If the number is odd
s = bin(int(s, 2) + 1)[2:] # Add 1 and convert back to binary
steps += 1
return steps
Explanation:
- Initialization:
steps = 0initializes the counter. - Loop:
while s != "1"continues the loop until the binary stringsis "1". - Even Check:
if s[-1] == '0'checks if the last character of the string is '0', indicating an even number.s = s[:-1]removes the last character, effectively dividing the number by 2.
- Odd Check:
elsehandles the case where the number is odd.s = bin(int(s, 2) + 1)[2:]converts the binary string to an integer, adds 1, and converts it back to a binary string.
- Increment Counter:
steps += 1increments the counter after each operation. - Return:
return stepsreturns the total number of steps taken to reduce the number to 1.
This approach ensures that we follow the rules and count the steps accurately.
Similar Questions
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