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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.

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Solution

Sure, let's break down the steps to solve the problem:

  1. Initialize a counter: This will keep track of the number of steps taken to reduce the number to 1.

  2. Loop until the number is 1: We will repeatedly apply the given rules until the number becomes 1.

  3. 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.
  4. Increment the counter: Each time a rule is applied, increment the counter.

  5. 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 = 0 initializes the counter.
  • Loop: while s != "1" continues the loop until the binary string s is "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: else handles 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 += 1 increments the counter after each operation.
  • Return: return steps returns 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.

This problem has been solved

Similar Questions

You are given a binary string s that contains at least one '1'.You have to rearrange the bits in such a way that the resulting binary number is the maximum odd binary number that can be created from this combination.Return a string representing the maximum odd binary number that can be created from the given combination.Note that the resulting string can have leading zeros.

Given a binary representation in the form of a string(s) of a number n, the task is to find a binary representation of n+1.Note: Output binary string should not contain leading zeros.Example 1:Input: s = "10"Output: 11Explanation: "10" is the binary representation of 2 and binary representation of 3 is "11"Example 2:Input: s = "111"Output: 1000Explanation: "111" is the binary representation of 7 and binary representation of 8 is "1000"Your Task: ย You don't need to read input or print anything. Complete the function binaryNextNumber()which takes s as input parameter and returns the string.Expected Time Complexity: O(n)Expected Auxiliary Space:ย O(n) to store resultant string ย Constraints:1 <= n <= 105

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Given a number, swap the adjacent bits in the binary representation of the number, and print the new number formed after swapping.Input FormatThe first line of input contains T - the number of test cases. Each of the next T lines contains a number N.Output FormatFor each test case, print the new integer formed after swapping adjacent bits, separated by a new line.Constraints1 <= T <= 1000000 <= N <= 109ExampleInput410743100Output51123152ExplanationTest-Case 1Binary Representation of 10: 000...1010After swapping adjacent bits: 000...0101 (5)Test-Case 2Binary Representation of 7: 000...0111After swapping adjacent bits: 000...1011 (11)

Write a program that takes in a positive integer as input, and outputs a string of 1's and 0's representing the integer in reverse binary. For an integer x, the algorithm is:As long as x is greater than 0 Output x % 2 (remainder is either 0 or 1) x = x / 2Note: The above algorithm outputs the 0's and 1's in reverse order.Ex: If the input is:6the output is:0116 in binary is 110; the algorithm outputs the bits in reverse.

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