I encountered this interesting problem during a recent coding assessment, and I wanted to document my approach (including where I fell short). While I didn’t fully complete the solution within the time limit, I believe my approach was on the right track. Here’s the problem and my solution attempt.

The Challenge

The task involves transforming a binary sequence through particular operations until it reaches a terminal state.

Problem

You are given a string B representing a non-negative integer N in binary format. You must perform the following operations until N becomes 0:

  • if N is odd, decrease it by 1;
  • if N is even, halve it.

Your task is to determine how many operations are required to reduce N to 0.

For example, if B = "101100", it represents N = 44. The value would transform as follows:

  • N = 44 (even): divide by 2 → 22
  • N = 22 (even): divide by 2 → 11
  • N = 11 (odd): subtract 1 → 10
  • N = 10 (even): divide by 2 → 5
  • N = 5 (odd): subtract 1 → 4
  • N = 4 (even): divide by 2 → 2
  • N = 2 (even): divide by 2 → 1
  • N = 1 (odd): subtract 1 → 0

It took 8 operations to reduce the value to 0.

Implement a function:

func countOperations(_ B: inout String) -> Int

that calculates and returns the number of operations needed to transform B to 0.

Examples:

1. For B = "101100" (44 in decimal), the function should return 8 as shown above.

2. For B = "1001" (9 in decimal), the function should return 5:

  • N = 9 (odd): subtract 1 → 8
  • N = 8 (even): divide by 2 → 4
  • N = 4 (even): divide by 2 → 2
  • N = 2 (even): divide by 2 → 1
  • N = 1 (odd): subtract 1 → 0

3. For B = "10101010111", the function should return 16.

4. For a string B consisting of "1" repeated 500,000 times, the function should return 999,999.

Design an efficient algorithm with these constraints:

  • B contains only the characters '0' and '1'
  • The length of B is between 1 and 1,500,000
  • The binary representation follows the standard convention where the leftmost bit is most significant
  • B may contain leading zeros



My Approach

Here’s my Swift implementation, which uses a recursive strategy to count the operations:

import Foundation
import Glibc
// This function counts operations needed to reduce a binary number to zero
// by either halving (for even numbers) or decrementing by one (for odd numbers)
public func countOperations(_ B: inout String) -> Int {
    
    // Validate input is within acceptable range
if B.binaryToDecimal > 1500000 {
    return 0
}

/// Recursive helper to track the transformation process
func transform(_ binary: String, operationCount: Int) -> Int {
    let numericValue = binary.binaryToDecimal
    
    // Terminal case: we've reached zero
    if numericValue <= 0 {
        return operationCount
    }
    
    // For even values, halve the number
    if numericValue % 2 == 0 {
        let nextValue = (numericValue / 2).decimalToBinary()
        return transform(nextValue, operationCount: operationCount + 1)
    } else {
        // For odd values, decrement by one
        let nextValue = (numericValue - 1).decimalToBinary()
        return transform(nextValue, operationCount: operationCount + 1)
    }
}

return transform(B, operationCount: 0)
}

/ Utility extension to convert binary string to decimal
extension String {
	var binaryToDecimal: Int { return Int(strtoul(self, nil, 2)) }
}

// Utility extension to convert decimal back to binary representation
extension Int {
func decimalToBinary() -> String {
return String(self, radix: 2)
}
}



Key Insights

While I didn’t complete the solution during the interview, my approach focused on:

  1. Using recursion to track the steps
  2. Converting between binary strings and integers efficiently
  3. Handling the base case (reaching zero) to return the total operations

One improvement I could have made would be adding better handling for the special case mentioned in example 4, where the input is a string of 400,000 ones.