Number of steps required to convert a binary number to one

Given a binary string str, the task is to print the numbers of steps required to convert it to one by the following operations:

  1. If ‘S’ is odd add 1 to it.
  2. If ‘S’ is even divide it by 2.

Examples:

Input: str = “1001001”
Output: 12

Input: str = “101110”
Output: 8

Number ‘101110’ is even, after dividing it by 2 we get an odd number ‘10111’ so we will add 1 to it. Then we’ll get ‘11000’ which is even and can be divide three times continuously in a row and get ’11’ which is odd, adding 1 to it will give us ‘100’ which is even and can be divided 2 times in a row. As, a result we get 1.
So 8 times the above two operations were required in this number.



Below is the step by step algorithm to solve this problem:

  • Initialize the string S as a binary number.
  • If the size of the binary is 1, then the required number of actions will be 0.
  • If the last digit is 0, then its an even number so one operation is required to divide it by 2.
  • After encountering 1, traverse till you get 0, with every digit one operation will take place.
  • After encountering 0 after 1 while traversing, replace 0 by 1 and start from step 4 again.

Below is the implementation of above algorithm:

C++

// C++ program to count the steps 
// required to convert a number to 1  
  
#include <bits/stdc++.h>
using namespace std;
#define ll long long
  
// function to calculate the number of actions
int calculate_(string s)
{
    // if the size of binary is 1
    // then the number of actions will be zero
    if (s.size() == 1)
        return 0;
  
    // initializing the number of actions as 0 at first
    int count_ = 0;
    for (int i = s.length() - 1; i > 0;) {
        // start traversing from the last digit
        // if its 0 increment the count and decrement i
        if (s[i] == '0') {
            count_++;
            i--;
        }
        // if s[i] == '1'
        else {
            count_++;
  
            // stop until you get 0 in the binary
            while (s[i] == '1' && i > 0) {
                count_++;
                i--;
            }
            if (i == 0)
                count_++;
  
            // when encounter a 0 replace it with 1
            s[i] = '1';
        }
    }
    return count_;
}
  
// Driver code
int main()
{
    string s;
    s = "10000100000";
  
    cout <<  calculate_(s);
    return 0;
}

PHP

<?php
// PHP program to count the steps 
// required to convert a number to 1 
  
// function to calculate the
// number of actions 
function calculate_($s
    // if the size of binary is 1 
    // then the number of actions 
    // will be zero 
    if (strlen($s) == 1) 
        return 0; 
  
    // initializing the number of 
    // actions as 0 at first 
    $count_ = 0; 
    for ($i = strlen($s) - 1; $i > 0;)
    
        // start traversing from the last 
        // digit if its 0 increment the
        // count and decrement i 
        if ($s[$i] == '0'
        
            $count_++; 
            $i--; 
        
          
        // if $s[$i] == '1' 
        else 
        
            $count_++; 
  
            // stop until you get 0 in the binary 
            while ($s[$i] == '1' && $i > 0) 
            
                $count_++; 
                $i--; 
            
            if ($i == 0) 
                $count_++; 
  
            // when encounter a 0 replace 
            // it with 1 
            $s[$i] = '1'
        
    
    return $count_
  
// Driver code 
  
$s = "10000100000"
echo calculate_($s);
  
// This code is contributed 
// by Shivi_Aggarwal
?>

Output:

16


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Improved By : Shivi_Aggarwal