Find the minimum number of steps to reach M from N

Given two integers N and M. The task is to find the minimum number of steps to reach M from N by performing given operations. 
 

1. Multiply a number x by 2. So, x becomes 2*x.
2. Subtract one from the number x. So, x becomes x-1.

Examples: 
 

Input : N = 4, M = 6
Output : 2
Explanation : Perform operation number 2 on N. 
So, N becomes 3 and then perform operation number 1. 
Then, N becomes 6. So, the minimum number of steps is 2. 

Input : N = 10, M = 1
Output : 9
Explanation : Perform operation number two 
9 times on N. Then N becomes 1.

Approach : 
The idea is to reverse the problem as follows: We should get the number N starting from M using the operations: 
 

1. Divide the number by 2 if it is even.
2. Add 1 to the number.

Now, the minimum number of operations would be: 
 

1. If N > M, return the difference between them, that is, number of steps will be adding 1 to M until it becomes equal to N.
2. Else if N < M. 
   
   • Keep dividing M by 2 until it becomes less than N. If M is odd, add 1 to it first and then divide by 2. Once M is less than N, add the difference between them to the count along with the count of above operations.

Below is the implementation of the above approach: 
 

// CPP program to find minimum number
// of steps to reach M from N
#include <bits/stdc++.h>
using namespace std;

// Function to find a minimum number
// of steps to reach M from N
int Minsteps(int n, int m)
{
    int ans = 0;
    
    // Continue till m is greater than n
    while(m > n)
    {
        // If m is odd
        if(m&1) 
        {
            // add one
            m++;
            ans++;
        }
        
        // divide m by 2        
        m /= 2;
        ans++;
    }
    
    // Return the required answer
    return ans + n - m;
}

// Driver code
int main()
{
    int n = 4, m = 6;
   
    cout << Minsteps(n, m);
    
    return 0;
}

// Java program to find minimum number
// of steps to reach M from N
class CFG
{
    
// Function to find a minimum number
// of steps to reach M from N
static int Minsteps(int n, int m)
{
    int ans = 0;
    
    // Continue till m is greater than n
    while(m > n)
    {
        // If m is odd
        if(m % 2 != 0) 
        {
            // add one
            m++;
            ans++;
        }
        
        // divide m by 2     
        m /= 2;
        ans++;
    }
    
    // Return the required answer
    return ans + n - m;
}

// Driver code
public static void main(String[] args)
{
    int n = 4, m = 6;
    
    System.out.println(Minsteps(n, m));
}
}

// This code is contributed by Code_Mech

# Python3 program to find minimum number
# of steps to reach M from N

# Function to find a minimum number
# of steps to reach M from N
def Minsteps(n, m):

    ans = 0
    
    # Continue till m is greater than n
    while(m > n):

        # If m is odd
        if(m & 1):
            
            # add one
            m += 1
            ans += 1
        
        # divide m by 2     
        m //= 2
        ans += 1
    
    # Return the required answer
    return ans + n - m

# Driver code
n = 4
m = 6

print(Minsteps(n, m))

# This code is contributed by mohit kumar

// C# program to find minimum number
// of steps to reach M from N
using System;

class GFG
{
    
// Function to find a minimum number
// of steps to reach M from N
static int Minsteps(int n, int m)
{
    int ans = 0;
    
    // Continue till m is greater than n
    while(m > n)
    {
        // If m is odd
        if(m % 2 != 0) 
        {
            // add one
            m++;
            ans++;
        }
        
        // divide m by 2     
        m /= 2;
        ans++;
    }
    
    // Return the required answer
    return ans + n - m;
}

// Driver code
public static void Main()
{
    int n = 4, m = 6;
    
    Console.WriteLine(Minsteps(n, m));
}
}

// This code is contributed 
// by Akanksha Rai

<?php
// PHP program to find minimum number
// of steps to reach M from N

// Function to find a minimum number
// of steps to reach M from N
function Minsteps($n, $m)
{
    $ans = 0;
    
    // Continue till m is greater than n
    while($m > $n)
    {
        // If m is odd
        if($m % 2 != 0) 
        {
            // add one
            $m++;
            $ans++;
        }
        
        // divide m by 2     
        $m /= 2;
        $ans++;
    }
    
    // Return the required answer
    return $ans + $n - $m;
}

// Driver code
$n = 4; $m = 6;

echo(Minsteps($n, $m));

// This code is contributed by Code_Mech
?>

<script>
// JavaScript program to find minimum number
// of steps to reach M from N

// Function to find a minimum number
// of steps to reach M from N
function Minsteps(n, m)
{
    let ans = 0;
    
    // Continue till m is greater than n
    while(m > n)
    {
        // If m is odd
        if(m&1)
        {
            // add one
            m++;
            ans++;
        }
        
        // divide m by 2        
        m = Math.floor(m / 2);
        ans++;
    }
    
    // Return the required answer
    return ans + n - m;
}

// Driver code
    let n = 4, m = 6;    
    document.write(Minsteps(n, m));

// This code is contributed by Surbhi Tyagi.
</script>

2

Time Complexity: O(log₂m)

Auxiliary Space: O(1)