Convert a number m to n using minimum number of given operations - GeeksforGeeks

10 Mar, 2022
Convert a number m to n with minimum operations. The operations allowed are :  
Multiply by 2, i.e., do m = 2 * mSubtract 1, i.e., do m = m – 1
Multiply by 2, i.e., do m = 2 * m
Subtract 1, i.e., do m = m – 1
Print -1 if it is not possible to convert.Examples :  
Input : m = 3, n = 11
Output : 3
1st operation: *2 = 3*2 = 6
2nd operation: *2 = 6*2 = 12
3rd operation: -1 = 12-1 = 11

Input : m = 15, n = 20
Output : 6
1st operation: -1 '5' times = 15 + (-1*5) = 10
2nd operation: *2 = 10*2 = 20

Input : m = 0, n = 8
Output : -1
Using the given set of operations 'm' 
cannot be converted to 'n'

Input : m = 12, n = 8
Output : 4
 
The idea is based on below facts. 1) If m is less than 0 and n is greater than 0, then not possible. 2) If m is greater than n, then we can reach n using subtractions only. 3) Else (m is less than n), we must do m*2 operations. Following two cases arise. ......a) If n is odd, we must do a -1 operation to reach it. ......b) If n is even, we must do a *2 operation to reach it.Algorithm:  
int convert(m,n)
    if (m == n) 
    return 0;
    
    // not possible
    if (m <= 0 && n > 0)  
    return -1;

    // m is greater than n
    if (m > n) 
        return m-n;

    // n is odd
    if (n % 2 == 1) 
    // perform '-1' 
    return 1 + convert(m, n+1);
        
    // n is even
    else 
    // perform '*2' 
    return 1 + convert(m, n/2);
Note: The list of operations so generated should be applied in reverse order. For example:  
m = 3, n = 11
                convert(3,11)
                     |       --> n is odd:   operation '-1'
                convert(3,12) 
                     |       --> n is even:  operation '*2' 
                convert(3,6)
                     |       --> n is even:  operation '*2' 
                convert(3,3) 
                     |       --> m == n
                   return 
Therefore, the sequence of operations is '*2', '*2', '-1'.
 
C++
Java
Python3
C#
PHP
Javascript
// C++ implementation to convert// a number m to n using minimum// number of given operations#include <bits/stdc++.h>using namespace std; // Function to find minimum// number of given operations// to convert m to nint convert(int m, int n){    if (m == n)        return 0;     // only way is to do    // -1 (m - n) times    if (m > n)        return m - n;     // not possible    if (m <= 0 && n > 0)        return -1;     // n is greater and n is odd    if (n % 2 == 1)         // perform '-1' on m        // (or +1 on n)        return 1 + convert(m, n + 1);     // n is even    else        // perform '*2' on m        // (or n/2 on n)        return 1 + convert(m, n / 2);} // Driver codeint main(){    int m = 3, n = 11;    cout << "Minimum number of operations : "         << convert(m, n);    return 0;}
// Java implementation to convert// a number m to n using minimum// number of given operations class ConvertNum{    // function to find minimum    // number of given operations    // to convert m to n    static int convert(int m, int n)    {        if (m == n)            return 0;             // only way is to do        // -1 (m - n) times        if (m > n)            return m - n;             // not possible        if (m <= 0 && n > 0)            return -1;             // n is greater and n is odd        if (n % 2 == 1)                 // perform '-1' on m            // (or +1 on n)            return 1 + convert(m, n + 1);             // n is even        else            // perform '*2' on m            // (or n / 2 on n)            return 1 + convert(m, n / 2);    }         // Driver Code    public static void main (String[] args)    {        int m = 3, n = 11;        System.out.println("Minimum number of " +                                "operations : " +                                  convert(m, n));    }}
# Python implementation to convert# a number m to n using minimum# number of given operations # Function to find minimum# number of given operations# to convert m to ndef convert(m, n):     if(m == n):        return 0     # only way is to do    # -1(m - n): times    if(m > n):        return m - n     # not possible    if(m <= 0 and n > 0):        return -1     # n is greater and n is odd    if(n % 2 == 1):         # perform '-1' on m        #(or +1 on n):        return 1 + convert(m, n + 1)     # n is even    else:                 # perform '*2' on m        #(or n/2 on n):        return 1 + convert(m, n / 2) # Driver codem = 3n = 11print("Minimum number of operations :",                          convert(m, n)) # This code is contributed by# Sanjit_Prasad
// C# implementation to convert// a number m to n using minimum// number of given operationsusing System; class GFG{    // function to find minimum    // number of given operations    // to convert m to n    static int convert(int m, int n)    {        if (m == n)            return 0;             // only way is to do        // -1 (m - n) times        if (m > n)            return m - n;             // not possible        if (m <= 0 && n > 0)            return -1;             // n is greater and n is odd        if (n % 2 == 1)                 // perform '-1' on m            // (or +1 on n)            return 1 + convert(m, n + 1);             // n is even        else            // perform '*2' on m            // (or n / 2 on n)            return 1 + convert(m, n / 2);    }         // Driver code    public static void Main ()    {        int m = 3, n = 11;        Console.Write("Minimum number of " +                           "operations : " +                             convert(m, n));    }} // This code is contributed by nitin mittal
<?php// PHP implementation to convert// a number m to n using minimum// number of given operations // Function to find minimum// number of given operations// to convert m to nfunction convert($m, $n){    if ($m == $n)        return 0;     // only way is to do    // -1 (m - n) times    if ($m > $n)        return $m - $n;     // not possible    if ($m <= 0 && $n > 0)        return -1;     // n is greater and n is odd    if ($n % 2 == 1)         // perform '-1' on m        // (or +1 on n)        return 1 + convert($m, $n + 1);     // n is even    else        // perform '*2' on m        // (or n/2 on n)        return 1 + convert($m, $n / 2);} // Driver code{    $m = 3; $n = 11;    echo "Minimum number of ".              "operations : ",              convert($m, $n);    return 0;}     // This code is contributed// by nitin mittal.?>
<script>// javascript implementation to convert// a number m to n using minimum// number of given operations // function to find minimum// number of given operations// to convert m to nfunction convert(m , n){    if (m == n)        return 0;     // only way is to do    // -1 (m - n) times    if (m > n)        return m - n;     // not possible    if (m <= 0 && n > 0)        return -1;     // n is greater and n is odd    if (n % 2 == 1)         // perform '-1' on m        // (or +1 on n)        return 1 + convert(m, n + 1);     // n is even    else        // perform '*2' on m        // (or n / 2 on n)        return 1 + convert(m, n / 2);} // Driver Codevar m = 3, n = 11;document.write("Minimum number of " +                        "operations : " +                          convert(m, n)); // This code is contributed by Princi Singh</script>
Output :  
Minimum number of operations : 3
References : http://tech.queryhome.com/112705/convert-number-with-minimum-operations-operations-allowedThis article is contributed by Ayush Jauhari. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. 
nitin mittal
aeros15
Sanjit_Prasad
princi singh
sumitgumber28
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