Convert a number m to n with minimum operations. The operations allowed are :

- 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++

`// 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 n` `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` `int` `main()` `{` ` ` `int` `m = 3, n = 11;` ` ` `cout << ` `"Minimum number of operations : "` ` ` `<< convert(m, n);` ` ` `return` `0;` `}` |

## Java

`// 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));` ` ` `}` `}` |

## Python3

`# 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 n` `def` `conver(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` `+` `conver(m, n ` `+` `1` `)` ` ` `# n is even` ` ` `else` `:` ` ` ` ` `# perform '*2' on m` ` ` `#(or n/2 on n):` ` ` `return` `1` `+` `conver(m, n ` `/` `2` `)` `# Driver code` `m ` `=` `3` `n ` `=` `11` `print` `(` `"Minimum number of operations :"` `,` ` ` `conver(m, n))` `# This code is contributed by` `# Sanjit_Prasad` |

## C#

`// C# implementation to convert` `// a number m to n using minimum` `// number of given operations` `using` `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` `// 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 n` `function` `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.` `?>` |

## Javascript

`<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 n` `function` `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` `var` `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-allowed

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