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.
- Multiply a number x by 2. So, x becomes 2*x.
- Subtract one from the number x. So, x becomes x-1.
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.
The idea is to reverse the problem as follows: We should get the number N starting from M using the operations:
- Divide the number by 2 if it is even.
- Add 1 to the number.
Now, the minimum number of operations would be:
- 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.
- 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:
// If m is odd
if($m % 2 != 0)
// add one
// divide m by 2
$m /= 2;
// Return the required answer
return $ans + $n – $m;
// Driver code
$n = 4; $m = 6;
// This code is contributed by Code_Mech
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