Reduce a number to 1 by performing given operations | Set 3

Given an integer N, the task is to find the number of steps required to reduce the given number N to 1 by performing the following operations:

1. If the number is a power of 2, then divide the number by 2.
2. Otherwise, subtract the greatest power of 2 smaller than N from N.

Examples:

Input: N = 2 
Output: 1
Explanation: The given number can be reduced to 1 by following the following steps:
Divide the number by 2 as N is a power of 2 which modifies the N to 1.
Therefore, the N can be reduced to 1 in only 1 step.

Input: N = 7 
Output: 2
Explanation: The given number can be reduced to 1 by following the following steps:
Subtract 4 the greatest power of 2 less than N. After the step the N modifies to N = 7-4 = 3.
Subtract 2 the greatest power of 2 less than N. After the step the N modifies to N = 3-2 = 1.
Therefore, the N can be reduced to 1 in 2 steps.

Method 1 –  

Approach: The idea is to recursively compute the minimum number of steps required.  

• If the number is a power of 2, then we are allowed to only divide the number by 2.
• Else we can subtract the greatest power of 2 smaller than N from N.
• So, we will use recursion for both the operations whenever valid and return number of operations.

Below is the implementation of the above approach:

2

Method 2 – 

Approach: The given problem can be solved using bitwise operators. Follow the steps below to solve the problem:

• Initialize two variables say res with value 0 and MSB with value log₂(N) to store the number of steps needed to reduce the number to 1 and the most significant bit of N.
• Iterate while N is not equal to 1:
  • Check if the number is the power of 2 then divide N by 2.
  • Otherwise, subtract the largest power of 2 less than N from N i.e update N as N=N-2^MSB.
  • Increment res by 1 and decrement MSB by 1.
• Finally, print res.

Below is the implementation of the above approach:

2

Time Complexity: O(log(N))
Auxiliary Space: O(1)