Convert 0 to N by adding 1 or multiplying by 2 in minimum steps
Given a positive integer N, the task is to find the minimum number of addition operations required to convert the number 0 to N such that in each operation any number can be multiplied by 2 or add the value 1 to it.
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Input: N = 6
Following are the operations performed to convert 0 to 6:
Add 1 –> 0 + 1 = 1.
Multiply 2 –> 1 * 2 = 2.
Add 1 –> 2 + 1 = 3.
Multiply 2 –> 3 * 2 = 6.
Therefore number of addition operations = 2.
Input: N = 3
Approach: This problem can be solved by using the Bit Manipulation technique. In binary number representation of N, while operating each bit whenever N becomes odd (that means the least significant bit of N is set) then perform the addition operation. Otherwise, multiply by 2. The final logic to the given problem is to find the number of set bits in N.
Below is the implementation of the above approach:
Time Complexity: O(log N)
Auxiliary Space: O(1)