# Count bases which contains a set bit as the Most Significant Bit in the representation of N

Count bases which contains a set bit as the Most Significant Bit in the representation of NGiven a positive integer N, the task is to count the number of different bases in which, when N is represented, the most significant bit of N is a found to be a set bit.Examples:Input: N = 6Output: 4Explanation: The number 6 can be represented in 5 different bases, i.e. base 2, base 3, base 4, base 5, base 6.(6)10  in base 2: (110)2(6)10  in base 3: (20)3(6)10  in base 4: (12)4(6)10  in base 5: (11)5(6)10  in base 6: (10)6The base representation for (6)10 in base 2, base 4, base 5, base 6 starts with 1. Hence, the required count of bases is 4.Input: N = 5Output: 4Approach: The given problem can be solved by finding the MSB of the given number N for every possible base and count those bases that have MSB as 1. Follow the steps below to solve the problem:Initialize a variable, say count as 0, to store the required result.Iterate over the range [2, N] using a variable, say B, and perform the following steps:Store the highest power of base B required to represent number N in a variable P. This can be easily achieved by finding the value of (log N to the base B) i.e., logB(N) truncated to the nearest integer.To find the value of logB(N) use the log property: logB(N) = log(N)/log(B)Store the most significant digit of N by dividing N by (B)P. If it is equal to 1, then increment the value of the count by 1.After completing the above steps, print the value of count as the result.Below is the implementation of the above approach:C++  #include using namespace std;  int countOfBase(int N){        int count = 0;          for (int i = 2; i 