Count of integers of the form (2^x * 3^y) in the range [L, R]

Given a range [L, R] where 0 ≤ L ≤ R ≤ 108. The task is to find the count of integers from the given range that can be represented as (2x) * (3y).

Examples:

Input: L = 1, R = 10
Output: 7
The numbers are 1, 2, 3, 4, 6, 8 and 9

Input: L = 100, R = 200
Output: 5
The numbers are 108, 128, 144, 162 and 192

Approach: Since the numbers, which are powers of two and three, quickly grow, you can use the following algorithm. For all the numbers of the form (2x) * (3y) in the range [1, 108] store them in a vector. Later sort the vector. Then the required answer can be calculated using an upper bound. Pre-calculating these integers will be helpful when there are a number of queries of the form [L, R].

Below is the implementation of the above approach:

#include

using namespace std;

  

#define MAXI (int)(1e8)

  

vector<int> v;

  

void precompute()

{

  

    

    

    int x = 1, y = 1;

  

    

    

    while (x <= MAXI) {

  

        

        while (x * y <= MAXI) {

  

            

            v.push_back(x * y);

  

            

            y *= 3;

        }

  

        

        x *= 2;

  

        

        y = 1;

    }

  

    

    sort(v.begin(), v.end());

}

  

void countNum(int l, int r)

{

    cout << upper_bound(v.begin(), v.end(), r)

                - upper_bound(v.begin(), v.end(), l - 1);

}

  

int main()

{

    int l = 100, r = 200;

  

    

    precompute();

  

    countNum(l, r);

  

    return 0;

}



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