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).


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:


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;





    countNum(l, r);


    return 0;


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