Count all sub-sequences having product <= K – Recursive approach in C++

In this tutorial, we will be discussing a program to find the number of sub-sequences having product <= k.

For this we will be provided with an array and a value K. Our task is to find the number of sub sequences having their product as K.

Example

 Live Demo

#include <bits/stdc++.h>
#define ll long long
using namespace std;
//keeping count of discarded sub sequences
ll discard_count = 0;
ll power(ll a, ll n){
   if (n == 0)
      return 1;
   ll p = power(a, n / 2);
   p = p * p;
   if (n & 1)
      p = p * a;
   return p;
}
//recursive approach to count
//discarded sub sequences
void solve(int i, int n, float sum, float k,
float* a, float* prefix){
   if (sum > k) {
      discard_count += power(2, n - i);
      return;
   }
   if (i == n)
      return;
      float rem = prefix[n - 1] - prefix[i];
   if (sum + a[i] + rem > k)
      solve(i + 1, n, sum + a[i], k, a, prefix);
   if (sum + rem > k)
      solve(i + 1, n, sum, k, a, prefix);
}
int countSubsequences(const int* arr,
int n, ll K){
   float sum = 0.0;
   float k = log2(K);
   float prefix[n], a[n];
   for (int i = 0; i < n; i++) {
      a[i] = log2(arr[i]);
      sum += a[i];
   }
   prefix[0] = a[0];
   for (int i = 1; i < n; i++) {
      prefix[i] = prefix[i - 1] + a[i];
   }
   ll total = power(2, n) - 1;
   if (sum <= k) {
      return total;
   }
   solve(0, n, 0.0, k, a, prefix);
   return total - discard_count;
}
int main() {
   int arr[] = { 4, 8, 7, 2 };
   int n = sizeof(arr) / sizeof(arr[0]);
   ll k = 50;
   cout << countSubsequences(arr, n, k);
   return 0;
}

Output

9