Count All Increasing Subsequences in C++

In this tutorial, we will be discussing a program to find the number of increasing sequences.

For this we will be provided with an array containing digits 0 to 9. Our task is to count all the sequences present in the array such that the next element is greater than the previous element.

Example

 Live Demo

#include<bits/stdc++.h>
using namespace std;
//counting the possible subsequences
int count_sequence(int arr[], int n){
   int count[10] = {0};
   //scanning each digit
   for (int i=0; i<n; i++){
      for (int j=arr[i]-1; j>=0; j--)
         count[arr[i]] += count[j];
      count[arr[i]]++;
   }
   //getting all the possible subsequences
   int result = 0;
   for (int i=0; i<10; i++)
      result += count[i];
   return result;
}
int main(){
   int arr[] = {3, 2, 4, 5, 4};
   int n = sizeof(arr)/sizeof(arr[0]);
   cout << count_sequence(arr,n);
   return 0;
}

Output

14