Program to find number of unique subsequences same as target in C++

Suppose we have two lowercase strings s and t, we have to find the number of subsequences of s that are equal to t. If the answer is very large then return result by 10^9 + 7.

So, if the input is like s = "abbd" t = "bd", then the output will be 2, as there are two possible subsequences "bd".

• s[1] concatenate s[3]

• s[2] concatenate s[3].

To solve this, we will follow these steps −

• m := 10^9 + 7

• if size of t is same as 0, then −

  • return 0

• if t is same as s, then −

  • return 1

• if size of t > size of s, then −

  • return 0

• Define an array table of size same as size of t + 1 and fill with 0

• table[0] := 1

• for initialize i := 0, when i < size of s, update (increase i by 1), do −

  • Define an array onsave := table

  • for initialize j := 0, when j < size of table, update (increase j by 1), do −

    • if s[i] is same as t[j], then −

      • table[j + 1] = (table[j + 1] mod m + onsave[j] mod m)

• table[j + 1] = (table[j + 1] mod m + onsave[j] mod m)

Let us see the following implementation to get better understanding −

Example

 Live Demo

#include <bits/stdc++.h>
using namespace std;
int solve(string s, string t) {
   int m = 1000000007;
   if (t.size() == 0)
      return 0;
   if (t == s)
      return 1;
   if (t.size() > s.size())
      return 0;
   vector<int> table(t.size() + 1, 0);
   table[0] = 1;
   for (int i = 0; i < s.size(); i++) {
      vector<int> onsave = table;
      for (int j = 0; j < table.size(); j++) {
         if (s[i] == t[j]) {
            table[j + 1] = (table[j + 1] % m + onsave[j] % m) %m;
         }
      }
   }
   return table[t.size()] % m;
}
main(){
   string s = "abbd", t = "bd";
   cout << (solve(s, t));
}

Input

"abbd", "bd"

Output

2