sequence pattern matching

// check if s1 forms a subsequence in s2 ..  means lcs(s1,s2) = s1.length();
int solve(string s1 ,  string s2){

    int sa = s1.length();
    int sb = s2.length();
    vector<vector<int>> dp (sa+1 ,vector<int>(sb+1,0));
    // a represents the ath element .. b represents the knapsack present

    for(int a=1;a<=sa;a++){
        for(int b=1;b<=sb;b++){
            if(s1[a-1] == s2[b-1] ){
            dp[a][b] = 1 + dp[a-1][b-1]; //here we can choose ith element again
            }else{
            dp[a][b] = max(dp[a-1][b] , dp[a][b-1]); // cant choose the ath element becuase its weight is more
            }
        }
    }




    return (dp[sa][sb] == sa); // gives to length of lcs
}