longest shortest subsequence code example

Example: shortest common supersequence

string scs_string(string x,string y,int n,int m) {
    int dp[n+1][m+1];
    for(int i=0;i<=n;i++) {
        for(int j=0;j<=m;j++) {
            if(i==0 || j==0) {
                dp[i][j] = 0;
                continue;
            }
            if(x[i-1]==y[j-1]) {
                dp[i][j] = 1+dp[i-1][j-1];
            }
            else
                dp[i][j] = max(dp[i-1][j],dp[i][j-1]);
        }
    }
    string s;
    int i=n;
    int j=m;
    while(i>0 && j>0) {
        if(x[i-1]==y[j-1]) {
            s.push_back(x[i-1]);
            i--;
            j--;
        }
        else {
            if(dp[i-1][j]>dp[i][j-1]) {
                s.push_back(x[i-1]); 
                cout<<x[i-1]<<" , "<<y[j-1]<<endl;
                i--;
            }
            else {
                s.push_back(y[j-1]);
                cout<<x[i-1]<<" , "<<y[j-1]<<endl;
                j--;
            }
        }
    }
    while(i>0) {
        s.push_back(x[i-1]);
        i--;
    }
    while(j>0) {
        s.push_back(x[j-1]);
        j--;
    }
    reverse(s.begin(),s.end());
    return s;
}