The   shortest common supersequence   is a problem closely related to the   longest common subsequence,   which you can use as an external function for this task.



Task

Given two strings 



u


{\displaystyle u}

 and 



v


{\displaystyle v}

, find the shortest possible sequence 



s


{\displaystyle s}

, which is the shortest common super-sequence of 



u


{\displaystyle u}

 and 



v


{\displaystyle v}

 where both 



u


{\displaystyle u}

 and 



v


{\displaystyle v}

 are a subsequence of 



s


{\displaystyle s}

. Defined as such, 



s


{\displaystyle s}

 is not necessarily unique.

Demonstrate this by printing 



s


{\displaystyle s}

 where 



u
=


{\displaystyle u=}

“abcbdab” and 



v
=


{\displaystyle v=}

“bdcaba”.



Also see

 Wikipedia: shortest common supersequence 


#include <iostream>
 
std::string scs(std::string x, std::string y) {
    if (x.empty()) {
        return y;
    }
    if (y.empty()) {
        return x;
    }
    if (x[0] == y[0]) {
        return x[0] + scs(x.substr(1), y.substr(1));
    }
    if (scs(x, y.substr(1)).size() <= scs(x.substr(1), y).size()) {
        return y[0] + scs(x, y.substr(1));
    } else {
        return x[0] + scs(x.substr(1), y);
    }
}
 
int main() {
    auto res = scs("abcbdab", "bdcaba");
    std::cout << res << '\n';
    return 0;
}