how to save string in longest common subsequence recursive algorithm - c++

Question

I'm trying to implement a naive approach of the longest common subsequence algorithm. I'm using a recursive approach, passing two strings into the function lcs. I successfully counted the number of characters in the longest subsequence.
My problem is printing the characters of the lcs. I thought I could do this by storing matched characters in a string called sub and passing it as a parameter. However, I'm stuck on how to save the string. I've always struggled with recursion, and would appreciate any tips on approaching this problem the right way.
#include <iostream>
#include <string>
#include <math.h>
using namespace std;
int lcs(string a, string b,string sub){
int aLen = a.length();
int bLen = b.length();
if (aLen==0 || bLen==0){
return 0;
}
if(a.at(aLen-1)==b.at(bLen-1)){
return 1+lcs(a.substr(0,aLen-1),b.substr(0,bLen-1),a.at(aLen-1)+sub); // add letter to subsequence
}
else {
return max(lcs(a.substr(0,aLen-1),b.substr(0,bLen),sub),lcs(a.substr(0,aLen),b.substr(0,bLen-1),sub));
}
}
int main(int argc, const char * argv[])
{
char sub[]="";
int charsInLCS = lcs("sdmc","msdc",sub); //i want to output "sdc"
cout << charsInLCS << endl;
return 0;
}

Answer 1

Be careful, your base case is wrong as you never check a[0] against b[0]. Also, passing string copies is very expensive, much faster to pass just the indexes and work with that. We need to keep track of what characters we matched when a[idxa] == b[idxb]. Here is a solution using vectors:
#include <iostream>
#include <string>
#include <queue>
#include <math.h>
#include <algorithm> // std::reverse
using namespace std;
string s1, s2;
int lcs(int idx1, int idx2, vector<char> &v){
if (idx1 == -1 || idx2 == -1){
return 0;
}
if (s1[idx1] == s2[idx2]) {
v.push_back(s1[idx1]); // record that we used this char
return 1 + lcs(idx1 - 1, idx2 - 1, v);
} else {
vector<char> v1, v2;
int p1 = lcs(idx1 - 1, idx2, v1);
int p2 = lcs(idx1, idx2 - 1, v2);
if (p1 > p2) { // we used the chars we already had in v + the ones in v1
v.insert(v.end(), v1.begin(), v1.end());
return p1;
} else { // we used the chars we already had in v + the ones in v2
v.insert(v.end(), v2.begin(), v2.end());
return p2;
}
}
}
int main(int argc, const char * argv[])
{
s1 = "sdmc";
s2 = "msdc";
vector<char> v; // chars we used
int sol = lcs(s1.length() - 1, s2.length() - 1, v); //i want to output "sdc"
cout << sol << " ";
reverse(v.begin(), v.end());
for (auto num : v) {
cout << num;
}
return 0;
}