## C++, dynamic_programming, longest_common_subsequence.cpp

``````// Longest common subsequence - Dynamic Programming
#include <iostream>
using namespace std;

void Print(int trace[20][20], int m, int n, string a) {
if (m == 0 || n == 0) {
return;
}
if (trace[m][n] == 1) {
Print(trace, m - 1, n - 1, a);
cout << a[m - 1];
} else if (trace[m][n] == 2) {
Print(trace, m - 1, n, a);
} else if (trace[m][n] == 3) {
Print(trace, m, n - 1, a);
}
}

int lcs(string a, string b) {
int m = a.length(), n = b.length();
int res[m + 1][n + 1];
int trace[20][20];

// fills up the arrays with zeros.
for (int i = 0; i < m + 1; i++) {
for (int j = 0; j < n + 1; j++) {
res[i][j] = 0;
trace[i][j] = 0;
}
}

for (int i = 0; i < m + 1; ++i) {
for (int j = 0; j < n + 1; ++j) {
if (i == 0 || j == 0) {
res[i][j] = 0;
trace[i][j] = 0;
}

else if (a[i - 1] == b[j - 1]) {
res[i][j] = 1 + res[i - 1][j - 1];
trace[i][j] = 1;  // 1 means trace the matrix in upper left
// diagonal direction.
} else {
if (res[i - 1][j] > res[i][j - 1]) {
res[i][j] = res[i - 1][j];
trace[i][j] =
2;  // 2 means trace the matrix in upwards direction.
} else {
res[i][j] = res[i][j - 1];
trace[i][j] =
3;  //  means trace the matrix in left direction.
}
}
}
}
Print(trace, m, n, a);
return res[m][n];
}

int main() {
string a, b;
cin >> a >> b;
cout << lcs(a, b);
return 0;
}
``````