Finding LCS using DP - c++

Question

I have used Dynamic Programming to find longest common sub-sequence b/w two strings. What is wrong in the code. Why it always gives answer as 0?
#include<bits/stdc++.h>
using namespace std;
int dp[20][20];
void initialize()
{
for(int i=0;i<20;i++)
for(int j=0;j<20;j++)
dp[i][j]=-1;
}
int lcs(string a,string b,int m,int n)
{
if(m==0||n==0)
return 0;
if(dp[m][n]!=-1)
return dp[m][n];
if(a[m-1]==b[n-1])
return dp[m-1][n-1] = 1+lcs(a,b,m-1,n-1);
if(a[m-1]!=b[n-1])
return dp[n-1][m-1]=max(dp[n][m-1]=lcs(a,b,n,m-1),dp[n-1][m]=lcs(a,b,n-1,m));
}
int main()
{
string a="AGGTAB",b="GXTXAYB";
cout<<lcs(a,b,a.length(),b.length());
}

Answer 1

You've forgotten to call initialize()
18th line, it should be dp[m][n], not dp[m-1][n-1]
Commented 19th line code, as it is no need & for make the code compatible for all compilers
i.e., some compiler may give warning: control reaches end of non-void function [-Wreturn-type]
Made some code change in 20th line, as it seems you confused with variables m & n.
Code:
#include<bits/stdc++.h>
using namespace std;
int dp[20][20];
void initialize()
{
for(int i=0;i<20;i++)
for(int j=0;j<20;j++)
dp[i][j]=-1;
}
int lcs(string a,string b,int m,int n)
{
if(m==0||n==0)
return 0;
if(dp[m][n]!=-1)
return dp[m][n];
if(a[m-1]==b[n-1])
return dp[m][n] = 1+lcs(a,b,m-1,n-1);
//if(a[m-1]!=b[n-1])
return dp[m][n]=max(lcs(a,b,m-1,n),lcs(a,b,m,n-1));
}
int main()
{
string a="AGGTAB",b="GXTXAYB";
initialize();
cout<<lcs(a,b,a.length(),b.length());
}
Output:
4