## Longest Common Subsequence 1

QUESTION

The longest common subsequence (or LCS) of groups A and B is the longest group of elements from A and B that are common between the two groups and in the same order in each group. \n\nFor example, the sequences \”1234\” and \”1224533324\” have an LCS of \”1234\”.

``````#include<stdio.h>
#include<string.h>

int i,j,m,n,c[20][20];
char x[20],y[20],b[20][20];

void print(int i,int j)
{
if(i==0 || j==0)
return;
if(b[i][j]=='c')
{
print(i-1,j-1);
printf("%c",x[i-1]);
}
else if(b[i][j]=='u')
print(i-1,j);
else
print(i,j-1);
}

void lcs()
{
m=strlen(x);
n=strlen(y);
for(i=0;i<=m;i++)
c[i][0]=0;
for(i=0;i<=n;i++)
c[0][i]=0;

//c, u and l denotes cross, upward and downward directions respectively
for(i=1;i<=m;i++)
for(j=1;j<=n;j++)
{
if(x[i-1]==y[j-1])
{
c[i][j]=c[i-1][j-1]+1;
b[i][j]='c';
}
else if(c[i-1][j]>=c[i][j-1])
{
c[i][j]=c[i-1][j];
b[i][j]='u';
}
else
{
c[i][j]=c[i][j-1];
b[i][j]='l';
}
}
}

int main()
{

scanf("%s",x);
scanf("%s",y);
printf("\nThe Longest Common Subsequence is ");
lcs();
print(m,n);
return 0;
}``````