# C Program for Longest Common Subsequence Problem

In this post I am sharing C program for Longest Common Subsequence Problem.
LCS problem is a dynamic programming approach in which we find the longest subsequence which is common in between two given strings. A subsequence is a sequence which appears in the same order but not necessarily contiguous. For example ACF, AFG, AFGHD, FGH are some subsequences of string ACFGHD. So for a string of length n there can be total 2^n subsequences. The LCS algorithm is widely used in bioinformatics.

For string ACFGHD and ABFHD, the longest common subsequence is AFHD. The function that is used to find the longest common subsequence of two strings is given below.

Below I have shared the C program for longest common subsequence problem and a video tutorial that will help you understand LCS algorithm easily.

## C Program for Longest Common Subsequence Problem

```#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()
{
printf("Enter 1st sequence:");
scanf("%s",x);
printf("Enter 2nd sequence:");
scanf("%s",y);
printf("\nThe Longest Common Subsequence is ");
lcs();
print(m,n);
return 0;
}```

Output

### 11 thoughts on “C Program for Longest Common Subsequence Problem”

1. In the main() function in the scanf() statement before x and y, ‘&'(ampersand) is missing…

2. Your logic behind this program is good bro but what if there are more then one lcs are possible. For example
I have
X = ABCBDAB
Y = BDCABA

LCS are:
BCBA
BCAB
BDAB

then how am i able to print them all ??