Printing Longest Common Subsequence

string comman_string(string s1, string s2) {
        int x=s1.length(),y=s2.length(),i,j;
        int a[x+1][y+1];
        memset(a,0,sizeof(a));
        for(i=1;i<=x;i++)
        {
            for(j=1;j<=y;j++)
            {
                if(s1[i-1]==s2[j-1])
                {
                    a[i][j]=max(a[i-1][j-1]+s1[i-1],a[i][j-1]);
                }
                else a[i][j]=max(a[i-1][j],a[i][j-1]);
            }
        }
        int index = a[x][y];

        char lcs[index+1];
        lcs[index] = '\0';
        i = m, j = n;
        while (i > 0 && j > 0)
        {
          if (s1[i-1] == s2[j-1])
          {
            lcs[index-1] = s1[i-1]; // Put current character in result
            i--; j--; index--;     // reduce values of i, j and index
          }

          else if (a[i-1][j] > a[i][j-1])
          i--;
          else
          j--;
       }
        int index = L[m][n];

        return lcs;
    }