Consider:
a c p r c
x s o p c
v o v n i
w g f m n
q a t i t
An alphabet i_index is adjacent to another alphabet j_index in the tile if i_index is next to j_index in any of the following positions:
* * *
* x *
* * *
Here all the * indicates the location which are adjacent to x.
The task is to find a given string in the tile. The condition is that all the characters of the given string should be adjacent, and no one character in the tile may be used more than once to construct the given string.
I have came up with a simply backtracking solution, for which the solutions are pretty fast, but the worst case time is really worse.
For an example: Say the tile has 4x4 filled with all a's , therefore 16 a's, and the string to find is aaaaaaaaaaaaaaab, that is, 15 a's and one b . One what is to eliminate strings with characters which does not appear in the tile. But still worst case can still appear with say the tile have abababababababab and the string to find is abababababababbb .
My attempt is like this:
#include <stdio.h>
#include <string.h>
#include <ctype.h>
#define MAX 5
int sp (char mat[MAX][MAX], char *pat, int c, int i, int j)
{
int r = 0;
char temp;
if (c == strlen (pat))
return 1;
if (((i<0) || (j<0)) || (i>=MAX) || (j>=MAX))
return 0;
if (mat[i][j] != pat[c])
return 0;
if (isupper (mat[i][j]))
return 0;
/* Save character and mark location to indicate
* DFS has visited this node, to stop other branches
* to enter here and cross over path
*/
temp = mat[i][j];
mat[i][j] = 0;
r |= sp (mat, pat, c+1, i-1, j-1);
r |= sp (mat, pat, c+1, i-1, j);
r |= sp (mat, pat, c+1, i-1, j+1);
r |= sp (mat, pat, c+1, i, j+1);
r |= sp (mat, pat, c+1, i+1, j+1);
r |= sp (mat, pat, c+1, i+1, j);
r |= sp (mat, pat, c+1, i+1, j-1);
r |= sp (mat, pat, c+1, i, j-1);
/* restore value */
mat[i][j] = temp;
/* mark if success */
if ((mat[i][j] == pat[c]) && (r == 1))
mat[i][j] = toupper (mat[i][j]);
return r;
}
/* Testing the `sp` module */
int main (void)
{
char mat[MAX][MAX] = {
{'a', 'c', 'p', 'r', 'c'},
{'x', 's', 'o', 'p', 'c'},
{'v', 'o', 'v', 'n', 'i'},
{'w', 'g', 'f', 'm', 'n'},
{'q', 'a', 't', 'i', 't'}
};
char pat[] = "microsoft";
int i, j;
for (i=0; i<5; i++)
{
for (j=0; j<5; j++)
printf ("%c ", mat[i][j]);
printf ("\n");
}
for (i=0; i<5; i++)
for (j=0; j<5; j++)
sp (mat, pat, 0, i, j);
printf ("\n\n\n");
for (i=0; i<5; i++)
{
for (j=0; j<5; j++)
{
if (isupper (mat[i][j]))
printf ("%c ", mat[i][j]);
else
printf (". ");
}
printf ("\n");
}
printf ("\n");
return 0;
}
which prints:
a c p r c
x s o p c
v o v n i
w g f m n
q a t i t
. . . R .
. S O . C
. O . . I
. . F M .
. . T . .
The function sp does the work, performs the back tracking.
Is there a better way ? or is it possible to lower the worst case time ?
