/*
 * AndroidPW.c: Compute the number of Android grid-path passwords.
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
 *
 * Copyright (c) 2011 Paul E. McKenney, IBM Corporation.
 */

#include <stdio.h>

/*
 * Nodes numbered like a touch-tone phone, only starting with zero:
 *
 *  0 1 2
 *  3 4 5
 *  6 7 8
 *
 * Rules governing paths:
 *	Can move only in straight line segments from one node to another.
 *	If the previous line segment arrived at a node, the next must leave it.
 *	Cannot visit a node twice.
 *	Cannot pass through a node without visiting unless already visited.
 *		Example: 0->8 is allowed only if 4 already visited.
 *		Otherwise, attemping 0->8 gets you 0->4->8.
 *	A path must visit at least four nodes. (new)
 *	
 */

/*
 * Key for connectmatrix[n][m]:
 *	0: Cannot go from n to m.
 *	1: Can always go from n to m if m unvisited.
 *	-p: Can go from n to m is p has already been visited.
 *
 * Alternative approach: use bitmask, where bit i indicates that i must
 * already have been visited.  Explicit check required to avoid n->n
 * line segments.  Automate creation of the matrix, though!
 */
char connectmatrix[9][9] = {
/*       0   1   2   3   4   5    6   7   8 */
/*      --  --  --  --  --  --   --  --  -- */
/*0*/ {  0,  1, -1,  1,  1,  1,  -3,  1, -4 },
/*1*/ {  1,  0,  1,  1,  1,  1,   1, -4,  1 },
/*2*/ { -1,  1,  0,  1,  1,  1,  -4,  1, -5 },
/*3*/ {  1,  1,  1,  0,  1, -4,   1,  1,  1 },
/*4*/ {  1,  1,  1,  1,  0,  1,   1,  1,  1 },
/*5*/ {  1,  1,  1, -4,  1,  0,   1,  1,  1 },
/*6*/ { -3,  1, -4,  1,  1,  1,   0,  1, -7 },
/*7*/ {  1, -4,  1,  1,  1,  1,   1,  0,  1 },
/*8*/ { -4,  1, -5,  1,  1,  1,  -7,  1,  0 },
};

/* Mapping vector to rotate a path 90 degrees counter-clockwise. */
char rotatevector[9] = { 6, 3, 0, 7, 4, 1, 8, 5, 2 };

/*
 * Does "path" already visit node "next"?
 */
int contains(char *path, int length, char next)
{
	int i;

	for (i = 0; i < length; i++)
		if (path[i] == next)
			return 1;
	return 0;
}

/*
 * Rotate "path" 90 degrees counterclockwise in place, overwriting "path".
 */
void rotate(char *path, int length)
{
	int i;

	for (i = 0; i < length; i++)
		path[i] = rotatevector[path[i]];
}

/*
 * Print "path".  If "rotationallowed", print the four rotations.
 */
void dumppath(char *path, int length, int rotationallowed)
{
	int i;
	char rotpath[10];

	for (i = 0; i < length; i++) {
		printf("%d ", path[i]);
		rotpath[i] = path[i];
	}
	printf("\n");
	if (rotationallowed) {
		rotate(rotpath, length);
		dumppath(rotpath, length, 0);
		rotate(rotpath, length);
		dumppath(rotpath, length, 0);
		rotate(rotpath, length);
		dumppath(rotpath, length, 0);
	}
}

/*
 * Recursively search the path space given an initial node.
 */
int trynext(char *path, int length, int rotationallowed)
{
	int cur = path[length - 1];
	int i;
	int step;
	int sum = length >= 4;

	if (contains(path, length - 1, cur))
		return 0;
	if (length >= 4)
		dumppath(path, length, rotationallowed);
	for (i = 0; i <= 8; i++) {
		step = connectmatrix[cur][i];
		if (step == 0)
			continue;
		if (step < 0 && !contains(path, length, -step))
			continue;
		path[length] = i;
		sum += trynext(path, length + 1, rotationallowed);
	}
	return sum;
}

/*
 * Generate the initial node for trynext().
 */
int startpath(int cur, int rotationallowed)
{
	char path[10];

	path[0] = cur;
	return trynext(path, 1, rotationallowed);
}

int main(int argc, char *argv[])
{
	int i;
	int j;
	int sum = 0;

	for (i = 0; i <= 8; i++) {
		if (connectmatrix[i][i] != 0)
			printf("Node %d fails to exclude itself.\n", i);
		if (connectmatrix[i][8 - i] != -4 && i != 4)
			printf("Node %d fails to consider center node.\n", i);
		for (j = 0; j < i; j++) {
			if (connectmatrix[i][j] != connectmatrix[j][i])
				printf("Asymmetry: nodes %d and %d.\n", i, j);
		}
	}

	sum += 4 * startpath(0, 1);
	sum += 4 * startpath(1, 1);
	sum += startpath(4, 0);
	printf("Number of paths: %d\n", sum);
}