Ant in a Maze problem
Ant in a maze is another problem that can be solved using backtracking algorithm.In this problem there is a NxN maze in which one corner of maze is entry point and other is exit point.Now there is an ant in a maze who wants to go from entry to exit.For doing this there are certain constraints like an ant can move only forward or downward but no backward and upward.For the sake of simplicity we are taking 4x4 Maze.The maze can be denoted by a matrix with values 0 and 1.0 means the path is blocked and 1 means the path is available.The maze and the path for ant from entry to exit is
bool isvalid(int maze[4][4], int x, int y)
{
if(x >= 0 && x < 4 && y >= 0 && y < 4) // if x,y is inside maze then return true
{
if(maze[x][y]==1)
return true;
}
return false;
}
void printpath(int Path[4][4])
{
for (int i = 0; i < 4; i++)
{
for (int j = 0; j < 4; j++)
printf(" %d ", Path[i][j]);
printf("\n");
}
}
The block which are in grey color are dead end in the maze that is the ant cannot go through such blocks.The red path is the path travelled by ant from entry to exit.The matrix representation of the above maze without the path will be (input to be taken)
maze[4][4]={{1,1,0,0},
{1,1,0,1},
{0,1,0,0},
{1,1,1,1}
}
and the matrix representation of path travelled by ant will be (output to be displayed)
Path[4][4]={{1,1,0,0},
{0,1,0,0},
{0,1,0,0},
{0,1,1,1}
}
Algorithm :
1) Mark current block in a matrix as 1
2) Move horizontally in forward direction and recursively check whether this leads to solution.
3) If the above step doesn't lead to the valid solution then move downwards and check whether this leads to the solution.
4) If none of the above solutions work then unmark the block as 0 and return false.
Program :
#include<stdio.h>
#include<conio.h>
bool Findpath(int maze[4][4], int x, int y, int Path[4][4])
{
if(x == 3 && y == 3) //Exit point is reached
{
Path[x][y] = 1;
return true;
}
if(isvalid(maze, x, y) == true) // Check if maze[x][y] is valid
{
Path[x][y] = 1; // mark x,y as part of solution
if (Findpath(maze, x+1, y, Path) == true) // Move forward in x direction
return true;
if (Findpath(maze, x, y+1, Path) == true) // If moving in x direction doesn't give solution Move down
return true;
Path[x][y] = 0; // If the above steps didn't work then Backtrack that is unmark x,y as part of solution
return false;
}
printpath(Path);
return false;
}
bool isvalid(int maze[4][4], int x, int y)
{
if(x >= 0 && x < 4 && y >= 0 && y < 4) // if x,y is inside maze then return true
{
if(maze[x][y]==1)
return true;
}
return false;
}
void printpath(int Path[4][4])
{
for (int i = 0; i < 4; i++)
{
for (int j = 0; j < 4; j++)
printf(" %d ", Path[i][j]);
printf("\n");
}
}
int main()
{
int maze[4][4] = { {1, 1, 0, 0},
{1, 1, 0, 1},
{0, 1, 0, 0},
{1, 1, 1, 1}
};
int Path[4][4] = { {0, 0, 0, 0},
{0, 0, 0, 0},
{0, 0, 0, 0},
{0, 0, 0, 0}
};
bool a=Findpath(maze,0,0,Path);
if(a==false)
{
printf("Solution doesnot Exist\n");
return false;
}
getch();
}
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