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Rat in a Maze with multiple steps or jump allowed?
The rat in maze problem is one of the well-known problem of the backtracking. Here we will see that problem with little variation. Suppose one NxN maze M is given. The starting point is top left corner M[0, 0], and the destination is right bottom corner M[N – 1, N - 1]. One rat is placed at the starting point. Our goal is to find a path from starting point to ending point that can be by the rat to reach the destination. Here the rat can jump (The variation). Now there are some constraints
- The rat can move either towards the right or towards the down.
- Maze with 0 in cell indicates that the cell is blocked.
- Non-zero cells are indicating valid path.
- The number inside the cell indicates the number of maximum jump the rat can make from that cell.
Algorithm
ratInMaze
begin if destination is reached, then print the solution matrix else 1. Place the current cell inside the solution matrix as 1 2. Move forward or jump (check max jump value) and recursively check if move leads to solution or not. 3. If the move taken from the step 2 is not correct, then move down, and check it leads to the solution or not 4. If none of the solutions in step 2 and 3 are correct, then make the current cell 0. end if end
Example
#include <iostream>
#define N 4
using namespace std;
void dispSolution(int sol[N][N]) {
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++)
cout << sol[i][j] << " ";
cout << endl;
}
}
bool isSafe(int maze[N][N], int x, int y) { //check whether x,y is valid or not
// when (x, y) is outside of the maze, then return false
if (x >= 0 && x < N && y >= 0 && y < N && maze[x][y] != 0)
return true;
return false;
}
bool ratMazeSolve(int maze[N][N], int x, int y, int sol[N][N]) {
if (x == N - 1 && y == N - 1) { //if destination is found, return true
sol[x][y] = 1;
return true;
}
if (isSafe(maze, x, y)) {
sol[x][y] = 1; //mark 1 into solution matrix
for (int i = 1; i <= maze[x][y] && i < N; i++) {
if (ratMazeSolve(maze, x + i, y, sol)) //move right
return true;
if (ratMazeSolve(maze, x, y + i, sol)) //move down
return true;
}
sol[x][y] = 0; //if the solution is not valid, then make it 0
return false;
}
return false;
}
bool solveMaze(int maze[N][N]) {
int sol[N][N] = { { 0, 0, 0, 0 },
{ 0, 0, 0, 0 },
{ 0, 0, 0, 0 },
{ 0, 0, 0, 0 }
};
if (!ratMazeSolve(maze, 0, 0, sol)) {
cout << "Solution doesn't exist";
return false;
}
dispSolution(sol);
return true;
}
main() {
int maze[N][N] = { { 2, 1, 0, 0 },
{ 3, 0, 0, 1 },
{ 0, 1, 0, 1 },
{ 0, 0, 0, 1 }
};
solveMaze(maze);
}Output
1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1
Updated on: 31-Jul-2019
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