Find all possible paths through a maze

问题

I'm trying to create a program that will traverse a randomly generated maze where 1's are open and 0's are walls. starting in the top left and ending in the bottom right. The path can go up, down, left, and right.

Currently, my program gives me a solution, but I'm having trouble getting it to print more than one path.

I've read several different versions of this problem, but I'm unable to find one quite with my parameters.

Here's my code, I omitted the part where I randomly generate my maze.

#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <stdbool.h>

int  n, minMatrix, solIndex = 1, minLen = 10000000; //I use the latter 3 variables in order to find the shortest path, not relevant for now


bool solveMaze(int mat[n][n],int x, int y, int sol[][n], int count){

int i, j;
  if((!(x >= 0 && x <n  && y >=0 && y < n)) || mat[x][y] == 0 || sol[x][y] == 1){
    return false;
  }

  if(x == n-1 && y == n-1){
    sol[x][y] = 1;

    printf("Solution %d is:\n", solIndex);
    for(i = 0; i < n; i++)
    {
      for( j=0;j<n;j++)
      {
        printf("%d", sol[i][j]);
      }
      printf("\n");
    }

    if(count<minLen)
    {
      minLen = count;
      minMatrix = solIndex;
    }
    solIndex +=1;
    sol[x][y] = 0;
    return true;
  }

  sol[x][y] = 1;

  if(solveMaze(mat, x+1, y, sol, count+1)){
    return true;
  }

  if(solveMaze(mat, x-1, y, sol, count+1)){
    return true;
  }

  if(solveMaze(mat, x, y+1, sol, count+1)){
    return true;
  }

  if(solveMaze(mat, x, y-1, sol, count+1)){
    return true;
  }
  sol[x][y] = 0;
  return false;

}

I've omitted the part of my main where I randomly generate my maze.

int main(){

if(!solveMaze(**mat, 0, 0, sol, 0)){
    printf("No possible paths, run program again\n");
  }
  else{
    printf("the shortest path is %d\n", minMatrix);
  }
}

For instance if I have the maze

It gives me the first path that it finds

Though it takes a roundabout way of getting there, due to the preferences of going in order of down, up, right, and left, it is still one path.

So ultimately, I'm not sure how to iterate for multiple paths.

回答1:

Straightforward fully working solution using the example maze from this similar question (which was marked as duplicate but was standalone compilable): Find all paths in a maze using DFS

It uses a simple DFS with straightforward recursion, which seems the same approach as in the question here. It keeps track of the current track in a single string instance and modifies the maze in place to block off the current track.

#include <iostream>
#include <string>

const int WIDTH = 6;
const int HEIGHT = 5;

void check(int x, int y, int dest_x, int dest_y, 
           int (&maze)[HEIGHT][WIDTH], std::string& path) {
  if (x < 0 || y < 0 || x >= WIDTH|| y >= HEIGHT || !maze[y][x]) {
    return;        
  }
  int len = path.size();
  path += (char) ('0' + x);
  path += ',';
  path += (char) ('0' + y);

  if (x == dest_x && y == dest_y) {
    std::cout << path << "\n";
  } else {
    path += " > ";
    maze[y][x] = 0;  
    check (x + 0, y - 1, dest_x, dest_y, maze, path);
    check (x + 0, y + 1, dest_x, dest_y, maze, path);
    check (x - 1, y + 0, dest_x, dest_y, maze, path);
    check (x + 1, y + 0, dest_x, dest_y, maze, path);
    maze[y][x] = 1;
  }

  path.resize(len);
}


int main() {
  int maze[HEIGHT][WIDTH] = {
      {1,0,1,1,1,1},
      {1,0,1,0,1,1},
      {1,1,1,0,1,1},
      {0,0,0,0,1,0},
      {1,1,1,0,1,1}};

  std::string path;
  check(0, 0, 4, 3, maze, path);
  return 0;
}

Runnable version: https://code.sololearn.com/cYn18c5p7609

回答2:

i finally found you the solution to your question. but honestly it's not a solution that i did develope, some other people (namely: Schröder) had this idea before!

the problem is described by Schröder, but have a look at the german translation speaking of permutating a binary tree.

transform your path and all reachable nodes into a binary tree and permutate it! (but be warned, there may be many many solutions)

as you can see these are all solutions for crossing a 4x4 square (missing the mirrored part, but thats alas).

来源：https://stackoverflow.com/questions/37151831/find-all-possible-paths-through-a-maze

标签

maze