CareerCup

Classic application of recursion + backtracking.

My solution assumes that you are given a starting position in the maze, and that getting out of the maze is equivalent to reach a free position in the borders. With that in mind, all you have to do is branch on every direction (left, right, up, down), recursively finding the path until a border position is reached, or until you have tried every possibility and none worked (meaning it is impossible to get out of the maze from that starting position).

Just be careful to keep track of visited positions in a given path search, so that you don't recurse infinitely. Also, as positions are added to the path, we can keep track of the current path in a vector (C++ jargon for growable array), so that we can print it when we reach one of the border positions.

C++ implementation, tested and (apparently) working:

#include <cassert>
#include <iostream>
#include <sstream>
#include <vector>

using namespace std;

bool find_path_aux(const vector<vector<char> > &maze, vector<vector<bool> > &visited,
		   vector<string> &path, int curr_x, int curr_y) {

	if (curr_x < 0 || curr_x >= (int) maze.size() || curr_y < 0 || curr_y >= (int) maze[0].size())
		return true;

	if (visited[curr_x][curr_y] || maze[curr_x][curr_y] == 'X')
		return false;

	assert(maze[curr_x][curr_y] == '_');

	visited[curr_x][curr_y] = true;
	ostringstream oss;
	oss << "( " << curr_x << ", " << curr_y << " )";
	path.push_back(oss.str());

	for (int i = -1; i < 2; i++)
		for (int j = -1; j < 2; j++)
			if ((i == 0) != (j == 0))
				if (find_path_aux(maze, visited, path, curr_x+i, curr_y+j))
					return true;

	path.pop_back();
	visited[curr_x][curr_y] = false;

	return false;
}

bool find_path(const vector<vector<char> > &maze, vector<string> &path, int pos_x, int pos_y) {
	path.clear();
	vector<vector<bool> > visited(maze.size(), vector<bool>(maze[0].size(), false));
	return find_path_aux(maze, visited, path, pos_x, pos_y);
}

int main(void) {
	cout << "Enter maze dimensions N and M for an NxM maze, followed by each entry separated by a blank," << endl;
	cout << "followed by the initial position" << endl;
	cout << "> ";

	unsigned rows, cols;
	while (cin >> rows >> cols) {
		vector<vector<char> > maze(rows, vector<char>(cols));
		for (unsigned i = 0; i < rows; i++)
			for (unsigned j = 0; j < cols; j++)
				cin >> maze[i][j];

		unsigned pos_x, pos_y;
		cin >> pos_x >> pos_y;

		vector<string> path;
		if (find_path(maze, path, pos_x, pos_y)) {
			if (path.size() > 0)
				cout << path[0];
			for (vector<string>::size_type i = 1; i < path.size(); i++)
				     cout << " -> " << path[i];
			     cout << endl;
		} else {
			cout << "Impossible" << endl;
		}

		cout << "> ";
	}

	return 0;
}