When you want to search the shortest path for search space like a maze, the breadth-first search is a good solution for you because you have to search the same state so many times with the depth first-search.

The breadth-first search has a weak point. It needs memory that is proportional to a number of state.

This is an example of the breadth-first search:

- Description

You have a maze which size is M * N. The maze consists of path and wall.

You can move 4 direction (up, down, right and left) in one turn.

Solve the shortest path from the start to the goal.

- Constraint

N, M >= 100

- Sample Input

10 10

#S######.#

......#..#

.#.##.##.#

.#........

##.##.####

....#....#

.#######.#

....#.....

.####.###.

....#...G#

- Sample OutputMy solution is like this. You can find it on my github repository.

22

#include#include #include using namespace std; const int INF = 1000000; const int MAX_N = 100; const int MAX_M = 100; typedef pair P; char maze[MAX_N][MAX_M+1]; // maze int n, m; // size of maze int sx, sy; // start position int gx, gy; // goal position //shortest path for each point int d[MAX_N][MAX_M]; //vector for for moving direction int dx[4] = {1, 0, -1, 0}; int dy[4] = {0, 1, 0, -1}; //solve the shortest path from (sx, sy) to (gx, gy) int bfs() { queue q; //initialize every point with INF before search for(int i = 0; i < n; i++) { for (int j = 0; j < m; j++) { d[i][j] = INF; } } q.push(P(sx,sy)); d[sx][sy] = 0; while(q.size()) { P tmp = q.front(); q.pop(); //if you find goal then you finish search if ((tmp.first == gx)&&(tmp.second == gy)){ break; } for(int i = 0; i < 4; i++) { int nx = tmp.first + dx[i]; int ny = tmp.second + dy[i]; if ((0 <= nx) && (nx < n) && (0 <= ny) && (ny < m) && (maze[nx][ny] != '#') && (d[nx][ny] == INF)) { // if d[nx][ny] == INF then it is a position that // you have already visited. q.push(P(nx,ny)); d[nx][ny] = d[tmp.first][tmp.second] + 1; } } } return d[gx][gy]; } void solve() { int res = bfs(); cout << res << endl; } int main(int argc, char* argv[]) { if (argc != 2) { cout << "./a.out "; return 1; } ifstream ifs(argv[1]); if (!ifs) { cout << "can't open file:" << argv[1] << endl; return 1; } string buf; getline(ifs, buf); sscanf(buf.c_str(), "%d %d", &n, &m); for(int i = 0; i < n; i++) { getline(ifs, buf); for (int j = 0; j < m; j++) { maze[i][j] = buf[j]; if (maze[i][j] == 'S') { sx = i; sy = j; } if (maze[i][j] == 'G') { gx = i; gy = j; } } } solve(); return 0; }