Grassfire Algorithm

blue cell: obstacles, black cell = start( or end)

$$\text{distance measure}:~\text{Manhattan distance}=|x_2 - x_1 | + |y_2 - y_1|$$

Grassfire 알고리즘을 써서 최단경로를 찾는 문제는 DFS로도 구현할 수 있으나 비효율적이고(왜 그런지는 쉽게 알 수 있다) BFS로 구현하는 것이 더 적합하다. 

void grassfire(CPoint q, int **map, int w, int h, int **dist) {
    // left-top-right-bottom;
    const int dx[] = {-1,  0, 1, 0};
    const int dy[] = { 0, -1, 0, 1};
    for (int y = 0; y < h; y++) 
        for (int x = 0; x < w; x++) 
            dist[y][x] = INF;  //unvisited cells;

    std::queue<CPoint> Q;
    dist[q.y][q.x] = 0;     //start( or end) position: distance = 0;
    Q.push(q);
    while (!Q.empty()) {
        CPoint p = Q.front(); Q.pop();
        int distance = dist[p.y][p.x];
        // 4-way search;
        for (int i = 0; i < 4; i++) {
            CPoint q = CPoint(p.x + dx[i], p.y + dy[i]);
            if (q.x < 0|| q.y < 0|| q.x >= w|| q.y >= h) continue;
            if (map[q.y][q.x] == 0 && dist[q.y][q.x] == INF) {
                dist[q.y][q.x] = distance + 1;
                Q.push(q);
            }
        }
    }
};
// back tracking;
CPoint back_track(CPoint p, int **dist, int w, in h) {
    // left-top-right-bottom;
    const int dx[] = {-1,  0, 1, 0};
    const int dy[] = { 0, -1, 0, 1};
    int depth = dist[p.y][p.x]; 
    if (--depth < 0) return p;
    for (int i = 0; i < 4; i++) {
        CPoint q = CPoint(p.x + dx[i], p.y + dy[i]);
        if (q.x < 0 || q.y < 0 || q.x >= w || q.y >= h) continue; // out of ROI;
        else if (dist[q.y][q.x] == depth)
            return q;
    }
    return p; // never hit;
}