lintcode 787. The Maze 、788. The Maze II 、

787. The Maze

https://www.cnblogs.com/grandyang/p/6381458.html

与number of island不一样，递归的函数返回值是bool，不是void。

maze = -1用来表示已经访问的节点。

dp用来记录每个位置的是否能访问，如果dp != -1，就表示这个地方已经访问过了，可以避免多余的访问。

一直滑动用while循环来做，这里并没有没移动一次就增加一个访问。

int x = i,y = j必须这样写，因为之后的4种迭代都是从i、j这个位置出发，x、y在每一次迭代过程中已经发生了变化。

vector的初始化用{}，如果是vector<vector<int>>，初始化用{{},{},{}}

class Solution {
public:
    /**
     * @param maze: the maze
     * @param start: the start
     * @param destination: the destination
     * @return: whether the ball could stop at the destination
     */
    bool hasPath(vector<vector<int>> &maze, vector<int> &start, vector<int> &destination) {
        // write your code here
        int m = maze.size();
        if(m <= 0)
            return false;
        int n = maze[0].size();
        if(n <= 0)
            return false;
        vector<vector<int>> dp(m,vector<int>(n,-1));
        return hasPath(maze,dp,start[0],start[1],destination[0],destination[1]);
    }
    bool hasPath(vector<vector<int>>& maze,vector<vector<int>>& dp,int i,int j,int di,int dj){
        if(i == di && j == dj)
            return true;
        if(dp[i][j] != -1)
            return dp[i][j];
        maze[i][j] = -1;
        int m = maze.size(),n = maze[0].size();
        bool res = false;
        for(auto dir : dirs){
            int x = i,y = j;
            while(x >= 0 && x < m && y >= 0 && y < n && maze[x][y] != 1){
                x += dir[0];
                y += dir[1];
            }
            x -= dir[0];
            y -= dir[1];
            if(maze[x][y] != -1)
                res |= hasPath(maze,dp,x,y,di,dj);
        }
        return res;
    }
    vector<vector<int>> dirs{{0,-1},{1,0},{0,1},{-1,0}};
};

自己写了一遍：

因为一直移动，所以需要一直进行dir的移动计算，直到不满足条件。

注意，这里

maze[new_x][new_y] != 1

而不是写的==0，对于-1的位置，也就是已经遍历过的点，你还是可以继续经过这里去其他地方。这个-1更多的是表示从这个点出发已经访问过了。

class Solution {
public:
    /**
     * @param maze: the maze
     * @param start: the start
     * @param destination: the destination
     * @return: whether the ball could stop at the destination
     */
    bool hasPath(vector<vector<int>> &maze, vector<int> &start, vector<int> &destination) {
        // write your code here
        if(maze.empty())
            return false;
        if(maze[0].empty())
            return false;
        if(start.empty() || destination.empty())
            return false;
        return hasPath(maze,start[0],start[1],destination[0],destination[1]);
    }
    bool hasPath(vector<vector<int>>& maze,int x,int y,int destination_x,int destination_y){
        if(x == destination_x && y == destination_y)
            return true;
        maze[x][y] = -1;
        bool flag = false;
        for(int i = 0;i < dirs.size();i++){
            int new_x = x;
            int new_y = y;
            while(new_x >= 0 && new_x < maze.size() && new_y >= 0 && new_y < maze[0].size() && maze[new_x][new_y] != 1){
                new_x += dirs[i][0];
                new_y += dirs[i][1];
            }
            new_x -= dirs[i][0];
            new_y -= dirs[i][1];
            if(maze[new_x][new_y] != -1)
                flag |= hasPath(maze,new_x,new_y,destination_x,destination_y);
        }
        return flag;
    }
    vector<vector<int>> dirs{{-1,0},{1,0},{0,-1},{0,1}};
};

788. The Maze II

思路：用一个矩阵记录到每个位置的最短距离，初始化为INT_MAX，如果终点到最后仍然为INT_MAX，则表明不可达

错误解法一：

这个解法使用了visited数组，表示已经被访问过，这容易造成有些地方不可达。如果从另一个方向到当前位置

class Solution {
public:
    /**
     * @param maze: the maze
     * @param start: the start
     * @param destination: the destination
     * @return: the shortest distance for the ball to stop at the destination
     */
    int shortestDistance(vector<vector<int>> &maze, vector<int> &start, vector<int> &destination) {
        // write your code here
        int m = maze.size();
        if(m <= 0)
            return -1;
        int n = maze[0].size();
        if(n <= 0)
            return -1;
        if(maze[start[0]][start[1]] == 1 || maze[destination[0]][destination[1]] == 1)
            return -1;
        vector<vector<int>> distance(m,vector<int>(n,INT_MAX));
        vector<vector<bool>> visited(m,vector<bool>(n,false));
        queue<pair<int,int>> q;
        q.push(make_pair(start[0],start[1]));
        distance[start[0]][start[1]] = 0;
        while(!q.empty()){
            int x = q.front().first;
            int y = q.front().second;
            q.pop();
            visited[x][y] = true;
            for(auto dir : dirs){
                int x_new = x + dir[0];
                int y_new = y + dir[1];
                int des = distance[x][y];
                while(x_new >= 0 && x_new < m && y_new >= 0 && y_new < n && !visited[x_new][y_new] && maze[x_new][y_new] == 0){
                    x_new += dir[0];
                    y_new += dir[1];
                    des++;
                }
                x_new -= dir[0];
                y_new -= dir[1];
                if(des < distance[x_new][y_new]){
                    distance[x_new][y_new] = des;
                    if(x_new != destination[0] || y_new != destination[1])
                        q.push(make_pair(x_new,y_new));
                }
            }
        }
        return distance[destination[0]][destination[1]] == INT_MAX ? -1 : distance[destination[0]][destination[1]];
    }
    vector<vector<int>> dirs{{-1,0},{0,-1},{1,0},{0,1}};
};

错误解法二：

class Solution {
public:
    /**
     * @param maze: the maze
     * @param start: the start
     * @param destination: the destination
     * @return: the shortest distance for the ball to stop at the destination
     */
    int shortestDistance(vector<vector<int>> &maze, vector<int> &start, vector<int> &destination) {
        // write your code here
        int m = maze.size();
        if(m <= 0)
            return -1;
        int n = maze[0].size();
        if(n <= 0)
            return -1;
        if(maze[start[0]][start[1]] == 1 || maze[destination[0]][destination[1]] == 1)
            return -1;
        vector<vector<int>> distance(m,vector<int>(n,INT_MAX));
        queue<pair<int,int>> q;
        q.push(make_pair(start[0],start[1]));
        distance[start[0]][start[1]] = 0;
        while(!q.empty()){
            int x = q.front().first;
            int y = q.front().second;
            q.pop();
            int des = distance[x][y];
            for(auto dir : dirs){
                int x_new = x + dir[0];
                int y_new = y + dir[1];
                while(x_new >= 0 && x_new < m && y_new >= 0 && y_new < n && maze[x_new][y_new] == 0){
                    x_new += dir[0];
                    y_new += dir[1];
                    des++;
                }
                x_new -= dir[0];
                y_new -= dir[1];
                if(des < distance[x_new][y_new]){
                    distance[x_new][y_new] = des;
                    if(x_new != destination[0] || y_new != destination[1])
                        q.push(make_pair(x_new,y_new));
                }
            }
        }
        return distance[destination[0]][destination[1]] == INT_MAX ? -1 : distance[destination[0]][destination[1]];
    }
    vector<vector<int>> dirs{{-1,0},{0,-1},{1,0},{0,1}};
};

正确解法：

class Solution {
public:
    /**
     * @param maze: the maze
     * @param start: the start
     * @param destination: the destination
     * @return: the shortest distance for the ball to stop at the destination
     */
    int shortestDistance(vector<vector<int>> &maze, vector<int> &start, vector<int> &destination) {
        // write your code here
        int m = maze.size();
        if(m <= 0)
            return -1;
        int n = maze[0].size();
        if(n <= 0)
            return -1;
        if(maze[start[0]][start[1]] == 1 || maze[destination[0]][destination[1]] == 1)
            return -1;
        vector<vector<int>> distance(m,vector<int>(n,INT_MAX));
        queue<pair<int,int>> q;
        q.push(make_pair(start[0],start[1]));
        distance[start[0]][start[1]] = 0;
        while(!q.empty()){
            int x = q.front().first;
            int y = q.front().second;
            q.pop();
            for(auto dir : dirs){
                int x_new = x + dir[0];
                int y_new = y + dir[1];
                int des = distance[x][y];
                while(x_new >= 0 && x_new < m && y_new >= 0 && y_new < n && maze[x_new][y_new] == 0){
                    x_new += dir[0];
                    y_new += dir[1];
                    des++;
                }
                x_new -= dir[0];
                y_new -= dir[1];
                if(des < distance[x_new][y_new]){
                    distance[x_new][y_new] = des;
                    if(x_new != destination[0] || y_new != destination[1])
                        q.push(make_pair(x_new,y_new));
                }
            }
        }
        return distance[destination[0]][destination[1]] == INT_MAX ? -1 : distance[destination[0]][destination[1]];
    }
    vector<vector<int>> dirs{{-1,0},{0,-1},{1,0},{0,1}};
};