多口味LeetCode --- 63. 不同路径 II

不念不忘少年蓝@ 2023-02-20 15:55 19阅读 0赞

**题目描述：**

一个机器人位于一个 m x n 网格的左上角 (起始点在下图中标记为“Start”)  
机器人每次只能向下或者向右移动一步。机器人试图达到网格的右下角(在下图中标记为“Finish”)。

现在考虑网格中有障碍物。那么从左上角到右下角将会有多少条不同的路径？

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzI4MzM5Nw_size_16_color_FFFFFF_t_70_pic_center]

网格中的障碍物和空位置分别用 1 和 0 来表示。

说明：m 和 n 的值均不超过 100。

**示例 1:**

输入:
    [
      [0,0,0],
      [0,1,0],
      [0,0,0]
    ]
    输出: 2
    解释:
    3x3 网格的正中间有一个障碍物。
    从左上角到右下角一共有 2 条不同的路径：
    1. 向右 -> 向右 -> 向下 -> 向下
    2. 向下 -> 向下 -> 向右 -> 向右

--------------------

**解题思路:** 动态规划

终点  f \[ i \] \[ j \] f\[i\]\[j\] f\[i\]\[j\] 般可从两个方向到达，即最后一步向右走  f \[ i \] \[ j − 1 \] f\[i\]\[j-1\] f\[i\]\[j−1\]，最后一步向左走，即  f \[ i − 1 \] \[ j \] f\[i-1\]\[j\] f\[i−1\]\[j\]

--------------------

**代码：**

C++写法：

class Solution {
        
    public:
        int uniquePathsWithObstacles(vector<vector<int>>& obstacleGrid) {
        
            int  n=obstacleGrid.size(), m=obstacleGrid[0].size();
            vector<vector<long long>> f(n, vector<long long>(m));
            for(int i=0;i<n;i++)
                for(int j=0;j<m;j++)
                {
        
                    if (obstacleGrid[i][j] != 0)
                        continue;
                    if (i==0 && j==0)  // 等价写法 if (!i && !j)
                        f[i][j] = 1;
                    if (i>0)
                        f[i][j] += f[i-1][j];
                    if (j>0)
                        f[i][j] += f[i][j-1];
                }
            return f[n-1][m-1];
        }
    };

--------------------

python写法1：

import numpy as np
    class Solution(object):
        def uniquePathsWithObstacles(self, obstacleGrid):
            
            n , m = len(obstacleGrid), len(obstacleGrid[0])
            f = np.zeros((n, m), dtype = int)
            for i in range(n):
                for j in range(m):
                    if obstacleGrid[i][j] != 0:
                        continue
                    if i == 0 and j == 0:
                        f[i][j] = 1
                    if i > 0:
                        f[i][j] += f[i-1][j]
                    if j > 0:
                        f[i][j] += f[i][j-1]
            return f[n-1][m-1]

--------------------

python写法2：

class Solution(object):
        def uniquePathsWithObstacles(self, obstacleGrid):
            m = len(obstacleGrid)
            n = len(obstacleGrid[0])
    
            if obstacleGrid[0][0] == 1:
                return 0
    
            obstacleGrid[0][0] = 1
            
            for i in range(1,m):
                obstacleGrid[i][0] = int(obstacleGrid[i][0] == 0 and obstacleGrid[i-1][0] == 1)  # 若当前位置为0，前上一行为1，则走不通，需要将当前位置变为1
    
            for j in range(1,n):
                obstacleGrid[0][j] = int(obstacleGrid[0][j] == 0 and obstacleGrid[0][j-1] == 1)
    
            for i in range(1, m):
                for j in range(1, n):
                    if obstacleGrid[i][j] == 0:
                        obstacleGrid[i][j] = obstacleGrid[i-1][j] + obstacleGrid[i][j-1]
                    else:
                        obstacleGrid[i][j] = 0
    
            return obstacleGrid[m-1][n-1]

--------------------

**参考链接:**

[https://www.bilibili.com/video/BV15441117yb?from=search&seid=7069180317390303584][https_www.bilibili.com_video_BV15441117yb_from_search_seid_7069180317390303584]

--------------------

**题目来源：**

[https://leetcode-cn.com/problems/unique-paths-ii][https_leetcode-cn.com_problems_unique-paths-ii]

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzI4MzM5Nw_size_16_color_FFFFFF_t_70_pic_center]: https://img-blog.csdnimg.cn/20200628084111718.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzI4MzM5Nw==,size_16,color_FFFFFF,t_70#pic_center
[https_www.bilibili.com_video_BV15441117yb_from_search_seid_7069180317390303584]: https://www.bilibili.com/video/BV15441117yb?from=search&seid=7069180317390303584
[https_leetcode-cn.com_problems_unique-paths-ii]: https://leetcode-cn.com/problems/unique-paths-ii