LeetCode Problems #797

2018年9月30日

#797. All Paths From Source to Target

问题描述：

Given a directed, acyclic graph of N nodes.  Find all possible paths from node 0 to node N-1, and return them in any order.

The graph is given as follows:  the nodes are 0, 1, ..., graph.length - 1.  graph[i] is a list of all nodes j for which the edge (i, j) exists.

样例:

Example:
Input: [[1,2], [3], [3], []] 
Output: [[0,1,3],[0,2,3]] 
Explanation: The graph looks like this:
0--->1
|    |
v    v
2--->3
There are two paths: 0 -> 1 -> 3 and 0 -> 2 -> 3.

Note:

• The number of nodes in the graph will be in the range [2, 15].
• You can print different paths in any order, but you should keep the order of nodes inside one path.

问题分析：

本题难度为Medium！已给出的函数定义为：

class Solution:
    def allPathsSourceTarget(self, graph):
        """
        :type graph: List[List[int]]
        :rtype: List[List[int]]
        """

其中graph为一个二维数组，返回值为一个存储列表单元的列表；

本题是找出从源结点0到目标结点N-1的所有路径。

 

算法如下：

从源结点0出发，记录到path列表中，即path=[0]

调用递归函数dfs，cur=0，des=N-1，path=[0]

        若cur==des，则将path添加到result中

        否则若cur有出度，对于每一个出度结点each：

                复制路径cp_path=path，将每一个出度结点添加到复制的路径中

                 调用递归函数dfs，cur=each，des=N-1，cp_path

result即为存储的所有路径

 

代码实现：

#coding=utf-8
class Solution:
    def allPathsSourceTarget(self, graph):
        """
        :type graph: List[List[int]]
        :rtype: List[List[int]]
        """
        def dfs(cur, des, path):
            if cur==des: #到达目标点
                result.append(path)
            elif len(graph[cur])!=0: #未到达目标点，且cur点出度不为0，进行递归
                for each in graph[cur]: #对每个出度进行递归
                    cp_path=path.copy() #复制临时路径
                    cp_path.append(each)
                    dfs(each,des,cp_path)
        result=[]
        dfs(0,len(graph)-1,[0])
        return result

此算法可以在Leetcode上Accrpted，但只能处理有向无环图dag；若遇到有向有环图，则会陷入死循环导致：RecursionError: maximum recursion depth exceeded in comparison。

 

改进算法代码如下：

添加一个visited列表记录访问过的结点，从而防止递归陷入死循环。

#coding=utf-8
class Solution:
    def allPathsSourceTarget(self, graph):
        """
        :type graph: List[List[int]]
        :rtype: List[List[int]]
        """
        def dfs(cur, des, path, visited):
            if cur==des: #到达目标点
                result.append(path)
            elif len(graph[cur])!=0: #未到达目标点，且cur点出度不为0，进行递归
                for each in graph[cur]: #对每个出度进行递归
                    if visited[each]==0:
                        cp_path=path.copy() #复制临时路径
                        cp_path.append(each) #添加结点
                        cp_visited=visited.copy() #复制临时访问列表
                        cp_visited[each]=1 #标记结点
                        dfs(each,des,cp_path,cp_visited)
        result=[]
        visited=[0 for i in range(len(graph))]
        visited[0]=1
        dfs(0,len(graph)-1,[0],visited)
        return result