# Program to check we can visit any city from any city or not in Python

Suppose we have n cities represented as a number in range [0, n) and we also have a list of one-way roads that connects one city to another. We have to check whether we can reach any city from any city.

So, if the input is like n = 3, roads = [[0, 1],[0, 2],[1,0],[1,2],[2,0],[2,1]], then the output will be True, as You can go 0 to 1 and 1 to 0

To solve this, we will follow these steps−

• Define a function dfs() . This will take i, visited, g

• mark i as visited

• for each j in g[i], do

• if j is not visited, then

• dfs(j, visited, g)

• Define a function travel() . This will take g

• visited := a new set

• dfs(0, visited, g)

• return true when size of visited is same as n

• From the main method, do the following−

• graph := an empty map

• rev_graph := an empty map

• for each source u, and destination v in roads, do

• insert v at the end of graph[u]

• insert u at the end of rev_graph[v]

• return true when travel(graph) and travel(rev_graph) both are true

Let us see the following implementation to get better understanding −

## Example

Live Demo

class Solution:
from collections import defaultdict
graph = defaultdict(list)
rev_graph = defaultdict(list)
graph[u].append(v)
rev_graph[v].append(u)
def dfs(i, visited, g):
for j in g[i]:
if j not in visited:
dfs(j, visited,g)
def travel(g):
visited = set()
dfs(0, visited, g)
return len(visited)==n
return travel(graph) and travel(rev_graph)
ob = Solution()
n = 3
print(ob.solve(n, roads))

## Input

3, [[0, 1],[0, 2],[1,0],[1,2],[2,0],[2,1]]

## Output

True

Updated on: 05-Oct-2020

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