Program to check given graph is a set of trees or not in Python

Python Server Side Programming Programming

Suppose we have a graph, represented as a list of edges. We have to check whether the graph is a collection of trees (forest) or not.

So, if the input is like

then the output will be True

To solve this, we will follow these steps −

Define a function dfs() . This will take node, prev
if node in seen, then
- return False
insert node into seen
for each adjacent node n in e[node], do
- if n is not same as prev, then
  - if dfs(n, node) is false, then
    - return False
return True
From the main method, do the following −
e := an empty map
for each start node u and end node v in edges, do
- insert v at the end of e[u]
- insert u at the end of e[v]
seen := a new set
for each node in e, do
- if node is not seen and dfs(node, -1) is false, then
  - return False
return True

Let us see the following implementation to get better understanding −

Example

Live Demo

from collections import defaultdict
class Solution:
   def solve(self, edges):
      e = defaultdict(list)
      for t,f in edges:
         e[t].append(f)
         e[f].append(t)

      seen = set()

      def dfs(node, prev):
         if node in seen:
            return False
         seen.add(node)
      for adj in e[node]:
         if adj != prev:
            if not dfs(adj, node):
               return False
      return True

   for node in e:
      if node not in seen and not dfs(node, -1):
         return False
   return True

ob = Solution()
edges = [[0, 1],[0, 2],[4, 3]]
print(ob.solve(edges))

Input

[[0, 1],[0, 2],[4, 3]]

Output

True

Arnab Chakraborty

Published on 08-Oct-2020 10:42:17

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