mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-27 15:01:08 +00:00
71 lines
1.4 KiB
Python
71 lines
1.4 KiB
Python
"""
|
|
You are given a tree(a simple connected graph with no cycles). The tree has N
|
|
nodes numbered from 1 to N and is rooted at node 1.
|
|
|
|
Find the maximum number of edges you can remove from the tree to get a forest
|
|
such that each connected component of the forest contains an even number of
|
|
nodes.
|
|
|
|
Constraints
|
|
2 <= 2 <= 100
|
|
|
|
Note: The tree input will be such that it can always be decomposed into
|
|
components containing an even number of nodes.
|
|
"""
|
|
from __future__ import print_function
|
|
# pylint: disable=invalid-name
|
|
from collections import defaultdict
|
|
|
|
|
|
def dfs(start):
|
|
"""DFS traversal"""
|
|
# pylint: disable=redefined-outer-name
|
|
ret = 1
|
|
visited[start] = True
|
|
for v in tree.get(start):
|
|
if v not in visited:
|
|
ret += dfs(v)
|
|
if ret % 2 == 0:
|
|
cuts.append(start)
|
|
return ret
|
|
|
|
|
|
def even_tree():
|
|
"""
|
|
2 1
|
|
3 1
|
|
4 3
|
|
5 2
|
|
6 1
|
|
7 2
|
|
8 6
|
|
9 8
|
|
10 8
|
|
On removing edges (1,3) and (1,6), we can get the desired result 2.
|
|
"""
|
|
dfs(1)
|
|
|
|
|
|
if __name__ == '__main__':
|
|
n, m = 10, 9
|
|
tree = defaultdict(list)
|
|
visited = {}
|
|
cuts = []
|
|
count = 0
|
|
edges = [
|
|
(2, 1),
|
|
(3, 1),
|
|
(4, 3),
|
|
(5, 2),
|
|
(6, 1),
|
|
(7, 2),
|
|
(8, 6),
|
|
(9, 8),
|
|
(10, 8),
|
|
]
|
|
for u, v in edges:
|
|
tree[u].append(v)
|
|
tree[v].append(u)
|
|
even_tree()
|
|
print(len(cuts) - 1)
|