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