Merge pull request TheAlgorithms#204 from erdenezul/even_tree_problem

add even tree problem

Author: harshildarji

data_structures/Graph/even_tree.py

@@ -0,0 +1,69 @@
+"""
+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.
+"""
+# 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