From 5e8c2e11b13a2d7a4e66f107fadf1e310375b1ad Mon Sep 17 00:00:00 2001
From: formidablae <81068781+formidablae@users.noreply.github.com>
Date: Mon, 4 Apr 2022 01:45:27 +0200
Subject: [PATCH] Solving (19 of 20 tests passed) Arcade / Graphs / 3 In the
 Pseudoforest / 18 Is Wood Magical

---
 .../18_Is_Wood_Magical /main.py               | 45 +++++++++++++++++++
 1 file changed, 45 insertions(+)
 create mode 100644 Arcade/Graphs/3_In_the_Pseudoforest/18_Is_Wood_Magical /main.py

diff --git a/Arcade/Graphs/3_In_the_Pseudoforest/18_Is_Wood_Magical /main.py b/Arcade/Graphs/3_In_the_Pseudoforest/18_Is_Wood_Magical /main.py
new file mode 100644
index 0000000..d68309d
--- /dev/null
+++ b/Arcade/Graphs/3_In_the_Pseudoforest/18_Is_Wood_Magical /main.py	
@@ -0,0 +1,45 @@
+def colorGraph(n, G, color, pos, c):
+    if color[pos] != -1 and color[pos] != c:
+        return False
+
+    # color this pos as c and all its neighbours and 1-c
+    color[pos] = c
+    ans = True
+    for i in range(0, n):
+        if i in G[pos]:
+            if color[i] == -1:
+                ans &= colorGraph(n, G, color, i, 1-c)
+
+            if color[i] != -1 and color[i] != 1-c:
+                return False
+
+        if not ans:
+            return False
+
+    return True
+
+
+def isBipartite(n, G):
+    color = [-1] * n
+
+    #start is vertex 0
+    pos = 0
+    # two colors 1 and 0
+    return colorGraph(n, G, color, pos, 1)
+
+
+def solution(n, wmap):
+    wmap_new_form = { i: set() for i in range(n) }
+    for arc in wmap:
+        wmap_new_form[arc[0]].add(arc[1])
+        wmap_new_form[arc[1]].add(arc[0])
+    return isBipartite(n, wmap_new_form)
+    
+
+n = 5
+G = [[1, 2], [1, 3], [1, 4], [0, 2], [4, 0]]
+print(solution(n, G))  # True
+
+n = 5
+G = [[1, 2], [1, 3], [1, 4], [0, 2], [4, 0], [1, 0]]
+print(solution(n, G))  # False