Create largest-component-size-by-common-factor.py

Author: kamyu104

Python/largest-component-size-by-common-factor.py

@@ -0,0 +1,59 @@
+# Time:  O(f * n), f is the total number of unique prime factors
+# Soace: O(f * n)
+
+import collections
+
+
+class UnionFind(object):
+    def __init__(self, n):
+        self.set = range(n)
+        self.size = [1]*n
+
+    def find_set(self, x):
+        if self.set[x] != x:
+            self.set[x] = self.find_set(self.set[x])  # path compression.
+        return self.set[x]
+
+    def union_set(self, x, y):
+        x_root, y_root = map(self.find_set, (x, y))
+        if x_root == y_root:
+            return False
+        self.set[min(x_root, y_root)] = max(x_root, y_root)
+        self.size[max(x_root, y_root)] += self.size[min(x_root, y_root)]
+        return True
+
+
+class Solution(object):
+    def largestComponentSize(self, A):
+        """
+        :type A: List[int]
+        :rtype: int
+        """
+        def primeFactors(i):  # Prime factor decomposition
+            result = []
+            d = 2
+            if i%d == 0:
+                while i%d == 0:
+                    i /= d
+                result.append(d)
+            d = 3
+            while d*d <= i:
+                if i%d == 0:
+                    while i%d == 0:
+                        i /= d
+                    result.append(d)
+                d += 2
+            if i > 2:
+                result.append(i)
+            return result
+        
+        nodesWithCommonFactor = collections.defaultdict(list)
+        for i in xrange(len(A)):
+            for factor in primeFactors(A[i]):
+                nodesWithCommonFactor[factor].append(i)
+
+        union_find = UnionFind(len(A))
+        for _, nodes in nodesWithCommonFactor.iteritems():
+            for i in xrange(1, len(nodes)):
+                union_find.union_set(nodes[0], nodes[i])
+        return max(union_find.size)