Create gcd-sort-of-an-array.py

Author: kamyu104

Python/gcd-sort-of-an-array.py

@@ -0,0 +1,56 @@
+# Time:  O(n * α(n) + m * log(logm)) ~= O(n + m), m is the max of nums
+# Space: O(n)
+
+import itertools
+
+
+class UnionFind(object):  # Time: O(n * α(n)), Space: O(n)
+    def __init__(self, n):
+        self.set = range(n)
+        self.rank = [0]*n
+
+    def find_set(self, x):
+        stk = []
+        while self.set[x] != x:  # path compression
+            stk.append(x)
+            x = self.set[x]
+        while stk:
+            self.set[stk.pop()] = x
+        return x
+
+    def union_set(self, x, y):
+        x_root, y_root = map(self.find_set, (x, y))
+        if x_root == y_root:
+            return False
+        if self.rank[x_root] < self.rank[y_root]:  # union by rank
+            self.set[x_root] = y_root
+        elif self.rank[x_root] > self.rank[y_root]:
+            self.set[y_root] = x_root
+        else:
+            self.set[y_root] = x_root
+            self.rank[x_root] += 1
+        return True
+
+
+class Solution(object):
+    def gcdSort(self, nums):
+        """
+        :type nums: List[int]
+        :rtype: bool
+        """
+        def modified_sieve_of_eratosthenes(n, lookup, uf):  # Time: O(n * log(logn)), Space: O(n)
+            if n < 2:
+                return
+            is_prime = [True]*(n+1)
+            for i in xrange(2, len(is_prime)):
+                if not is_prime[i]:
+                    continue
+                for j in xrange(i+i, len(is_prime), i):
+                    is_prime[j] = False
+                    if j in lookup:  # modified
+                        uf.union_set(i-1, j-1)
+
+        max_num = max(nums)
+        uf = UnionFind(max_num)
+        modified_sieve_of_eratosthenes(max_num, set(nums), uf)
+        return all(uf.find_set(a-1) == uf.find_set(b-1) for a, b in itertools.izip(nums, sorted(nums)))