Create split-the-array-to-make-coprime-products.py

Author: kamyu104

Python/split-the-array-to-make-coprime-products.py

@@ -0,0 +1,45 @@
+# Time:  O(n * sqrt(r)), r = max(nums)
+# Space: O(sqrt(r))
+
+import collections
+
+
+# number theory
+class Solution(object):
+    def findValidSplit(self, nums):
+        """
+        :type nums: List[int]
+        :rtype: int
+        """
+        def factorize(x):
+            result = []
+            d = 2
+            while d*d <= x:
+                e = 0
+                while x%d == 0:
+                    x //= d
+                    e += 1
+                if e:
+                    result.append([d, e])
+                d += 1 if d == 2 else 2
+            if x > 1:
+                result.append([x, 1])
+            return result
+        
+        right = collections.Counter()
+        for x in reversed(nums):
+            for p, c in factorize(x):
+                right[p] += c
+        left = collections.Counter()
+        cnt = 0
+        for i in xrange(len(nums)-1):
+            for p, c in factorize(nums[i]):
+                if not left[p]:
+                    cnt += 1
+                left[p] += c
+                right[p] -= c
+                if not right[p]:
+                    cnt -= 1
+            if not cnt:
+                return i
+        return -1