Create ugly-number-iii.py

Author: kamyu104

Python/ugly-number-iii.py

@@ -0,0 +1,34 @@
+# Time:  O(logn)
+# Space: O(1)
+
+class Solution(object):
+    def nthUglyNumber(self, n, a, b, c):
+        """
+        :type n: int
+        :type a: int
+        :type b: int
+        :type c: int
+        :rtype: int
+        """
+        def gcd(a, b):
+            while b:
+                a, b = b, a % b
+            return a
+
+        def lcm(x, y):
+            return x//gcd(x, y)*y
+
+        def count(x, a, b, c, lcm_a_b, lcm_b_c, lcm_c_a, lcm_a_b_c):
+            return x//a + x//b + x//c - (x//lcm_a_b + x//lcm_b_c + x//lcm_c_a) + x//lcm_a_b_c
+
+        lcm_a_b, lcm_b_c, lcm_c_a = lcm(a, b), lcm(b, c), lcm(c, a)
+        lcm_a_b_c = lcm(lcm_a_b, lcm_b_c)
+
+        left, right = 1, 2*10**9
+        while left <= right:
+            mid = left + (right-left)//2
+            if count(mid, a, b, c, lcm_a_b, lcm_b_c, lcm_c_a, lcm_a_b_c) >= n:
+                right = mid-1
+            else:
+                left = mid+1
+        return left