Binary Search example

Author: rachitiitr

LeetCode/878.nth-magical-number.py

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+import math
+
+def countMultiples(x, a, b):
+    '''returns # of multiples of a or b in range [1, x]'''
+    lcm = a * b // math.gcd(a, b)
+    return x//a + x//b - x//lcm # x/2 + x/3 - x/6
+    
+class Solution:
+    def nthMagicalNumber(self, n: int, a: int, b: int) -> int:
+        # a = 2, b = 3 in our case
+        lo, hi = 1, min(a, b) * n # hi = 2*n remember?
+        while lo < hi:
+            mid = (lo + hi) >> 1
+            if countMultiples(mid, a, b) < n:
+                lo = mid + 1
+            else:
+                hi = mid
+                
+        return hi % (10**9 + 7)
+