Nth Magical Number — LeetCode 878 Python Solution

The problem

A positive integer is magical if it is divisible by either a or b. Given the three integers n, a, and b, return the nth magical number.

Example

Input

n = 1, a = 2, b = 3

Output

2

Python solution

class Solution:
    def nthMagicalNumber(self, n: int, a: int, b: int) -> int:
        mod = 10**9 + 7
        c = lcm(a, b)
        r = (a + b) * n
        return bisect_left(range(r), x=n, key=lambda x: x // a + x // b - x // c) % mod

Complexity

Pattern: Monotonic Stack

Answer "what is the next greater element" for every position in one pass. LeetCode 878. Nth Magical Number is filed here because the reference solution below belongs to the algorithm family this hub collects, even though its LeetCode tags point elsewhere.

The monotonic stack guide has the Python template for the pattern and the 225 LeetCode problems that use it.

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