Ugly Number III — LeetCode 1201 Python Solution

The problem

An ugly number is a positive integer that is divisible by a, b, or c. Given four integers n, a, b, and c, return the nth ugly number.

Example

Input

n = 3, a = 2, b = 3, c = 5

Output

4

Explanation

The ugly numbers are 2, 3, 4, 5, 6, 8, 9, 10... The 3rd is 4.

Python solution

class Solution:
    def nthUglyNumber(self, n: int, a: int, b: int, c: int) -> int:
        ab = lcm(a, b)
        bc = lcm(b, c)
        ac = lcm(a, c)
        abc = lcm(a, b, c)
        l, r = 1, 2 * 10**9
        while l < r:
            mid = (l + r) >> 1
            if (
                mid // a
                + mid // b
                + mid // c
                - mid // ab
                - mid // bc
                - mid // ac
                + mid // abc
                >= n
            ):
                r = mid
            else:
                l = mid + 1
        return l

Complexity

Pattern: Monotonic Stack

Answer "what is the next greater element" for every position in one pass. LeetCode 1201. Ugly Number III 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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