How do you solve Super Ugly Number on LeetCode?

Super Ugly Number (LeetCode #313) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log k) time complexity and O(n) space complexity. Key insight: Using a min-heap allows us to efficiently find the next super ugly number without generating all combinations.

What is the brute force solution for Super Ugly Number?

The brute force approach for Super Ugly Number is Brute Force, with O(n²) time complexity and O(n) space complexity. We can generate super ugly numbers by multiplying the previous ugly numbers with each prime in the list. This approach is straightforward but inefficient, as we may generate many unnecessary numbers. The optimal Optimal Solution approach improves this to O(n log k).

What algorithm or data structure is used to solve Super Ugly Number?

Super Ugly Number uses the following concepts: Array, Math, Dynamic Programming. The recommended patterns to study are: Heap (Min-Heap for efficient extraction of minimum values), Dynamic Programming (for understanding how to build up solutions from smaller subproblems).

What are the interview tips for Super Ugly Number?

Always explain your thought process clearly, especially when transitioning from brute force to optimal solutions. Discuss time and space complexities for both approaches to show your understanding. Practice explaining how data structures like heaps work, as they are commonly used in optimization problems.

What are common mistakes when solving Super Ugly Number?

Not using a set to track seen numbers, leading to duplicates in the heap. Forgetting to handle the case of large numbers, which can lead to overflow if not careful.

#313

Super Ugly Number

Medium

ArrayMathDynamic ProgrammingHeap (Min-Heap for efficient extraction of minimum values)Dynamic Programming (for understanding how to build up solutions from smaller subproblems)

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log k)
Space	O(n)	O(n)

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Intuition

Time O(n log k)Space O(n)

Instead of generating all super ugly numbers, we can use a min-heap to efficiently find the next super ugly number. This allows us to keep track of the smallest number generated from the primes without generating all combinations.

⚙️

Algorithm

4 steps

1Step 1: Initialize a min-heap and add the first super ugly number (1).
2Step 2: Use a set to track the numbers we've added to the heap to avoid duplicates.
3Step 3: Extract the smallest number from the heap, and for each prime, multiply it with the smallest number and add it back to the heap if it hasn't been added before.
4Step 4: Repeat until we extract the nth super ugly number.

solution.py15 lines

1# Full working Python code
2import heapq
3class Solution:
4    def nthSuperUglyNumber(self, n: int, primes: List[int]) -> int:
5        heap = [1]
6        seen = {1}
7        ugly = 0
8        for _ in range(n):
9            ugly = heapq.heappop(heap)
10            for prime in primes:
11                next_ugly = ugly * prime
12                if next_ugly not in seen:
13                    seen.add(next_ugly)
14                    heapq.heappush(heap, next_ugly)
15        return ugly

ℹ

Complexity note: The time complexity is O(n log k) where k is the number of primes. Each time we extract the minimum from the heap, it takes log k time, and we do this n times.

1Using a min-heap allows us to efficiently find the next super ugly number without generating all combinations.
2Tracking seen numbers prevents duplicates and ensures we only add unique products to the heap.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.