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[Leetcode]313. Super Ugly Number(C++)

题目描述

题目链接:313. Super Ugly Number

A super ugly number is a positive integer whose prime factors are in the array primes.

Given an integer n and an array of integers primes, return the nth super ugly number.

The nth super ugly number is guaranteed to fit in a 32-bit signed integer.

例子

例子 1

Input: n = 12, primes = [2,7,13,19] Output: 32 Explanation: [1,2,4,7,8,13,14,16,19,26,28,32] is the sequence of the first 12 super ugly numbers given primes = [2,7,13,19].

例子 2

Input: n = 1, primes = [2,3,5] Output: 1 Explanation:1 has no prime factors, therefore all of its prime factors are in the array primes = [2,3,5].

Constraints

  • 1 <= n <= 10^6
  • 1 <= primes.length <= 100
  • 2 <= primes[i] <= 1000
  • primes[i] is guaranteed to be a prime number.
  • `All the values of primes are unique and sorted in ascending order.

解题思路

这一题有一个比较简单的思路(非最优解),创建一个小顶堆(优先队列)和哈希表,哈希表存储小顶堆中存储过的元素,首先将所有质数和 1 压入小顶堆中(以及哈希表),每次弹出一个最小值,并和所有质数相乘,保证为超级丑数。如果该数没出现过则压入优先队列中,由于每次弹出的都是超级丑数(并且大小一定是递增的),因此第 n 个弹出的数即为结果。代码如下:

#include <limits.h>
#include <queue>
#include <unordered_set>
#include <vector>

class Solution {
public:
    int nthSuperUglyNumber(int n, std::vector<int>& primes) {
        if (n == 1) {
            return 1;  // the first super ugly number
        }

        int count = 0;
        std::priority_queue<int, std::vector<int>, std::greater<int>> pq;
        std::unordered_set<int> hset;

        pq.push(1);
        hset.insert(1);
        for (auto prime : primes) {
            pq.push(prime);
            hset.insert(prime);
        }

        int num = 1;
        while (count < n) {
            num = pq.top();
            pq.pop();
            for (auto prime : primes) {
                long new_ugly_num = num * prime;
                if (new_ugly_num <= INT_MAX && hset.count(new_ugly_num) == 0) {
                    hset.insert(new_ugly_num);
                    pq.push(new_ugly_num);
                }
            }
            count++;
        }

        return num;
    }
};
  • 时间复杂度: O(nklog(n))
  • 空间复杂度: O(n)

GitHub 代码同步地址: 313.SuperUglyNumber.cpp

其他题目: GitHub: Leetcode-C++-Solution 博客: Leetcode-Solutions

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