Super Ugly Number问题及解法

问题描述：

Write a program to find the nth super ugly number.

Super ugly numbers are positive numbers whose all prime factors are in the given prime list primes of size k. For example, [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] of size 4.

Note:
(1) 1 is a super ugly number for any given primes.
(2) The given numbers in primes are in ascending order.
(3) 0 < k ≤ 100, 0 < n ≤ 106, 0 < primes[i] < 1000.
(4) The nth super ugly number is guaranteed to fit in a 32-bit signed integer.

问题分析：

此类问题是一类朴素数学问题，我们可以采取找规律的方法求解。

给定一个素数数组，求其迭代相乘后第n个最小的数是多少，这里关键是primes数组每次迭代时每个元素应该和ugly数组中哪一个元素相乘，这里采用了一个索引记录数组idx，记录下一次primes每个元素应该和ugly那个元素相乘，依次即可求得答案。

过程详见代码：

class Solution {public:    int nthSuperUglyNumber(int n, vector<int>& primes) {        vector<int> idx(primes.size(), 0),res(n,INT_MAX);res[0] = 1;for (int i = 1; i < n; i++){for (int j = 0; j < primes.size(); j++){res[i] = min(res[i], primes[j] * res[idx[j]]);}for (int j = 0; j < primes.size();j++){while (primes[j] * res[idx[j]] <= res[i]) idx[j]++;}}return res[n - 1];    }};