USACO: Humble Numbers

【USACO3.1.3】Humble Numbers丑数(蒟蒻解析) (注:属于蒟蒻的分析,不存在高端代码操作,只有简单的实现过程) 【USACO3.1.3】Humble Numbers丑数 时间限制 :10000MS空间限制 :655360KB; 问题描述 对于一给定的素数集合 S = {p1, p2, ..., pK},考虑一个正整数集合,该集合中任一元素的质因数全部属于S。这个正整数集合包括,p1、p1p2、p1p1、p1p2p3...(... 阅读详情
Humble Numbers

For a given set of K prime numbers S = {p1, p2, ..., pK}, consider the set of all numbers whose prime factors are a subset of S. This set contains, for example, p1, p1p2, p1p1, and p1p2p3 (among others). This is the set of `humble numbers' for the input set S. Note: The number 1 is explicitly declared not to be a humble number.

Your job is to find the Nth humble number for a given set S. Long integers (signed 32-bit) will be adequate for all solutions.

PROGRAM NAME: humble

INPUT FORMAT

Line 1: Two space separated integers: K and N, 1 <= K <=100 and 1 <= N <= 100,000.
Line 2: K space separated positive integers that comprise the set S.

SAMPLE INPUT (file humble.in)

4 19
2 3 5 7

OUTPUT FORMAT

The Nth humble number from set S printed alone on a line.

SAMPLE OUTPUT (file humble.out)

27

                          

思路:

一个新的humble number可以从已得到的序列得到:H(n+1) = min{ H(i) * prime(j) > H(n), 0 <= i <= n, 0 <= j < k }

显然,对于prime[x],humb中有一个对应的起始位置nxpos[x](上一次找到这里发现H(nxpos[x]) * prime[x] > H(n + 1)),那么下次可以接着往下找,而不是从头开始找

 
 

常见消息队列:ActiveMQ、RabbitMQ、RocketMQ、Kafka的区别总结 常见消息队列:ActiveMQ、RabbitMQ、RocketMQ、Kafka的区别。 阅读详情

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