火车进站出站的问题满足卡特兰数...卡特兰数的相关知识如下: 卡特兰数又称卡塔兰数,是组合数学中一个常出现在各种计数问题中出现的数列.由以比利时的数学家欧仁·查理·卡塔兰 (1814–1894)命名. 前几项为 (OEIS中的数列A000108): 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 176…

题意: 给出一个数字n,假设火车从1~n的顺序分别进站,求有多少种出站序列. 思路: 卡特兰数的经典例子.n<101,用递推式解决.需要使用到大数.n=100时大概有200位以下. #include <bits/stdc++.h> using namespace std; ; vector<string> vect; void _mult(string num1, string num2, string &result ) { reverse(num1.begin()…

题意: 给你一个数n,表示有n辆火车,编号从1到n,入站,问你有多少种出站的可能.    (题于文末) 知识点: ps:百度百科的卡特兰数讲的不错,注意看其参考的博客. 卡特兰数(Catalan):前几项为 : 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670- 令h(0)=1,h(1)=1,catalan数满足递推式:      h(n)= h(0…

题目链接_HDU-1023 题目 As we all know the Train Problem I, the boss of the Ignatius Train Station want to know if all the trains come in strict-increasing order, how many orders that all the trains can get out of the railway. input The input contains sever…

题目链接:https://cn.vjudge.net/problem/HDU-1023 题意 卡特兰数的应用之一 求一个长度为n的序列通过栈后的结果序列有几种 思路 一开始不知道什么是卡特兰数,猜测是一个递推题 注意到在序列第i个元素入栈时,前几个元素都进过栈,就是通过栈的操作 设n个元素通过栈的结果序列个数为h[n],则有: \[ h_n=h_1h_{n-1}+h_2h_{n-2}+...+h_{n-1}h_1 \] 查了以后发现这是卡特兰数的规律,有通项: \[ h_n=h_{n-1}\fr…

考虑第1个火车出站的时刻,从1到n都有可能,如果它是第i个出栈,那么前面有规模为i-1的子问题,后面有规模为n-i的子问题.累加.…

Train Problem II Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 4358    Accepted Submission(s): 2391 Problem Description As we all know the Train Problem I, the boss of the Ignatius Train Stati…

题目连接 http://acm.hdu.edu.cn/showproblem.php?pid=1212 Train Problem II Description As we all know the Train Problem I, the boss of the Ignatius Train Station want to know if all the trains come in strict-increasing order, how many orders that all the t…

Problem Description As we all know the Train Problem I, the boss of the Ignatius Train Station want to know if all the trains come in strict-increasing order, how many orders that all the trains can get out of the railway.   Input The input contains…

链接:传送门 题意:裸卡特兰数,但是必须用大数做 balabala:上交高精度模板题,增加一下熟悉度 /************************************************************************* > File Name: hdu1023.cpp > Author: WArobot > Blog: http://www.cnblogs.com/WArobot/ > Created Time: 2017年05月11日 星期四 19…