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 several te…

Description A sequence consisting of one digit, the number 1 is initially written into a computer. At each successive time step, the computer simultaneously tranforms each digit 0 into the sequence 1 0 and each digit 1 into the sequence 0 1. So, afte…

Description Prof. Tigris is the head of an archaeological team who is currently in charge of an excavation in a site of ancient relics.        This site contains relics of a village where civilization once flourished. One night, examining a writing r…

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…

Description The 11th Zhejiang Provincial Collegiate Programming Contest is coming! As a problem setter, Edward is going to arrange the order of the problems. As we know, the arrangement will have a great effect on the result of the contest. For examp…

题目链接: http://acm.hdu.edu.cn/showproblem.php?pid=1023 题目大意: 一列N节的火车以严格的顺序到一个站里.问出来的时候有多少种顺序. 解题思路: 典型的求Catalan数的题目,可是结果会非常大,所以须要用大数来解决. Catalan公式为 h(n) = h(n-1) * (4*n-2) / (n + 1),h(0) = h(1) = 1. AC代码: #include<iostream> #include<algorithm> #…

Train Problem II Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others) Total Submission(s): 10372    Accepted Submission(s): 5543 Problem Description As we all know the Train Problem I, the boss of the Ignatius Train Sta…

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…

题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=1023 Train Problem II Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 12035    Accepted Submission(s): 6422 Problem Description As we all know the…