20160329 HDU1023 Train Problem II（卡塔兰数）

最新推荐文章于 2021-01-23 21:46:27 发布

Lbbbbpro029

最新推荐文章于 2021-01-23 21:46:27 发布

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文章标签：卡塔兰数

本文链接：https://blog.youkuaiyun.com/Lbbbbpro029/article/details/51029229

本文介绍卡塔兰数的基本概念及其在计算机科学领域的多种应用，如出栈次序、括号化、凸多边形的三角划分等。同时提供了一个通过递推公式计算卡塔兰数的C++实现示例。

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基本的卡塔兰数应用：出栈次序，括号化，凸多边形的三角划分，二叉树的构造等等。

利用递推公式h(n)=h(n-1)*(4n-2)/(n+1)求解

#include <iostream>
#include <string.h>
using namespace std;

char a[101][10000]={"null","1","2","5","14","42","132","429","1430","4862","16796","58786","208012","742900","2674440","9694845","35357670","129644790","477638700","1767263190","6564120420","24466267020","91482563640","343059613650","1289904147324","4861946401452","18367353072152","69533550916004","263747951750360","1002242216651368","3814986502092304","14544636039226909","55534064877048198","212336130412243110","812944042149730764","3116285494907301262","11959798385860453492","45950804324621742364","176733862787006701400","680425371729975800390","2622127042276492108820","10113918591637898134020","39044429911904443959240","150853479205085351660700","583300119592996693088040","2257117854077248073253720","8740328711533173390046320","33868773757191046886429490","131327898242169365477991900","509552245179617138054608572","1978261657756160653623774456","7684785670514316385230816156","29869166945772625950142417512","116157871455782434250553845880","451959718027953471447609509424","1759414616608818870992479875972","6852456927844873497549658464312","26700952856774851904245220912664","104088460289122304033498318812080","405944995127576985730643443367112","1583850964596120042686772779038896","6182127958584855650487080847216336","24139737743045626825711458546273312","94295850558771979787935384946380125","368479169875816659479009042713546950","1440418573150919668872489894243865350","5632681584560312734993915705849145100","22033725021956517463358552614056949950","86218923998960285726185640663701108500","337485502510215975556783793455058624700","1321422108420282270489942177190229544600","5175569924646105559418940193995065716350","20276890389709399862928998568254641025700","79463489365077377841208237632349268884500","311496878311103321137536291518809134027240","1221395654430378811828760722007962130791020","4790408930363303911328386208394864461024520","18793142726809884575211361279087545193250040","73745243611532458459690151854647329239335600","289450081175264899454283846029490767264392230","1136359577947336271931632877004667456667613940","4462290049988320482463241297506133183499654740","17526585015616776834735140517915655636396234280","68854441132780194707888052034668647142985206100","270557451039395118028642463289168566420671280440","1063353702922273835973036658043476458723103404520","4180080073556524734514695828170907458428751314320","16435314834665426797069144960762886143367590394940","64633260585762914370496637486146181462681535261000","254224158304000796523953440778841647086547372026600","1000134600800354781929399250536541864362461089950800","3935312233584004685417853572763349509774031680023800","15487357822491889407128326963778343232013931127835600","60960876535340415751462563580829648891969728907438000","239993345518077005168915776623476723006280827488229600","944973797977428207852605870454939596837230758234904050","3721443204405954385563870541379246659709506697378694300","14657929356129575437016877846657032761712954950899755100","57743358069601357782187700608042856334020731624756611000","227508830794229349661819540395688853956041682601541047340","896519947090131496687170070074100632420837521538745909320"};
int main()
{
    int n;
    while(cin>>n)
    {
        cout<<a[n]<<endl;
    }
    return 0;
}