HDOJ HDU 1130 How Many Trees?

题目

点此查看 HDOJ HDU 1130 How Many Trees?

分类

大数
卡特兰数

题意

求 n 个节点 二叉搜索树 有多少种

题解

先写几个数
1 2 5 14
熟悉的人已经看出是卡特兰数了
计算程序 说明 见 常用表 Catalan(卡特兰)数 1 - 100

代码

下面直接给出打表代码

#include <iostream>#define maxn 100using namespace std;string tab[maxn] = {    "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 r;    while(cin >> r)    {        cout << tab[r-1] << endl;    }    return 0;}