luogu1754

Posted 2020-10-11 探险家Mr.H

卡特兰数

打表

滑稽

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstdlib>
#include<cmath>
#include<cstring>
using namespace std;
string catalan[]=
{
    "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;
    cin>>n;
    cout<<catalan[n-1];
}

View Code

正经的递推式：

    f[0]=f[1]=1
    for(i=2;i<=n;i++)
        for(j=0;j<i;j++)
            f[i]=f[i]+f[j]*f[i-j-1];
//f[n]即为第n个catalan数