HDU1130 卡特兰数

How Many Trees?

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 3397    Accepted Submission(s):
1964

Problem Description

A binary search tree is a binary tree with root k such
that any node v reachable from its left has label (v) <label (k) and any node
w reachable from its right has label (w) > label (k). It is a search
structure which can find a node with label x in O(n log n) average time, where n
is the size of the tree (number of vertices).

Given a number n, can you
tell how many different binary search trees may be constructed with a set of
numbers of size n such that each element of the set will be associated to the
label of exactly one node in a binary search tree?

Input

The input will contain a number 1 <= i <= 100 per
line representing the number of elements of the set.

Output

You have to print a line in the output for each entry
with the answer to the previous question.

Sample Input

1
2
3

Sample Output

1
2
5

Source

UVA

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卡特兰数 

#include<iostream>
#include<cstring>
#include<string>
#include<cstdio>
#include<algorithm>
using namespace std;
const int base = ;
const int N =  + ;
int katelan[N][N];
int main()
{
    katelan[][] = ;
    katelan[][] = ;
    katelan[][] = ;
    for (int i = ; i <= ; i++)
    {
        for (int j =; j<; j++)//大数乘法
        {
            katelan[i][j] += katelan[i - ][j] * ( * i - );
            katelan[i][j + ] += katelan[i][j] / base;
            katelan[i][j] %= base;
        }
        int temp;
        for (int j = ; j > ; j--)//大数除法
        {
            temp=katelan[i][j] % (i + );
            katelan[i][j-]+=temp* base;
            katelan[i][j] /= (i + );
        }
    }
    int n;
    while (cin >> n)
    {
        int i = ;
        while (katelan[n][i] == )i--;
        cout << katelan[n][i--];
        while (i > )
            printf("%04d", katelan[n][i--]);
        cout << endl;
    }
    return ;
}