杭电_ACM_How Many Trees

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

#include <stdio.h>
int a[101][200] = {0};
void catalan()
{
    int carry, i, j, length, remainder;
    a[1][1] = 1;
    a[2][1] = 2;
    a[3][1] = 5;
    a[3][0] = 1;
    for (i = 4; i <= 100; i++)
    {
        length = a[i - 1][0];
        carry = 0;
        //handle multipling
        for (j = 1; j <= length; j++)
        {
            carry += a[i - 1][j] * (4 * i - 2);
            a[i][j] = carry % 10;
            carry /= 10;
        }
        //determine the length
        while (carry)
        {
            a[i][length++] = carry % 10;
            carry /= 10;
        }
        remainder = 0;
        //handle dividing
        for (j = length; j >= 1; j--)
        {
            remainder = remainder * 10 + a[i][j];
            a[i][j] = remainder / (i + 1);
            remainder %= (i + 1);
        }
        //determine the length
        while (!a[i][length])
        {
            length--;
        }
        a[i][0] = length;
    }
}
int main()
{
    int num, i;
    catalan();
    while (scanf("%d", &num) != EOF)
    {
        if (num < 4)
            printf("%d\n", a[num][1]);
        else
        {
            for (i = a[num][0]; i >= 1; i--)
            {
                printf("%d", a[num][i]);
            }
            puts("");
        }
    }
    return 0;
}

Key points

firstly, you must realize that it's a calatan question. Then you can solve it.