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HDU 1130 How Many Trees

发布时间:2019-10-14浏览(2326)

    HDU 1130 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
     卡特兰数,还是大数,实在恶心,不想用C语言写了,这个以后当大数模板用吧。
    LANGUAGE:JAVA
    CODE:
    import java.util.*;
    import java.math.*;
    public class Main{
        public static void main(String[] args) 
        {
            int n;
            Scanner in=new Scanner(System.in);
            BigInteger one=BigInteger.ONE;
            BigInteger four=new BigInteger("4");
            BigInteger two=new BigInteger("2");
            BigInteger st=null;
            BigInteger ans=null;
            while(in.hasNextInt())
            {
                n=in.nextInt();
                ans=BigInteger.ONE;
                for(int i=2;i<=n;i++)
                {
                    st=new BigInteger(""+i);
                    ans=ans.multiply(st.multiply(four).subtract(two)).divide(st.add(one));
                }
                System.out.println(ans);
            }
        }
    }