hdu 1130 How Many Trees
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题目大意: 就是给你1到N个数,让你求他能构成多少种二叉树
题目分析: 这里又是一种组合数学里的重要知识点!Catalan数的应用。
Catelan有直接的公式,用java的BigInteger类就可以迅速搞掉了,用c/c++要慢慢模拟,不过速度会更快~各有特色吧。Java用了140MS
令h(1)=1,h(0)=1,catalan数满足递归式:h(n)=(4*n-2)/(n+1)*h(n-1);
import java.math.BigInteger;import java.util.Scanner;public class Main{public static void main(String []args){Scanner cin=new Scanner(System.in);BigInteger h[]=new BigInteger[1005];h[0]=new BigInteger("1");h[1]=new BigInteger("1");BigInteger one=new BigInteger("1");BigInteger four=new BigInteger("4");BigInteger two=new BigInteger("2");for(int i=2;i<1005;i++){String str=String.valueOf(i);BigInteger n=new BigInteger(str);BigInteger temp=new BigInteger("0");h[i]=(n.multiply(four).subtract(two)).multiply(h[i-1]).divide(n.add(one));//h[i]=temp.divide(n.add(one));//h[i]=h[i-1].multiply(4*n-1).divide(n.add());}while(cin.hasNext()){//令h(1)=1,h(0)=1,catalan数满足递归式: //h(n)=(4*n-2)/(n+1)*h(n-1); int n=cin.nextInt();System.out.println(h[n]);}}}
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