hdu 3723 Delta Wave 夜

http://acm.hdu.edu.cn/showproblem.php?pid=3723

需要用到大整数 终于用java AC了

此题为经典 catalan 问题的变形

如果问题中的路径只能向上和向下的话就变成了 catalan 了，既然向上和向下的个数相等

枚举向上和向下的个数 每次枚举和剩下的向前状态个数进行组合 即可

代码：

import java.util.*;
import java.math.BigInteger;
import java.math.BigDecimal;

;

public class Main {

	public static void main(String[] args) {
		int N = 5005;
		BigInteger MOD = BigInteger.ONE;
		BigInteger k = BigInteger.TEN;
		for (int i = 0; i < 100; ++i) {
			MOD = MOD.multiply(k);
		}
		BigInteger[] catalan = new BigInteger[N];
		catalan[0] = BigInteger.ONE;
		for (int i = 1; i < N; ++i) {
			catalan[i] = catalan[i - 1].multiply(BigInteger.valueOf(4 * i - 2));
			catalan[i] = catalan[i].divide(BigInteger.valueOf(i + 1));
		}
		BigInteger[] C = new BigInteger[N * 2];
		Scanner in = new Scanner(System.in);
		int n;
		while (in.hasNext()) {
			n = in.nextInt();
			BigInteger ans = BigInteger.ZERO;
			C[0] = BigInteger.ONE;
			for (int i = 1; i <= n; ++i) {
				C[i] = C[i - 1].multiply(BigInteger.valueOf(n - i + 1));
				C[i] = C[i].divide(BigInteger.valueOf(i));
			}
			for (int i = 0; i <= n / 2; ++i) {
				BigInteger tmp = C[2 * i];
				tmp = tmp.multiply(catalan[i]);
				ans = ans.add(tmp);
			}
			ans = ans.mod(MOD);
			System.out.println(ans);
		}
	}

}