HDU 4359 Easy Tree DP? 带权二叉树的构造方法 dp

题意：

给定n deep

1、构造一个n个节点的带权树，且最大深度为deep，每个节点最多只能有2个儿子

2、每个节点的值为2^0, 2^1 ··· 2^(n-1)  任意两个节点值不能相同

3、对于一个节点，若他有左右儿子，则左子树的和 < 右子树的和

问：

有多少种构造方法。

思路：

dp

#include <stdio.h>
#include <iostream>
#include <algorithm>
#include <cstring>
using namespace std;
template <class T>
inline bool rd(T &ret) {
    char c; int sgn;
    if(c=getchar(),c==EOF) return 0;
    while(c!='-'&&(c<'0'||c>'9')) c=getchar();
    sgn=(c=='-')?-1:1;
    ret=(c=='-')?0:(c-'0');
    while(c=getchar(),c>='0'&&c<='9') ret=ret*10+(c-'0');
    ret*=sgn;
    return 1;
}
template <class T>
inline void pt(T x) {
    if (x <0) {
        putchar('-');
        x = -x;
    }
    if(x>9) pt(x/10);
    putchar(x%10+'0');
}
///////////////////////////////////
typedef long long ll;
const int N = 362;
const ll mod = 1000000000 + 7;

int d[N][N], p[N][N], c[N][N];
int main() {
	memset(d, 0, sizeof d);
	memset(p, 0, sizeof p);
	memset(c, 0, sizeof c);
	for (int i = 0; i < N; ++i) {
		c[i][0] = c[i][i] = 1;
		for (int j = 1; j < i; ++j)
			c[i][j] = (c[i - 1][j] + c[i-1][j-1]) % mod;
	}
	for (int i = 0; i < N; ++i)
		p[0][i] = 1;
	for (int i = 1; i < N; ++i)
		p[1][i] = 1;
	for (int i = 2; i < N; ++i)
		for (int j = 1; j < N; ++j) {
			p[i][j] += (ll)p[i-1][j-1] * 2 % mod;
			p[i][j] %= mod;
			if (i - 1 >= 2) {
				for (int k = 1; k <= i - 2; ++k) {
					p[i][j] += ((ll)c[i-2][k] * p[k][j-1] % mod) * p[i-1-k][j-1] % mod;
					p[i][j] %= mod;
				}
			}
			p[i][j] = (ll)p[i][j] * i % mod;
		}
	//int x, y; while (~scanf("%d%d", &x, &y)) printf("%d\n", p[x][y]);
	d[1][1] = 1; d[0][0] = 1;
	for (int i = 2; i < N; ++i)
		for (int j = i; j < N; ++j) {
			d[i][j] += (ll)2 * d[i-1][j-1] % mod;
			d[i][j] %= mod;
			if (j - 1 >= 2) {
				for (int k = 1; k <= j - 2; ++k) {
					d[i][j] += ((ll)c[j-2][k] * p[k][i-2] % mod) * d[i-1][j-1-k] % mod;
					d[i][j] %= mod;
					d[i][j] += ((ll)c[j-2][k] * d[i-1][k] % mod) * p[j-1-k][i-2] % mod;
					d[i][j] %= mod;
					d[i][j] += ((ll)c[j-2][k] * d[i-1][k] % mod) * d[i-1][j-1-k] % mod;
					d[i][j] %= mod;
				}
			}
			d[i][j] = (ll)d[i][j] * j % mod;
		}
	int T = 0, cas, u, v;
	scanf("%d", &cas);
	while (cas -- > 0) {
		rd(u); rd(v);
		printf("Case #");
		pt(++T);
		putchar(':');
		putchar(' ');
		pt(d[v][u]);
		putchar('\n');
	}
	return 0;
}