loj#2071. 「JSOI2016」最佳团体

题目链接

loj#2071. 「JSOI2016」最佳团体

题解

树形dp强行01分规

代码

#include<cstdio>
#include<cstring>
#include<algorithm>
#define gc getchar()
#define pc putchar
inline int read() {
	int x = 0,f = 1;
	char c = gc;
	while(c < '0' || c > '9') c = gc;
	while(c <= '9' && c >= '0') x = x * 10 + c - '0',c = getchar();
	return x * f;
}
void print(int x) {
	if(x < 0) {
		pc('-');
		x = -x;
	}
	if(x >= 10) print(x / 10);
	pc(x % 10 + '0') ;
}
#define eps 1e-3
const int maxn = 2505;
struct node {
	int next,v;
} edge[maxn << 1];
int head[maxn], num = 0;
void add_edge(int x,int v) {
	edge[++ num].v = v;
	edge[num].next = head[x];
	head[x] = num;
}
int n,k ;
double ans = -1.000;
int s[maxn],p[maxn],siz[maxn];
double val[maxn];
double dp[maxn][maxn];
double tmp[maxn];
void dfs(int x,int fa) {
	siz[x] = 0;
	dp[x][0] = 0.0;
	for(int i = head[x];i;i = edge[i].next) {
		int v = edge[i].v;
		if(v == fa) continue;
		dfs(v,x);
		for(int j = 0;j <= siz[x] + siz[v];++ j) tmp[j] = -74123423432.123;
		for(int j = 0;j <= siz[x];++ j) {
			for(int k = 0;k <= siz[v]; ++ k) {
				tmp[k + j] = std::max(tmp[k + j], dp[x][j] + dp[v][k]);
			}
		}
		siz[x] += siz[v];
		for(int i = 0;i <= siz[x];++ i) dp[x][i] = tmp[i];
	}
	++ siz[x];
	for(int i = siz[x];i >= 1;-- i) dp[x][i] = dp[x][i - 1] + val[x];
}
bool check(double mid) {
	for(int i = 0;i <= n;++ i)
		val[i] = 1.0 * p[i] - 1.0 * mid * s[i];
	dfs(0,0);
	return dp[0][k + 1] >= 0.0;
}
int main() {
	//freopen("team0.in","r",stdin);
	k = read(),n = read();
	for(int fa,i = 1;i <= n;++ i) {
		s[i] = read(),p[i] = read(),fa = read();
		add_edge(fa,i); add_edge(i,fa);
	}
	double l = 0,r = 1000.0;
	int cnt = 30 ;
	while(cnt --) {
		double mid = (r + l) / 2.0;
		if(check(mid)) ans = mid,l = mid;
		else r = mid;
	}
	printf ("%.3lf\n",l);
	return 0;
} 

/*
1 2
1000 1 0
1 1000 1
*/