loj#2071. 「JSOI2016」最佳团体

Posted 2021-01-10 Nico&11101001

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
",l);  
    return 0;    
} 

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