[JSOI2016]最佳团体

嘟嘟嘟

01分数规划+树形背包。

然后就没了。

结果我调了半天，原因还是树形背包不熟练。

我是用dfs序求的，转化的时候，是dp[i][j]转化到dp[i + 1][j + 1]或dp[i +siz[pos[i]]][j]，而不是像普通的dp从别的状态转化到dp[i][j]，所以最后的答案应该考虑到dp[n + 1][m + 1]，而不是只到n，而且初始化的时候也要到n + 1这一层。这也就是我为啥总WA第3个点。

 #include<cstdio>
 #include<iostream>
 #include<cmath>
 #include<algorithm>
 #include<cstring>
 #include<cstdlib>
 #include<cctype>
 #include<vector>
 #include<stack>
 #include<queue>
 using namespace std;
 #define enter puts("")
 #define space putchar(' ')
 #define Mem(a, x) memset(a, x, sizeof(a))
 #define rg register
 typedef long long ll;
 typedef double db;
 const db INF = 1e12;
 const db eps = 1e-;
 const int maxn = ;
 inline ll read()
 {
     ll ans = ;
     char ch = getchar(), last = ' ';
     while(!isdigit(ch)) {last = ch; ch = getchar();}
     while(isdigit(ch)) {ans = (ans << ) + (ans << ) + ch - ''; ch = getchar();}
     if(last == '-') ans = -ans;
     return ans;
 }
 inline void write(ll x)
 {
     if(x < ) x = -x, putchar('-');
     if(x >= ) write(x / );
     putchar(x %  + '');
 }

 int k, n, s[maxn], p[maxn];
 struct Edge
 {
     int nxt, to;
 }e[maxn];
 int head[maxn], ecnt = -;
 void addEdge(int x, int y)
 {
     e[++ecnt] = (Edge){head[x], y};
     head[x] = ecnt;
 }

 int dfsx[maxn], pos[maxn], cnt = ;
 int siz[maxn];
 void dfs(int now)
 {
     dfsx[now] = ++cnt; pos[cnt] = now;
     siz[now] = ;
     for(int i = head[now]; i != -; i = e[i].nxt)
     {
         dfs(e[i].to);
         siz[now] += siz[e[i].to];
     }
 }
 db dp[maxn][maxn], w[maxn];
 db calc(int i, db x)
 {
     return (db)p[i] - (db)s[i] * x;
 }
 bool judge(db x)
 {
     for(int i = ; i <= cnt; ++i) w[i] = calc(pos[i], x);
     for(int i = ; i <= cnt + ; ++i)
         for(int j = ; j <= k + ; ++j) dp[i][j] = -INF;
     dp[][] = ;
     for(int i = ; i <= cnt; ++i)
         for(int j = ; j <= min(i, k + ); ++j) if(dp[i][j] > -INF)
         {
             dp[i + ][j + ] = max(dp[i + ][j + ], dp[i][j] + w[i]);
             dp[i + siz[pos[i]]][j] = max(dp[i + siz[pos[i]]][j], dp[i][j]);
         }
     db ans = -INF;
     for(int i = ; i <= cnt + ; ++i) ans = max(ans, dp[i][k + ]);
     return ans > -eps;
 }

 int main()
 {
     Mem(head, -);
     k = read(); n = read();
     for(int i = ; i <= n; ++i)
     {
         s[i] = read(); p[i] = read();
         int x = read();
         addEdge(x, i);
     }
     dfs();
     db L = , R = 1e4;
     while(R - L > eps)
     {
         db mid = (L + R) / ;
         if(judge(mid)) L = mid;
         else R = mid;
     }
     printf("%.3lf\n", L);
     return ;
 }