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。
1 #include<cstdio> 2 #include<iostream> 3 #include<cmath> 4 #include<algorithm> 5 #include<cstring> 6 #include<cstdlib> 7 #include<cctype> 8 #include<vector> 9 #include<stack> 10 #include<queue> 11 using namespace std; 12 #define enter puts("") 13 #define space putchar(' ') 14 #define Mem(a, x) memset(a, x, sizeof(a)) 15 #define rg register 16 typedef long long ll; 17 typedef double db; 18 const db INF = 1e12; 19 const db eps = 1e-5; 20 const int maxn = 2505; 21 inline ll read() 22 { 23 ll ans = 0; 24 char ch = getchar(), last = ' '; 25 while(!isdigit(ch)) {last = ch; ch = getchar();} 26 while(isdigit(ch)) {ans = (ans << 1) + (ans << 3) + ch - '0'; ch = getchar();} 27 if(last == '-') ans = -ans; 28 return ans; 29 } 30 inline void write(ll x) 31 { 32 if(x < 0) x = -x, putchar('-'); 33 if(x >= 10) write(x / 10); 34 putchar(x % 10 + '0'); 35 } 36 37 int k, n, s[maxn], p[maxn]; 38 struct Edge 39 { 40 int nxt, to; 41 }e[maxn]; 42 int head[maxn], ecnt = -1; 43 void addEdge(int x, int y) 44 { 45 e[++ecnt] = (Edge){head[x], y}; 46 head[x] = ecnt; 47 } 48 49 int dfsx[maxn], pos[maxn], cnt = 0; 50 int siz[maxn]; 51 void dfs(int now) 52 { 53 dfsx[now] = ++cnt; pos[cnt] = now; 54 siz[now] = 1; 55 for(int i = head[now]; i != -1; i = e[i].nxt) 56 { 57 dfs(e[i].to); 58 siz[now] += siz[e[i].to]; 59 } 60 } 61 db dp[maxn][maxn], w[maxn]; 62 db calc(int i, db x) 63 { 64 return (db)p[i] - (db)s[i] * x; 65 } 66 bool judge(db x) 67 { 68 for(int i = 1; i <= cnt; ++i) w[i] = calc(pos[i], x); 69 for(int i = 1; i <= cnt + 1; ++i) 70 for(int j = 0; j <= k + 1; ++j) dp[i][j] = -INF; 71 dp[1][0] = 0; 72 for(int i = 1; i <= cnt; ++i) 73 for(int j = 0; j <= min(i, k + 1); ++j) if(dp[i][j] > -INF) 74 { 75 dp[i + 1][j + 1] = max(dp[i + 1][j + 1], dp[i][j] + w[i]); 76 dp[i + siz[pos[i]]][j] = max(dp[i + siz[pos[i]]][j], dp[i][j]); 77 } 78 db ans = -INF; 79 for(int i = 1; i <= cnt + 1; ++i) ans = max(ans, dp[i][k + 1]); 80 return ans > -eps; 81 } 82 83 int main() 84 { 85 Mem(head, -1); 86 k = read(); n = read(); 87 for(int i = 1; i <= n; ++i) 88 { 89 s[i] = read(); p[i] = read(); 90 int x = read(); 91 addEdge(x, i); 92 } 93 dfs(0); 94 db L = 0, R = 1e4; 95 while(R - L > eps) 96 { 97 db mid = (L + R) / 2; 98 if(judge(mid)) L = mid; 99 else R = mid; 100 } 101 printf("%.3lf ", L); 102 return 0; 103 }