CF219D Choosing Capital for Treeland

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树形dp。

首先一个很常规的想法就是如果u到v有一条边，那么建立cost(u, v) = 0, cost(v, u) = 1的两条边.

可以两遍dfs。

先任选一个点作为根节点，第一遍从下往上dfs，维护节点u到他的所有子节点的距离，很容易得出dis[u] = ∑dis[v] + cost(u, v) （v为u的儿子节点）。

第二遍从上往下dfs，维护节点u到所有节点的距离，考虑u和他的一个儿子节点v，两者到所有节点的区别只有cost(u, v)这条边是不一样的，如果cost(u, v) = 1,那么dis2[v] = dis2[u] - 1,否则dis2[v] = dis2[u] + 1.

 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 int INF = 0x3f3f3f3f;
19 const db eps = 1e-8;
20 const int maxn = 2e5 + 5;
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 * 10 + 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 n;
38 vector<int> v[maxn];
39 vector<bool> c[maxn];
40 int dis[maxn];
41 bool vis[maxn];
42 
43 void init()
44 {
45     for(int i = 1; i <= n; ++i) v[i].clear(), c[i].clear();
46     Mem(dis, 0); 
47 }
48 
49 void dfs1(int now)
50 {
51     vis[now] = 1;
52     for(int i = 0; i < (int)v[now].size(); ++i)
53     {
54         if(!vis[v[now][i]])
55         {
56             dis[now] += c[now][i];
57             dfs1(v[now][i]);
58             dis[now] += dis[v[now][i]];
59         }
60     }
61 }
62 void dfs2(int now)
63 {
64     vis[now] = 1;
65     for(int i = 0; i < (int)v[now].size(); ++i)
66     {
67         if(!vis[v[now][i]])
68         {
69             dis[v[now][i]] = dis[now] + (c[now][i] ? -1 : 1);
70             dfs2(v[now][i]);
71         }
72     }
73 }
74 
75 int main()
76 {
77     while(scanf("%d", &n) != EOF)
78     {
79         init(); 
80         for(int i = 1; i < n; ++i)
81         {
82             int x = read(), y = read();
83             v[x].push_back(y); c[x].push_back(0);
84             v[y].push_back(x); c[y].push_back(1); 
85         }
86         Mem(vis, 0); dfs1(1);
87         Mem(vis, 0); dfs2(1);
88         int Min = INF;
89         for(int i = 1; i <= n; ++i) Min = min(Min, dis[i]); 
90         write(Min); enter;
91         for(int i = 1; i <= n; ++i) if(dis[i] == Min) write(i), space;
92         enter;
93     }
94     return 0;
95 }

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