dp训练17 219D - Choosing Capital for Treeland

令dp[u]表示,以u为节点,向下走的路径数目。一次dfs能够做完。再令f[u]表示,以u为节点,向上走需要的代价。
对于u的子节点v,计算v向下走的代价,计算v向上走的代价。
向上走的代价=(u去掉v向下走的代价+f[u])
所以f[v]=(u去掉v向下走的代价)+f[u]

#include<iostream>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<cstdlib>
#include<climits>
#include<stack>
#include<vector>
#include<queue>
#include<set>
#include<bitset>
#include<map>
//#include<regex>
#include<cstdio>
#pragma GCC optimize(2)
#define up(i,a,b)  for(int i=a;i<b;i++)
#define dw(i,a,b)  for(int i=a;i>b;i--)
#define upd(i,a,b) for(int i=a;i<=b;i++)
#define dwd(i,a,b) for(int i=a;i>=b;i--)
//#define local
typedef long long ll;
typedef unsigned long long ull;
const double esp = 1e-6;
const double pi = acos(-1.0);
const int INF = 0x3f3f3f3f;
const int inf = 1e9;
using namespace std;
ll read()
{
    char ch = getchar(); ll x = 0, f = 1;
    while (ch<'0' || ch>'9') { if (ch == '-')f = -1; ch = getchar(); }
    while (ch >= '0' && ch <= '9') { x = x * 10 + ch - '0'; ch = getchar(); }
    return x * f;
}
typedef pair<int, int> pir;
#define lson l,mid,root<<1
#define rson mid+1,r,root<<1|1
#define lrt root<<1
#define rrt root<<1|1
const int N = 2e5 + 10;
struct eg {
    int to, next;
}edge[N<<1];
int head[N << 1];
int val[N << 1];
int sz[N];
int fa[N];
vector<int>ans[N];
int cnt;
int dp[N];
void addedge(int u, int v)
{
    edge[cnt].to = v;
    edge[cnt].next = head[u];
    val[cnt] = 1;
    head[u] = cnt++;
    edge[cnt].to = u;
    edge[cnt].next = head[v];
    head[v] = cnt++;
}
void dfs(int u, int f)
{
    fa[u] = f;
    sz[u] = 1;
    for (int i = head[u]; ~i; i = edge[i].next)
    {
        int v = edge[i].to;
        if (v == f)continue;
        dfs(v, u);
        if (val[i])
            dp[u] += dp[v] + 1;
        else dp[u] += dp[v];
        sz[u] += sz[v];
    }
}
int f[N];
void dfs2(int u)
{
    for (int i = head[u]; ~i; i = edge[i].next)
    {
        int v = edge[i].to;
        if (v == fa[u])continue;
        int cost;
        if (val[i])
            cost = sz[v] - 1 - dp[v] + sz[u] - sz[v] - 1 - (dp[u] - dp[v] - 1) + 1 + f[u];
        else cost = sz[v] - 1 - dp[v] + sz[u] - sz[v] - 1 - (dp[u] - dp[v]) + f[u];
        if (val[i])
            f[v] = 1 + sz[u] - sz[v] - 1 - (dp[u] - dp[v] - 1) + f[u];
        else f[v] = sz[u] - sz[v] - 1 - (dp[u] - dp[v]) + f[u];
        ans[cost].push_back(v);
        dfs2(v);
    }
}
int n;
int main()
{
    n = read();
    memset(head, -1, sizeof(head));
    int u, v;
    up(i, 0, n - 1)
    {
        u = read(), v = read();
        addedge(u, v);
    }
    dfs(1, 0);
    int cost_1 = n - 1 - dp[1];
    ans[cost_1].push_back(1);
    dfs2(1);
    up(i,0, n)
    {
        if (!ans[i].empty())
        {
            sort(ans[i].begin(), ans[i].end());
            cout << i << endl;
            for (auto k : ans[i])
                cout << k << " ";
            break;
        }
    }
    return 0;
}

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转载自www.cnblogs.com/LORDXX/p/12509296.html
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