Codeforces 700B Connecting Universities(树的中心)

题意：

给你树上的一些点，问你如何把他们两两分组，是的每组的距离总和最大。

分析：

很显然的就是，如果能够让这些点都经过最远的点，甚至是根的话，那么答案肯定是足够大的，仔细想想之后可以联想到树的重心，但是这个重心不是整个的重心，而是根据那选定的点的重心，找到之后一次dfs就好了。

代码：

//
//  Created by  CQU_CST_WuErli
//  Copyright (c) 2016 CQU_CST_WuErli. All rights reserved.
//
//#pragma comment(linker, "/STACK:102400000,102400000")
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#define CLR(x) memset(x,0,sizeof(x))
#define OFF(x) memset(x,-1,sizeof(x))
#define MEM(x,a) memset((x),(a),sizeof(x))
#define BUG cout << "I am here" << endl
#define lookln(x) cout << #x << "=" << x << endl
#define SI(a) scanf("%d", &a)
#define SII(a,b) scanf("%d%d", &a, &b)
#define SIII(a,b,c) scanf("%d%d%d", &a, &b, &c)
const int INF_INT=0x3f3f3f3f;
const long long INF_LL=0x7f7f7f7f;
const int MOD=1e9+7;
const double eps=1e-10;
const double pi=acos(-1);
typedef long long  ll;
using namespace std;

const int N = 200020;
int n, k;
vector<int> g[N];
int w[N];
int mx[N];
int sz[N];
int centroid;

void find(int fa, int u) {
    mx[u] = 0; sz[u] = w[u];
    for (auto & v: g[u]) {
        if (v == fa) continue;
        find(u, v);
        sz[u] += sz[v];
        mx[u] = max(mx[u], sz[v]);
    }
    mx[u] = max(mx[u], 2 * k - sz[u]);
    if (!centroid || mx[u] < mx[centroid]) centroid = u;
}

ll sum = 0;
void dfs(int fa, int u, int cnt) {
    if (w[u]) sum += cnt;
    for (auto& v : g[u]) {
        if (fa == v) continue;
        dfs(u, v, cnt + 1);
    }
}

int main(int argc, char const *argv[]) {
#ifdef LOCAL
    freopen("C:\\Users\\john\\Desktop\\in.txt","r",stdin);
    // freopen("C:\\Users\\john\\Desktop\\out.txt","w",stdout);
#endif
    SII(n, k);
    CLR(w);
    for (int i = 1; i <= 2 * k; i++) {
        int x; SI(x);
        w[x] = 1;
    }
    for (int i = 1; i < n; i++) {
        int u, v;
        SII(u, v);
        g[u].push_back(v);
        g[v].push_back(u);
    }
    centroid = 0;
    find(-1, 1);
    // lookln(centroid);
    sum = 0;
    dfs(-1, centroid, 0);
    cout << sum << endl;
    return 0;
}