POJ 1655 求樹的重心(樹形dp)

題目鏈接

樹的重心：
若樹上的一個節點滿足其所有的子樹中最大的子樹節點數最少，那麼這個點就是這棵樹的重心。
1.任選一個點爲根，只要統計出每個點的子樹大小，就能很快求出每個點子樹節點的數量的最大值。
2.求每個點子樹的大小同樣只需要自底向上的更新信息。
3.記sz[u]爲子樹u節點的數量(包括 u 本身)
4.sz[u] = 1 + 所有子節點v的sz之和

#include  <map>
#include  <set>
#include  <cmath>
#include  <queue>
#include  <cstdio>
#include  <vector>
#include  <climits>
#include  <cstring>
#include  <cstdlib>
#include  <iostream>
#include  <algorithm>
#include  <time.h>

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define forn(i, n) for (int i = 0; i < (int)(n); ++i)
#define for1(i, n) for (int i = 1; i <= (int)(n); ++i)
#define ford(i, a, b) for (int i = (int)(a); i >= (int)b; --i)
#define fore(i, a, b) for (int i = (int)(a); i <= (int)(b); ++i)
#define rep(i, l, r) for (int i = (l); i <= (r); i++)
#define per(i, r, l) for (int i = (r); i >= (l); i--)
#define ms(x, y) memset(x, y, sizeof(x))
#define SZ(x) ((int)(x).size())

using namespace std;

typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<pii> vpi;
typedef vector<vi> vvi;
typedef long long i64;
typedef vector<i64> vi64;
typedef vector<vi64> vvi64;
typedef pair<i64, i64> pi64;
typedef double ld;

template<class T> bool uin(T &a, T b) { return a > b ? (a = b, true) : false; }
template<class T> bool uax(T &a, T b) { return a < b ? (a = b, true) : false; }

const int maxn = 20000+100;
int tc, n, sz[maxn], fa[maxn], res[maxn];
vector<int> G[maxn];

void init(int n) {
    memset(fa, 0, sizeof(fa));
    memset(sz, 0, sizeof(sz));
    for (int i = 1; i <= n; ++i) G[i].clear();
}
void dfs1(int x, int par) {
    sz[x] = 1;
    fa[x] = par;
    for (int i = 0; i < int(G[x].size()); ++i) {
        int to = G[x][i];
        if (to == par) continue;
        dfs1(to, x);
        sz[x] += sz[to];
    }
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.precision(10);
    cout << fixed;
#ifdef LOCAL_DEFINE
    freopen("input.txt", "r", stdin);
#endif

    scanf("%d", &tc);
    while (tc--) {
        scanf("%d", &n);
        init(n);
        for (int i = 0; i < n - 1; ++i) {
            int u, v;
            scanf("%d%d", &u, &v);
            G[u].push_back(v);
            G[v].push_back(u);
        }
        dfs1(1, 0);

        for (int i = 1; i <= n; ++i) {
            int maxx = n - sz[i];
            for (int j = 0; j < int(G[i].size()); ++j) {
                int to = G[i][j];
                if (to == fa[i]) continue;    //!!
                maxx = max(maxx, sz[to]);
            }
            res[i] = maxx;
        }

        int ans = INT_MAX, node;
        for (int i = 1; i <= n; ++i) {
            if (res[i] < ans) {
                ans = res[i];
                node = i;
            }
        }

        printf("%d %d\n", node, ans);
    }

#ifdef LOCAL_DEFINE
    cerr << "Time elapsed: " << 1.0 * clock() / CLOCKS_PER_SEC << " s.\n";
#endif
    return 0;
}