AIM Tech Round 4 (Div. 1) C - Upgrading Tree 构造 + 树的重心

Posted 2021-02-02 cjlhy

C - Upgrading Tree

我发现我构造题好弱啊啊啊。

很明显能想到先找到重心， 然后我们的目标就是把所有点接到重心的儿子上，让重心的儿子子树变成菊花图，

这个先把重心到儿子的边连到 i ， 然后把 i 到 其 fa 的边连到重心的儿子上， 一直循环就好啦。

#include<bits/stdc++.h>
#define LL long long
#define fi first
#define se second
#define mk make_pair
#define PLL pair<LL, LL>
#define PLI pair<LL, int>
#define PII pair<int, int>
#define SZ(x) ((int)x.size())
#define ull unsigned long long

using namespace std;

const int N = 2e5 + 7;
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3f;
const int mod = 1e9 + 7;
const double eps = 1e-8;
const double PI = acos(-1);

int n, last, start, who, sum[N];
vector<int> G[N];
vector<pair<int,PII>> ans;

PII getCenter(int u, int fa) {
    PII tmp = mk(inf, u);
    sum[u] = 1;
    int mx = 0;
    for(int v : G[u]) {
        if(v == fa) continue;
        tmp = min(tmp, getCenter(v, u));
        sum[u] += sum[v];
        mx = max(mx, sum[v]);
    }
    mx = max(mx, n-sum[u]);
    return min(tmp, mk(mx, u));
}

void work(int u, int fa) {
    sum[u] = 1;
    for(int v : G[u]) if(v != fa)
        work(v, u), sum[u] += sum[v];
}

void dfs(int u, int fa) {
    if(fa != who) {
        ans.push_back(mk(who, mk(last, u)));
        ans.push_back(mk(u, mk(fa, start)));
        last = u;
    }
    for(int v : G[u])
        if(v != fa) dfs(v, u);
}

void solve(int u, int fa) {
    who = u;
    for(int v : G[u]) {
        if(v == fa) continue;
        start = v;
        last = v;
        dfs(v, u);
        ans.push_back(mk(u, mk(last, v)));
    }
}

int main() {
    scanf("%d", &n);
    for(int i = 1; i < n; i++) {
        int u, v; scanf("%d%d", &u, &v);
        G[u].push_back(v);
        G[v].push_back(u);
    }
    int root = getCenter(1, 0).se, root2 = -1;
    work(root, 0);
    for(int v : G[root])
        if(n % 2 == 0 && sum[v] == n/2)
            root2 = v;
    if(~root2) solve(root, root2), solve(root2, root);
    else solve(root, 0);
    printf("%d
", ans.size());
    for(auto t : ans) printf("%d %d %d
", t.fi, t.se.fi, t.se.se);
    return 0;
}

/*
*/