Codeforces Round #547 (Div. 3) G. Privatization of Roads in Treeland

二分找出r的大小，然后dfs对图染色。

#include "bits/stdc++.h"

using namespace std;
const int maxn = 2e5 + 100;
int n, k;
int ans[maxn];
int cnt[maxn];
int l, r, mid;
vector<pair<int, int> > e[maxn];
int vis[maxn];

bool check(int num) {
    int ret = 0;
    for (int i = 1; i <= n; i++) {
        if (cnt[i] > num) ret++;
    }
    return ret <= k;
}

void dfs(int now, int fa, int facolor) {
    int co = 1;
    if (co == facolor) co++;
    bool flag = (cnt[now] <= r);
    for (auto p:e[now]) {
        if (p.first != fa) {
            if (flag)
                ans[p.second] = co++;
            else
                ans[p.second] = 1;
            dfs(p.first, now, ans[p.second]);
            if (co == facolor) co++;
        }
    }
}


int main() {
//    freopen("input.txt", "r", stdin);
    cin >> n >> k;
    int a, b;
    for (int i = 1; i < n; i++) {
        cin >> a >> b;
        e[a].push_back(make_pair(b, i));
        e[b].push_back(make_pair(a, i));
        cnt[a]++;
        cnt[b]++;
    }
    l = 1, r = n - 1;
    while (l < r) {
        mid = (l + r) >> 1;
        if (check(mid)) {
            r = mid;
        } else {
            l = mid + 1;
        }
    }
    dfs(1, 0, 0);
    cout << r << endl;
    int space = 0;
    for (int i = 1; i < n; i++) {
        if (space) cout << " ";
        space = 1;
        cout << ans[i];
    }
    cout << endl;
    return 0;
}