This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
#define int long long
const int MAXN = 200005;
int n, K, cur_val, put[MAXN], actual[MAXN];
vector<pair<int, int>> adj[MAXN];
pair<int, bool> dfs(int x, int par){
int mx = 0, d_par = 0, c = 0, has = 0;
for(auto& [nxt, wt] : adj[x]){
if(nxt == par){
d_par = wt;
continue;
}
pair<int, bool> res = dfs(nxt, x);
if(res.second) c = min(c, res.first), has = 1;
else mx = max(mx, res.first);
}
if(has && mx + c <= 0){
// cout << x << " returning " << (c + d_par > 0 ? d_par : c + d_par) << ' ' << (c+d_par <= 0) << endl;
return {(c + d_par > 0 ? d_par : c + d_par), c+d_par <= 0};
}
if(mx + d_par > cur_val){
put[x] = 1;
// cout << x << " putting and returning " << (d_par - cur_val > 0 ? d_par : d_par - cur_val) << ' ' << 1 << endl;
return {d_par - cur_val > 0 ? d_par : d_par - cur_val, 1};
}
// cout << x << " returning " << d_par + mx << " 0" << endl;
return {d_par + mx, 0};
}
bool check(int val){
// cout << "CHECKING " << val << endl;
memset(put, 0, sizeof put);
int cnt = 0; cur_val = val;
dfs(0, -1);
for(int i = 0; i < n; i ++)
cnt += put[i];
return cnt <= K;
}
signed main(){
ios::sync_with_stdio(0);
cin.tie(0);
cin >> n >> K;
for(int i = 1; i < n; i ++){
int a, b, w; cin >> a >> b >> w;
adj[a-1].emplace_back(b-1, w);
adj[b-1].emplace_back(a-1, w);
}
int l = 0, r = 1e18, ans = -1;
while(l <= r){
int m = (l + r) >> 1;
if(check(m)){
ans = m; r = m-1;
for(int i = 0; i < n; i ++)
actual[i] = put[i];
} else l = m+1;
}
cout << ans << '\n';
set<int> numbers;
int num_taken = 0;
for(int i = 0; i < n; i ++)
numbers.insert(i);
for(int i = 0; i < n; i ++)
if(actual[i]){
cout << i+1 << ' ';
numbers.erase(i);
num_taken ++;
}
while(num_taken < K){
cout << *numbers.begin()+1 << ' ';
numbers.erase(numbers.begin());
num_taken ++;
}
}
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