#include <bits/stdc++.h>

using namespace std;
const int maxn = 1e6 + 7;
vector<int> g[maxn];
int par[maxn];
int in[maxn], out[maxn];
bool remain[maxn];
struct BIT
{
    int n, c[maxn];
    void init(int _n) {
        n = _n;
        memset(c, 0, (n + 2) << 2);
    }
    void update(int p, int d) {
        for(int i = p;i <= n;i += i & -i) c[i] += d;
    }
    int query(int p) {
        int res = 0;
        for(int i = p;i > 0;i -= i & -i) res += c[i];
        return res;
    }
}bit;
int time_tag;
void dfs(int u, int fa, int d)
{
    par[u] = fa;
    in[u] = ++time_tag;
    bit.update(in[u], d);
    bit.update(in[u]+1, -d);
    for(int i = 0;i < g[u].size();i ++) {
        int to = g[u][i];
        if(to != fa) dfs(to, u, d + 1);
    }
    out[u] = time_tag;
}
int main()
{
    int n, k;
    scanf("%d %d", &n, &k);
    bit.init(n);
    for(int i = 1;i < n;i ++) {
        int a, b;
        scanf("%d%d",&a,&b);
        g[a].push_back(b);
        g[b].push_back(a);
    }
    dfs(n,0,1);
    for(int rem=0,i = n;i >= 1;i --) {
        if(remain[i]) continue;
        int t = bit.query(in[i]);
        if(t + rem <= n - k) {
            for(int j = i;!remain[j] && j;j = par[j]) {
                remain[j] = 1;
                rem ++;
                bit.update(in[j], -1);
                bit.update(out[j]+1,1);
            }
        }
    }
    for(int i = 1;i <= n;i ++) if(!remain[i]) printf("%d ",i);
    return 0;
}
 

題目連結： http://codeforces.com/contest/980/problem/E
E. The Number Gamestime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard output

The nation of Panel holds an annual show called The Number Games, where each district in the nation will be represented by one contestant.

The nation has $n$

districts numbered from $1$ to $n$, each district has exactly one path connecting it to every other district. The number of fans of a contestant from district $i$ is equal to $2^i$

.

This year, the president decided to reduce the costs. He wants to remove $k$

contestants from the games. However, the districts of the removed contestants will be furious and will not allow anyone to cross through their districts.

The president wants to ensure that all remaining contestants are from districts that can be reached from one another. He also wishes to maximize the total number of fans of the participating contestants.

Which contestants should the president remove?

Input

The first line of input contains two integers $n$

and $k$ ($1\le k<n\le {10}^6$

) — the number of districts in Panel, and the number of contestants the president wishes to remove, respectively.

The next $n-1$

lines each contains two integers $a$ and $b$ ($1\le a,b\le n$, $a\ne b$), that describe a road that connects two different districts $a$ and $b$

in the nation. It is guaranteed that there is exactly one path between every two districts.

Output

Print $k$

space-separated integers: the numbers of the districts of which the contestants should be removed, in increasing order of district number.

ExamplesInputCopy

6 3
2 1
2 6
4 2
5 6
2 3

OutputCopy

1 3 4

InputCopy

8 4
2 6
2 7
7 8
1 2
3 1
2 4
7 5

OutputCopy

1 3 4 5

Note

In the first sample, the maximum possible total number of fans is $2^2+2^5+2^6=100$

. We can achieve it by removing the contestants of the districts 1, 3, and 4.

題意：給出一顆N個節點的樹，第i個節點的權值為2^i, 現在你必須刪除K個節點（K < N），並且保證剩下的點都聯通的情況下，使得剩下的點權值最大。

題解：用樹狀陣列，維護這個點到根的路徑上有幾個需要保留點。