題干：

After Farmer John realized that Bessie had installed a "tree-shaped" network among his N (1 <= N <= 10,000) barns at an incredible cost, he sued Bessie to mitigate his losses.?

Bessie, feeling vindictive, decided to sabotage Farmer John's network by cutting power to one of the barns (thereby disrupting all the connections involving that barn). When Bessie does this, it breaks the network into smaller pieces, each of which retains full connectivity within itself. In order to be as disruptive as possible, Bessie wants to make sure that each of these pieces connects together no more than half the barns on FJ.?

Please help Bessie determine all of the barns that would be suitable to disconnect.

Input

* Line 1: A single integer, N. The barns are numbered 1..N.?

* Lines 2..N: Each line contains two integers X and Y and represents a connection between barns X and Y.

Output

* Lines 1..?: Each line contains a single integer, the number (from 1..N) of a barn whose removal splits the network into pieces each having at most half the original number of barns. Output the barns in increasing numerical order. If there are no suitable barns, the output should be a single line containing the word "NONE".

Sample Input

10 1 2 2 3 3 4 4 5 6 7 7 8 8 9 9 10 3 8

Sample Output

3 8

Hint

INPUT DETAILS:?

The set of connections in the input describes a "tree": it connects all the barns together and contains no cycles.?

OUTPUT DETAILS:?

If barn 3 or barn 8 is removed, then the remaining network will have one piece consisting of 5 barns and two pieces containing 2 barns. If any other barn is removed then at least one of the remaining pieces has size at least 6 (which is more than half of the original number of barns, 5).

題目大意：

給一棵n個結點的樹。求去掉哪個點能使得剩下的每個連通子圖的節點數不超過n/2.輸出滿足條件的點，如果有多個這樣的點，則升序輸出。

輸入：第一個表示有n個結點，接下來n-1行每行兩個值，表示這兩個結點相連接。

解題報告：

? ?樹形dp。（跟樹的重心挺像，類似的方法dp就行了）

AC代碼：

#include<cstdio> #include<iostream> #include<algorithm> #include<queue> #include<map> #include<vector> #include<set> #include<string> #include<cmath> #include<cstring> #define ll long long #define pb push_back #define pm make_pair using namespace std; const int MAX = 2e5 + 5; vector<int> vv[MAX]; int dp[MAX],sum[MAX],n; int dfs(int cur,int root) {dp[cur] = 1, sum[cur] = 1;int up = vv[cur].size();for(int i = 0; i<up; i++) {int v = vv[cur][i];if(v == root) continue;int tmp = dfs(v,cur);sum[cur] += tmp;dp[cur] = max(dp[cur],tmp);}dp[cur] = max(dp[cur],n - sum[cur]);return sum[cur]; } int main() {while(~scanf("%d",&n)) {for(int i = 1; i<=n; i++) vv[i].clear(),dp[i]=1;for(int i = 1; i<=n-1; i++) {int x,y;scanf("%d%d",&x,&y);vv[x].pb(y);vv[y].pb(x);}dfs(1,-1);int flag = 0;for(int i = 1; i<=n; i++) {if(dp[i]*2 <= n) {flag = 1;printf("%d\n",i);}}if(flag == 0) puts("NONE");}return 0 ; } //14:34 - 14:40

?

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