如何通过移除边缘将一棵树切成两半? [英] How can I cut a tree into two by removing an edge?
问题描述
我的目标是从给定的树T去除边缘，从而导致形成两个单独的树T1和T2.
My goal is for the removal of an edge from a given tree T will result in the formation of two separate trees, T1 and T2.
给树T的每个顶点分配一个正整数.我的任务是删除边缘，以使生成树的Tree_diff最小化. Tree_diff定义如下:
Each vertex of the tree T is assigned a positive integer. My task is to remove an edge, such that the Tree_diff of the resultant trees is minimized. Tree_diff is defined as the following:
F(T) = Sum of numbers written on each vertex of a tree T
Tree_diff(T) = abs(F(T1) - F(T2))
输入格式:
- 第一行将包含整数N，即树中的顶点数.
- 下一行将包含N个由单个空格分隔的整数，即分配给每个顶点的值.
- 接下来的N-1行包含一对整数，每个整数之间用一个空格隔开，表示树的边缘.
在上面的输入中，顶点的编号从1到N.
In the above input, the vertices are numbered from 1 to N.
输出格式:一行包含Tree_diff的最小值.
Output Format: a single line containing the minimum value of Tree_diff.
约束:
- 3≤N≤105
- 1≤写入每个顶点≤1001的数字
样本输入
50
716 365 206 641 841 585 801 645 208 924 920 286 554 832 359 836 247 959 31 322 709 860 890 195 575 905 314 41 669 549 950 736 265 507 729 457 91 529 102 650 805 373 287 710 556 645 546 154 956 928
14 25
25 13
13 20
20 24
43 2
2 48
48 42
42 5
27 18
18 30
30 7
7 36
37 9
9 23
23 49
49 15
31 26
26 29
29 50
50 21
41 45
45 10
10 17
17 34
28 47
47 44
44 11
11 16
3 8
8 39
39 38
38 22
19 32
32 12
12 40
40 46
1 35
35 4
4 33
33 6
25 2
2 27
7 37
15 50
21 10
17 28
16 39
38 19
40 1
样本输出
525
我的代码是
import java.util.*;
class Solution{
private static int N;
private static ArrayList<Node> nodes;
public static int count=10000;
public static int count1=0;
private static class Node {
private Node parent;
private ArrayList<Node> children;
private int ID;
private int value;
private Node() {
parent = null;
ID=0;
value=0;
children = new ArrayList<Node>(100);
}
private void disconnectChild(Node child)
{
children.remove(child);
}
private void disconnect()
{
if (parent != null)
{
parent.disconnectChild(this);
parent = null;
}
}
}
public static void main( String args[] )
{
Scanner in = new Scanner(System.in);
N = in.nextInt();
nodes = new ArrayList<Node>(N);
for(int i = 0; i < N; i++)
nodes.add(new Node());
for(int i = 0; i < N; i++)
{
nodes.get(i).ID=i+1;
nodes.get(i).value = in.nextInt();
}
//construct the graph
for(int i = 0; i < N-1; i++)
{
int first = in.nextInt() - 1;
int second = in.nextInt() - 1;
if(nodes.get(second).parent == null)
{
nodes.get(first).children.add(nodes.get(second));
nodes.get(second).parent = nodes.get(first);
}
else
{
nodes.get(second).children.add(nodes.get(first));
nodes.get(first).parent = nodes.get(second);
}
}
for(int i=0;i<N;i++)
{
if(nodes.get(i).parent != null)
{
Node x1 = nodes.get(i);
while(x1.parent != null)
{
x1 = x1.parent;
}
count1 =0;
calculate(x1);
int m =count1;
int a = nodes.get(i).ID;
int b = nodes.get(i).parent.ID;
nodes.get(i).disconnect();
count1 =0;
calculate(nodes.get(a-1));
int x = count1;
int y = m - x;
int z = Math.abs(x-y);
nodes.get(b-1).children.add(nodes.get(a-1));
nodes.get(a-1).parent = nodes.get(b-1);
if(z<count)
count = z;
}
}
System.out.println(count);
}
public static void print(Node node)
{
if(node.children.size()!=0)
{
for(int i=0;i<node.children.size();i++)
print(node.children.get(i));
}
System.out.print(node.ID+" ");
}
public static void calculate(Node node)
{
count1 = count1 + node.value;
if(node.children.size()!=0)
{
for(int i=0;i<node.children.size();i++)
calculate(node.children.get(i));
}
}
}
我的代码对于较小的输入正常工作；对于上述输入，输出为
My code is working properly for smaller inputs; for the above input, the output was
0
预期输出为
525
有什么建议吗?
NB-这是一项家庭作业
推荐答案
您需要添加一种方法来断开子级与父级节点的连接.看起来像这样:
You need to add a method for disconnecting a child from a parent node. That would look something like this:
private void disconnectChild(Node child) {
children.remove(child);
}
然后您将像这样从disconnect()方法调用此方法:
You would then call this method from your disconnect() method like so:
private void disconnect()
{
if (parent != null)
{
parent.disconnectChild(this);
parent = null;
}
}
这篇关于如何通过移除边缘将一棵树切成两半?的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！
