hihoCoder 1050 树中的最长路 最详细的解题报告

题目来源：树中的最长路

解题思路：枚举每一个点作为转折点t，求出以t为根节点的子树中的‘最长路’以及与‘最长路’不重合的‘次长路’，用这两条路的长度之和去更新答案，最终的答案就是这棵树的最长路长度。只要以类似后序遍历的方式依次访问每个结点，从下往上依次计算每个结点的first值和second值，就能够用O(N)的时间复杂度来解决这个问题。

具体算法（java版，可以直接AC）

 import java.util.*;

 public class Main {

     public class Node {
         public Node parent;//父节点
         public List<Node> children;//子节点
         public int first;  //最长路
         public int second;//次长路
         public int val;

         public Node(int val, Node parent) {
             this.val = val;
             this.first = 0;
             this.second = 0;
             this.parent = parent;
             this.children = new ArrayList<Node>();
         }

         //更新节点的first和second
         public void update() {
             if (this.children.size() == 0) {//叶节点
                 this.first = this.second = 0;
             } else if (this.children.size() == 1) {//只有一个子节点
                 this.first = this.children.get(0).first + 1;
                 this.second = 0;
             } else {//大于等于2个子节点
                 int[] array = new int[this.children.size()];
                 for (int i = 0; i < this.children.size(); i++) {
                     array[i] = this.children.get(i).first;
                 }
                 Arrays.sort(array);
                 this.first = array[array.length - 1] + 1;
                 this.second = array[array.length - 2] + 1;
             }
         }

         //更新所有节点的first和second（在第一次建立树时调用）
         public void updateAll() {
             for (Node child : this.children) {
                 child.updateAll();
             }
             this.update();
         }
     }

     public int n;
     public int index;
     public int max;
     public Node[] nodeMap;

     public Main(Scanner scanner, int n) {
         this.n = n;
         this.nodeMap = new Node[this.n + 1];
         for (int i = 0; i < n - 1; i++) {
             this.create(scanner.nextInt(), scanner.nextInt());
         }
         this.index = 1;
         this.nodeMap[this.index].updateAll();//更新所有的节点
         this.max = this.nodeMap[this.index].first
                 + this.nodeMap[this.index].second;
         this.index++;
     }

     //创建树
     private void create(int from, int to) {
         Node parent = this.nodeMap[from];
         Node child = this.nodeMap[to];
         if (parent == null) {
             parent = new Node(from, null);
             this.nodeMap[from] = parent;
         }
         if (child == null) {
             child = new Node(to, parent);
             this.nodeMap[to] = child;
         }
         child.parent = parent;
         parent.children.add(child);
     }

     //将下标为i的节点设置为根节点
     private void setRoot(int i) {
         Node cur = this.nodeMap[i];
         Node parent = cur.parent;
         if (parent != null) {//如果存在父节点
             parent.children.remove(cur);//从父节点中删除子节点
             this.setRoot(parent.val);//递归计算父节点
             cur.children.add(parent);//将父节点变成子节点
             parent.parent = cur;
         }
         cur.update();//更新当前节点
     }

     public void solve() {
         while (this.index <= this.n) {
             this.setRoot(this.index);
             this.nodeMap[this.index].parent = null;//根节点的parent设置为null，否则出现死循环
             int sum = this.nodeMap[this.index].first
                     + this.nodeMap[this.index].second;
             this.index++;
             this.max = this.max > sum ? this.max : sum;//更新max
         }
     }

     public static void main(String[] args) {
         Scanner scanner = new Scanner(System.in);
         int N = scanner.nextInt();
         Main main = new Main(scanner, N);
         main.solve();
         System.out.println(main.max);
     }

 }