求一颗二叉树上的最远距离(树形DP)
一、题目
二叉树中，一个节点可以往上走和往下走，那么从节点A总能走到节点B。
节点A走到节点B的距离为:A走到B最短路径上的节点个数。
求一颗二叉树上的最远距离
二、思路
利用递归分别求出每个节点的左右子树中的最大距离，和该节点的高度。
三、代码实现
1 public class MaxDistanceInTree { 2 3 public static class Node{ 4 public int value; 5 public Node left; 6 public Node right; 7 8 public Node(int value) { 9 this.value = value; 10 } 11 } 12 13 public static class ReturnType{ 14 public int maxDistance; 15 public int h; 16 17 public ReturnType(int maxDistance, int h) { 18 this.maxDistance = maxDistance; 19 this.h = h; 20 } 21 } 22 23 public static ReturnType process(Node head){ 24 if(head==null){ 25 return new ReturnType(0, 0); 26 } 27 ReturnType leftReturnType = process(head.left); 28 ReturnType rightReturnType = process(head.right); 29 int includeHeadDistance = leftReturnType.h+1+rightReturnType.h; 30 int p1 = leftReturnType.maxDistance; 31 int p2 = rightReturnType.maxDistance; 32 int resDistance = Math.max(Math.max(p1, p2), includeHeadDistance); 33 int hitselef = Math.max(leftReturnType.h, rightReturnType.h)+1;//自身高度 34 return new ReturnType(resDistance, hitselef); 35 } 36 37 public static int maxDistance(Node head){ 38 int [] record = new int[1]; 39 return posOrder(head, record); 40 } 41 42 public static int posOrder(Node head,int[] record){ 43 if(head==null){ 44 record[0] = 0; 45 return 0; 46 } 47 int lMax = posOrder(head.left, record); 48 int maxFromLeft = record[0]; 49 int rMax = posOrder(head.right, record); 50 int maxFromRight = record[0]; 51 int curNodeMax = maxFromLeft+maxFromRight+1; 52 record[0] = Math.max(maxFromLeft, maxFromRight)+1;//当前节点的高度 53 return Math.max(Math.max(lMax, rMax), curNodeMax); 54 } 55 56 public static void main(String[] args) { 57 /** 58 * 1 59 * 2 3 60 * 4 5 6 7 61 * 8 9 62 */ 63 Node head1 = new Node(1); 64 head1.left = new Node(2); 65 head1.right = new Node(3); 66 head1.left.left = new Node(4); 67 head1.left.right = new Node(5); 68 head1.right.left = new Node(6); 69 head1.right.right = new Node(7); 70 head1.left.left.left = new Node(8); 71 head1.right.left.right = new Node(9); 72 System.out.println(maxDistance(head1)); 73 74 75 Node head2 = new Node(1); 76 head2.left = new Node(2); 77 head2.right = new Node(3); 78 head2.right.left = new Node(4); 79 head2.right.right = new Node(5); 80 head2.right.left.left = new Node(6); 81 head2.right.right.right = new Node(7); 82 head2.right.left.left.left = new Node(8); 83 head2.right.right.right.right = new Node(9); 84 System.out.println(maxDistance(head2)); 85 } 86 }
