Java数据结构——二叉树的遍历(汇总)
二叉树的遍历分为深度优先遍历(DFS)和广度优先遍历(BFS)
DFS遍历主要有:
- 前序遍历
- 中序遍历
- 后序遍历
一、递归实现DFS
Node.java:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 | public class Node { private Object data; Node richild; Node lechild; public Object getData() { return data; } public void setData(Object data) { this .data = data; } public Node getRichild() { return richild; } public void setRichild(Node richild) { this .richild = richild; } public Node getLechild() { return lechild; } public void setLechild(Node lechild) { this .lechild = lechild; } public Node(Object data, Node lechild, Node richild) { super (); this .data = data; this .richild = richild; this .lechild = lechild; } public Node() { super (); } } |
递归遍历:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 | public class BTree { private static Node root; //构造树 public static void init() { Node node1 = new Node( "A" , null , null ); Node node2 = new Node( "B" , node1, null ); Node node3 = new Node( "C" , null , null ); Node node4 = new Node( "D" , node2, node3); Node node5 = new Node( "E" , null , null ); Node node6 = new Node( "F" , null , node5); Node node7 = new Node( "G" , node4, node6); root = node7; } //访问节点 public static void visited(Node n) { System.out.print(n.getData() + " " ); } //前序遍历 public static void preOrder(Node n) { if (n != null ) { visited(n); preOrder(n.getLechild()); preOrder(n.getRichild()); } } //中序遍历 public static void inOrder(Node n) { if (n != null ) { inOrder(n.getLechild()); visited(n); inOrder(n.getRichild()); } } //后序遍历 public static void postOrder(Node n) { if (n != null ) { postOrder(n.getLechild()); postOrder(n.getRichild()); visited(n); } } public static void main(String[] args) { init(); System.out.print( "递归前序:" ); preOrder(root); System.out.println(); System.out.print( "递归中序:" ); inOrder(root); System.out.println(); System.out.print( "递归后序:" ); postOrder(root); System.out.println(); } } |
二、非递归实现DFS(依靠栈)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 | //前序遍历 public static void preOrder(Node n) { System.out.print( "非递归前序:" ); Stack<Node> stack = new Stack<>(); int index = 0 ; while (n != null || index > 0 ) { while (n != null ) { System.out.print(n.getData() + " " ); stack.push(n); index++; n = n.getLechild(); } n = stack.pop(); index--; n = n.getRichild(); } } //中序遍历 public static void inOrder(Node n) { System.out.print( "非递归中序:" ); Stack<Node> stack = new Stack<>(); int index = 0 ; while (n != null || index > 0 ) { while (n != null ) { stack.push(n); index++; n = n.getLechild(); } n = stack.pop(); System.out.print(n.getData() + " " ); index--; n = n.getRichild(); } } //后序遍历 public static void postOrder(Node n) { System.out.print( "非递归后序:" ); Stack<Node> stack = new Stack<>(); int index = 0 ; Node lastVisited = null ; while (n != null || index > 0 ) { while (n != null ) { stack.push(n); index++; n = n.getLechild(); } n = stack.peek(); if (n.getRichild() == null || n.getRichild() == lastVisited) { System.out.print(n.getData() + " " ); lastVisited = n; index--; stack.pop(); n = null ; } else { n = n.getRichild(); } } } |
三、实现层序遍历(依靠队列)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | public static void LevenOrder(Node root) { if (root == null ) { return ; } Queue<Node> queue = new LinkedList<>(); queue.add(root); Node temp = null ; while (!queue.isEmpty()) { temp = queue.poll(); visited(temp); if (temp.getLeChild() != null ) { queue.add(temp.getLeChild()); } if (temp.getRChild() != null ) { queue.add(temp.getChild()); } } } |
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