二叉树的基本操作及其代码实现

淩亂°似流年 2023-09-28 23:21 9阅读 0赞

**本文实现了如下二叉树的基本操作：**  
1.手动创建一棵二叉树 返回这棵树的根节点  
2.前序遍历  
3.中序遍历  
4.后序遍历  
5.迭代获取树中节点的个数  
6.递归获取节点的个数  
7.迭代获取叶子节点的个数  
8.递归获取叶子节点的个数  
9.获取第K层节点的个数  
10.获取二叉树的高度  
11.检测值为value的元素是否存在  
12.层序遍历  
13.判断一棵树是不是完全二叉树

**代码：**

package TreeOperation;
    
    //二叉树的基本操作
    
    import java.util.ArrayDeque;
    import java.util.Deque;
    import java.util.LinkedList;
    
    public class BinaryTree {
        
    
        public static int nodeSize;
        public static int leafSize = 0;
    
        //节点
        static class TreeNode {
        
            public char val;
            public TreeNode left;//左孩子的引用
            public TreeNode right;//右孩子的引用
    
            public TreeNode(char val) {
        
                this.val = val;
            }
        }
    
        /**
         * 创建一棵二叉树 返回这棵树的根节点
         *
         * @return
         */
        public static TreeNode createTree() {
        
            TreeNode a = new TreeNode('A');
            TreeNode b = new TreeNode('B');
            TreeNode c = new TreeNode('C');
            TreeNode d = new TreeNode('D');
            TreeNode e = new TreeNode('E');
            TreeNode f = new TreeNode('F');
            TreeNode g = new TreeNode('G');
            TreeNode h = new TreeNode('H');
    
            // 手动构建其关系
            a.left = b;
            a.right = c;
            b.left = d;
            b.right = e;
            c.left = f;
            c.right = g;
            d.left = null;
            d.right = null;
            e.left = null;
            e.right = h;
            f.left = null;
            f.right = null;
            g.left = null;
            g.right = null;
            h.left = null;
            h.right = null;
    
            // 返回根结点即可
            return a;
        }
    
        // 前序遍历
        public static void preOrder(TreeNode root) {
        
            Deque<TreeNode> stack = new ArrayDeque<>();
            if (root != null) {
        
                stack.push(root);
            }
            while (!stack.isEmpty()) {
        
                TreeNode cur = stack.pop();
                System.out.print(cur.val + " ");
                if (cur.right != null) {
        
                    stack.push(cur.right);
                }
                if (cur.left != null) {
        
                    stack.push(cur.left);
                }
            }
        }
    
        // 中序遍历
        static void inOrder(TreeNode root) {
        
            Deque<TreeNode> stack = new ArrayDeque<>();
            while (root != null || !stack.isEmpty()) {
        
                if (root != null) {
        
                    stack.push(root);
                    root = root.left;
                } else {
        
                    TreeNode cur = stack.pop();
                    System.out.print(cur.val + " ");
                    root = cur.right;
                }
            }
        }
    
        // 后序遍历
        static void postOrder(TreeNode root) {
        
            Deque<TreeNode> stack = new ArrayDeque<>();
            TreeNode cur = root;
            TreeNode tail = null;
    
            while (cur != null || !stack.isEmpty()) {
        
                while (cur != null) {
        
                    stack.push(cur);
                    cur = cur.left;
                }
                TreeNode top = stack.peek();
                if (top.right == null) {
        
                    System.out.print(top.val + " ");
                    tail = top;
                    stack.pop();
                } else if (top.right == tail) {
        
                    System.out.print(top.val + " ");
                    tail = top;
                    stack.pop();
                } else {
        
                    cur = top.right;
                }
            }
        }
    
        /**
         * 获取树中节点的个数：遍历思路
         */
        static void size(TreeNode root) {
        
            Deque<TreeNode> queue = new ArrayDeque<>();
            if (root != null) {
        
                queue.offer(root);
            }
            while (!queue.isEmpty()) {
        
                int size = queue.size();
                nodeSize += size;
                while (size-- != 0) {
        
                    TreeNode cur = queue.poll();
                    if (cur.left != null) {
        
                        queue.offer(cur.left);
                    }
                    if (cur.right != null) {
        
                        queue.offer(cur.right);
                    }
                }
            }
        }
    
        /**
         * 获取节点的个数：子问题的思路
         *
         * @param root
         * @return
         */
        static int size2(TreeNode root) {
        
            if (root == null) {
        
                return 0;
            }
            int leftCount = size2(root.left);
            int rightCount = size2(root.right);
            return leftCount + rightCount + 1;
        }
    
        /*
         获取叶子节点的个数：遍历思路
         */
        static void getLeafNodeCount1(TreeNode root) {
        
            Deque<TreeNode> queue = new ArrayDeque<>();
            if (root != null) {
        
                queue.offer(root);
            }
            while (!queue.isEmpty()) {
        
                int size = queue.size();
                while (size-- != 0) {
        
                    TreeNode cur = queue.poll();
                    if (cur.left == null && cur.right == null) {
        
                        leafSize++;
                    }
                    if (cur.left != null) {
        
                        queue.offer(cur.left);
                    }
                    if (cur.right != null) {
        
                        queue.offer(cur.right);
                    }
                }
            }
        }
    
        /*
         获取叶子节点的个数：子问题
         */
        static int getLeafNodeCount2(TreeNode root) {
        
            if (root == null) {
        
                return 0;
            }
            if (root.left == null && root.right == null) {
        
                return 1;
            }
            int left = getLeafNodeCount2(root.left);
            int right = getLeafNodeCount2(root.right);
            return left + right;
        }
    
        /*
        获取第K层节点的个数
         */
        static int getKLevelNodeCount(TreeNode root, int k) {
        
            Deque<TreeNode> queue = new ArrayDeque<>();
            if (root != null) {
        
                queue.offer(root);
            }
            while (!queue.isEmpty()) {
        
                int size = queue.size();
                k--;
                if (k == 0) {
        
                    return size;
                }
                while (size-- != 0) {
        
                    TreeNode cur = queue.poll();
                    if (cur.left != null) {
        
                        queue.offer(cur.left);
                    }
                    if (cur.right != null) {
        
                        queue.offer(cur.right);
                    }
                }
            }
            return 0;
        }
    
        /*
         获取二叉树的高度
         时间复杂度：O(N)
         */
        static int getHeight(TreeNode root) {
        
            if (root == null) {
        
                return 0;
            }
            int left = getHeight(root.left);
            int right = getHeight(root.right);
            return Math.max(left, right) + 1;
        }
    
        // 检测值为value的元素是否存在
        static TreeNode find(TreeNode root, char val) {
        
            if (root == null) {
        
                return null;
            }
            if (root.val == val) {
        
                return root;
            }
            TreeNode left = find(root.left, val);
            if (left != null) {
        
                return left;
            }
            TreeNode right = find(root.right, val);
            if (right != null) {
        
                return right;
            }
            return null;
        }
    
        //层序遍历
        static void levelOrder(TreeNode root) {
        
            Deque<TreeNode> queue = new ArrayDeque<>();
            if (root != null) {
        
                queue.offer(root);
            }
            while (!queue.isEmpty()) {
        
                int size = queue.size();
                while (size-- != 0) {
        
                    TreeNode cur = queue.poll();
                    System.out.print(cur.val + " ");
                    if (cur.left != null) {
        
                        queue.offer(cur.left);
                    }
                    if (cur.right != null) {
        
                        queue.offer(cur.right);
                    }
                }
            }
        }
    
        // 判断一棵树是不是完全二叉树
        static boolean isCompleteTree(TreeNode root) {
        
            if (root == null) {
        
                return true;
            }
    
            Deque<TreeNode> queue = new LinkedList<>();
            queue.offer(root);
    
            //层序遍历找到第一个null结点
            while (true) {
        
                TreeNode cur = queue.poll();
                if (cur == null) {
        
                    break;
                }
                queue.offer(cur.left);
                queue.offer(cur.right);
            }
            while (!queue.isEmpty()) {
        
                TreeNode cur = queue.poll();
                if (cur != null) {
        
                    return false;
                }
            }
            
            return true;
        }
    
        //验证
        public static void main(String[] args) {
        
            TreeNode root = createTree();
            System.out.println("-------------------------");
            System.out.println("先序遍历：");
            preOrder(root);
            System.out.println();
            System.out.println("-------------------------");
            System.out.println("中序遍历：");
            inOrder(root);
            System.out.println();
            System.out.println("-------------------------");
            System.out.println("后序遍历：");
            postOrder(root);
            System.out.println();
            System.out.println("-------------------------");
            System.out.println("层序遍历：");
            levelOrder(root);
            System.out.println();
            System.out.println("-------------------------");
            size(root);
            System.out.println("层序遍历求得树的节点数为：" + nodeSize);
            System.out.println("-------------------------");
            System.out.println("递归求得树的节点数为：" + size2(root));
            System.out.println("-------------------------");
            getLeafNodeCount1(root);
            System.out.println("层序遍历求得树的叶子数为：" + leafSize);
            System.out.println("-------------------------");
            System.out.println("递归求得树的节点数为：" + getLeafNodeCount2(root));
            System.out.println("-------------------------");
            System.out.println("第k层的节点数为：" + getKLevelNodeCount(root, 4));
            System.out.println("-------------------------");
            System.out.println("树的高度为：" + getHeight(root));
            System.out.println("-------------------------");
            System.out.println("查找val并输出：" + find(root, 'F').val);
            System.out.println("-------------------------");
            System.out.println("判断是否是完全二叉树：" + isCompleteTree(root));
        }
    }