二叉搜索树（Binary Search Tree）原理及实现（Java）

  二叉搜索树（Binary Search Tree）—— 二叉树中非常经典的一种数据结构。
满足条件
  左子树的所有节点小于root；
  右子树的所有节点大于root；
  节点值不能重复。

缺陷
  Search Best case: O(logN)，Worst case：O(N)
  Insert Best case: O(logN)，Worst case：O(N)
  当BST不平衡时（N为BST中节点的数量），极端情况下类似于单链表，search和insert操作的时间复杂度均为O(N)。


Operation

    public void insert(T v); // 将新的节点插入BST
    public boolean search(T v); // 查找当前BST中是否有节点的值为v
    public void delete(T v); // 删除BST中含有v的节点
    public int getSize(); // 返回BST节点数量

java代码
  以如下BST为例测试上述操作的正确性

  BST.java

public class BST> {
    private BSTNode root;
    private int size;

    private class BSTNode {
        private T value;
        private BSTNode left;
        private BSTNode right;

        BSTNode(T value) {
            this.value = value;
        }
    }

    BST(T value) {
        this.root = new BSTNode(value);
        this.size += 1;
    }

    
    public void insert(T v) {
        root = insertHelper(root, v);
        this.size += 1;
    }

    private BSTNode insertHelper(BSTNode curNode, T value) {
        if (curNode == null) {
            return new BSTNode(value);
        } else if (curNode.value.compareTo(value) > 0) {
            curNode.left = insertHelper(curNode.left, value);
        } else if (curNode.value.compareTo(value) < 0) {
            curNode.right = insertHelper(curNode.right, value);
        }
        return curNode;
    }

    
    public boolean search(T v) {
        return searchHelper(root, v);
    }

    private boolean searchHelper(BSTNode curNode, T value) {
        if (curNode == null) {
            return false;
        } else if (curNode.value.compareTo(value) == 0) {
            return true;
        } else if (curNode.value.compareTo(value) > 0) {
            return searchHelper(curNode.left, value);
        } else {
            return searchHelper(curNode.right, value);
        }
    }

    
    public void delete(T v) {
        root = deleteHelper(root, v);
    }

    private BSTNode deleteHelper(BSTNode curNode, T value) {
        if (curNode == null) {
            return null;
        } else if (curNode.value.compareTo(value) > 0) {
            curNode.left = deleteHelper(curNode.left, value);
        } else if (curNode.value.compareTo(value) < 0) {
            curNode.right = deleteHelper(curNode.right, value);
        } else {
            if (checkLeaf(curNode)) {
                this.size -= 1;
                return null;
            } else if (checkOnlyLeftChild(curNode)) {
                this.size -= 1;
                return curNode.left;
            } else if (checkOnlyRightChild(curNode)) {
                this.size -= 1;
                return curNode.right;
            } else {
                BSTNode successor = getSuccessor(curNode);
                curNode.value = successor.value;
                successor.value = value;
                curNode.right = deleteHelper(curNode.right, value);
            }
        }
        return curNode;
    }

    
    private BSTNode getSuccessor(BSTNode curNode) {
        return getSuccessorHelper(curNode.right);
    }

    private BSTNode getSuccessorHelper(BSTNode curNode) {
        if (curNode.left == null) {
            return curNode;
        } else {
            return getSuccessorHelper(curNode.left);
        }
    }

    private boolean checkLeaf(BSTNode curNode) {
        return curNode.left == null && curNode.right == null;
    }

    private boolean checkOnlyLeftChild(BSTNode curNode) {
        return curNode.left != null && curNode.right == null;
    }

    private boolean checkOnlyRightChild(BSTNode curNode) {
        return curNode.right != null && curNode.left == null;
    }

    public int getSize() {
        return size;
    }
}

  Test.java

public class Test {

    public static void main(String[] args) {
        BST test = new BST<>(7);
        test.insert(3);
        test.insert(15);
        test.insert(1);
        test.insert(6);
        test.insert(8);
        test.insert(9);
        test.insert(4);

        System.out.println(test.getSize());     // 8
        System.out.println(test.search(1));  // 删除叶子节点
        test.delete(1);
        System.out.println(test.search(1));
        System.out.println(test.search(6));  // 删除只有一个child的节点
        test.delete(6);
        System.out.println(test.search(6));
        System.out.println(test.search(7));  // 删除有两个child的节点
        test.delete(7);
        System.out.println(test.search(7));
        System.out.println(test.getSize());     // 5
    }

}