搜索树

1. 二叉搜索树

1.1 二叉搜索树概念

若左子树不为空，则左子树上所有节点的值都小于根节点的值

若右子树不为空，则右子树上所有节点的值都大于根节点的值

如果中序遍历( 左根右 )，结果从小到大有序。所以，二叉搜索树也叫二叉排序树

1.2 二叉搜索树的实现

class BinarySearchTree {

    static class TreeNode {
        public int val;
        public TreeNode left;
        public TreeNode right;

        public TreeNode(int val) {
            this.val = val;
        }
    }

    public TreeNode root;

    // 查找
    public boolean search(int val) {
        TreeNode cur = root;
        while (cur != null) {
            if (val == cur.val) {
                return true;
            }else if (val < cur.val) {
                cur = cur.left;
            }else {
                cur = cur.right;
            }
        }
        return false;
    }

    // 插入
    public void insert(int val) {
        TreeNode node = new TreeNode(val);
        if (root == null) {
            root = node;
            return;
        }

        // 先让cur走到null
        TreeNode cur = root;
        TreeNode prev = null;
        while (cur != null) {
            if (val > cur.val) {
                prev = cur;
                cur = cur.right;
            }else if (val < cur.val){
                prev = cur;
                cur = cur.left;
            }else {
                return;
            }
        }

        // 插入
        if (val > prev.val) {
            prev.right = node;
        }else {
            prev.left = node;
        }
    }

    // 删除节点
    public void remove(int val) {
        TreeNode cur = root;
        TreeNode prev = root;
        while (cur != null) {
            if (val > cur.val) {
                prev = cur;
                cur = cur.right;
            } else if (val < cur.val) {
                prev = cur;
                cur = cur.left;
            } else {
                removeNode(prev,cur);
                return;
            }
        }
    }

    private void removeNode(TreeNode parent,TreeNode cur) {
        if (cur.left == null) {
            if (cur == root) {
                root = cur.right;
            } else if (cur == parent.left) {
                parent.left = cur.right;
            }else {
                parent.right = cur.right;
            }
        } else if (cur.right == null) {
            if (cur == root) {
                root = cur.left;
            }else if (cur == parent.left) {
                parent.left = cur.left;
            }else {
                parent.right = cur.left;
            }
        } else {
            TreeNode cp = cur;
            TreeNode c = cur.right;
            while (c.left != null) {
                cp = c;
                c = c.left;
            }
            cur.val = c.val;
            if (cp.left == c) {
                cp.left = c.right;
            }else {
                cp.right = c.right;
            }
        }

    }

}

class Test {
    public static void main(String[] args) {
        BinarySearchTree binarySearchTree = new BinarySearchTree();
        binarySearchTree.insert(10);
        binarySearchTree.insert(7);
        binarySearchTree.insert(15);
        binarySearchTree.insert(3);
        binarySearchTree.insert(20);
        binarySearchTree.insert(16);
        binarySearchTree.insert(12);
        binarySearchTree.remove(15);

     }
}

删除思路分三种情况：

1. 删除节点左边为空