Geeks Splay Tree Insert 树的插入操作

Splay树的插入操作，只需要处理好插入节点的孩子节点就可以了，最重要的是不要破坏了BST的基本规则。

因为高度并不是Splay树的首要因素，所以插入的时候也是使用splay操作，然后在根节点插入。

参考：http://www.geeksforgeeks.org/splay-tree-set-2-insert-delete/

对比一下使用插入创建的树和手工创建数的区别，先序遍历的结果：

#pragma once
#include<stdio.h>
#include <stdlib.h>

class SplayTree_Insertion
{
	struct Node
	{
		int key;
		Node *left, *right;
		Node(int k) : key(k), left(NULL), right(NULL) {}
		~Node()
		{
			if (left) delete left, left = NULL;
			if (right) delete right, right = NULL;
		}
	};

	Node *rightRotate(Node *x)
	{
		Node *y = x->left;
		x->left = y->right;
		y->right = x;

		return y;
	}

	Node *leftRotate(Node *x)
	{
		Node *y = x->right;
		x->right = y->left;
		y->left = x;

		return y;
	}

	Node *splay(Node *root, const int key)
	{
		if (!root || key == root->key) return root;

		if (key < root->key)
		{
			if (!root->left) return root;

			if (key < root->left->key)
			{
				root->left->left = splay(root->left->left, key);
				root = rightRotate(root);//不应root->left
			}
			else if (root->left->key < key)
			{
				root->left->right = splay(root->left->right, key);
				if (root->left->right) root->left = leftRotate(root->left);
			}
			return root->left? rightRotate(root) : root;
		}
		if (!root->right) return root;
		if (root->right->key < key)
		{
			root->right->right = splay(root->right->right, key);
			root = leftRotate(root);
		}
		else if (key < root->right->key)
		{
			root->right->left = splay(root->right->left, key);
			if (root->right->left) root->right = rightRotate(root->right);
		}
		return root->right? leftRotate(root) : root;
	}

	Node *insert(Node *root, int k)
	{
		if (!root) return new Node(k);

		root = splay(root, k);

		if (root->key == k) return root;

		Node *newNode = new Node(k);

		//learn how to handle the insertion is the best way.
		if (k < root->key)
		{
			newNode->right = root;
			newNode->left = root->left;
			root->left = NULL;
		}
		else
		{
			newNode->left = root;
			newNode->right = root->right;
			root->right = NULL;
		}
		return newNode;
	}

	void preOrder(Node *root)
	{
		if (root != NULL)
		{
			printf("%d ", root->key);
			preOrder(root->left);
			preOrder(root->right);
		}
	}
public:
	SplayTree_Insertion()
	{
		Node *root = new Node(100);
		root->left = new Node(50);
		root->right = new Node(200);
		root->left->left = new Node(40);
		root->left->left->left = new Node(30);
		root->left->left->left->left = new Node(20);
		root = insert(root, 25);
		printf("Preorder traversal of the modified Splay tree is \n");
		preOrder(root);
		putchar('\n');

		delete root;

		runInsert();
	}

	void runInsert()
	{
		Node *root = NULL;
		int keys[] = {100, 50, 200, 40, 30, 20, 25};
		int n = sizeof(keys) / sizeof(keys[0]);
		for (int i = 0; i < n; i++)
		{
			root = insert(root, keys[i]);
		}

		printf("Inser create Preorder traversal Splay tree is \n");
		preOrder(root);
		putchar('\n');

		delete root;
	}
};

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