1066. Root of AVL Tree (25)

最新推荐文章于 2019-11-09 15:48:28 发布

原创最新推荐文章于 2019-11-09 15:48:28 发布 · 339 阅读

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本文介绍了一种自平衡二叉搜索树——AVL树的实现方法，重点讲解了单旋转与双旋转的原理及操作步骤，并通过一个C++程序实例展示了如何插入节点并保持树的平衡。

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1.这道题比较重要，主要考察AVL树的建立

2.需要掌握单旋转，双旋转，插入等操作

//#include<string>
//#include<stack>
//#include<unordered_set>
//#include <sstream>
//#include "func.h"
//#include <list>
#include <iomanip>
#include<unordered_map>
#include<set>
#include<queue>
#include<map>
#include<vector>
#include <algorithm>
#include<stdio.h>
#include<iostream>
#include<string>
#include<memory.h>
#include<limits.h>
#include<stack>
using namespace std;
/*
5
88 70 61 96 120

7
88 70 61 96 120 95 65
*/
struct AvlNode{
	int val, height;
	AvlNode*l, *r;
	AvlNode() :val(-1), height(-1), l(NULL), r(NULL){};
	AvlNode(int x) :val(x), height(0), l(NULL), r(NULL){};
};
static int Height(AvlNode* T)
{
	if (T == NULL) return -1;
	else return T->height;
}
static AvlNode* SingleRotateLeft(AvlNode* k2)
{
	AvlNode*k1 = k2->l;
	k2->l = k1->r;
	k1->r = k2;
	k2->height = max(Height(k2->l), Height(k2->r)) + 1;
	k1->height = max(Height(k1->l), k2->height) + 1;
	return k1;
}
static AvlNode* SingleRotateRight(AvlNode* k1)
{
	AvlNode*k2 = k1->r;
	k1->r = k2->l;
	k2->l = k1;
	k1->height = max(Height(k1->l), Height(k1->r)) + 1;
	k2->height = max(Height(k2->r), k1->height) + 1;
	return k2;
}
static AvlNode* DoubleRotateLeft(AvlNode* k3)
{
	k3->l = SingleRotateRight(k3->l);
	return SingleRotateLeft(k3);
}

static AvlNode* DoubleRotateRight(AvlNode* k3)
{
	k3->r = SingleRotateLeft(k3->r);
	return SingleRotateRight(k3);
}

static AvlNode* Insert(int x, AvlNode*T)
{
	if (T == NULL)
		T = new AvlNode(x);
	else if (x < T->val)
	{
		T->l = Insert(x, T->l);
		if (Height(T->l) - Height(T->r) == 2)
		{
			if (x < T->l->val)
				T = SingleRotateLeft(T);
			else
				T = DoubleRotateLeft(T);
		}
	}
	else if (x > T->val)
	{
		T->r = Insert(x, T->r);
		if (Height(T->r) - Height(T->l) == 2)
		{
			if (x>T->r->val)
				T = SingleRotateRight(T);
			else
				T = DoubleRotateRight(T);
		}
	}
	T->height = max(Height(T->l), Height(T->r)) + 1;
	return T;
}
int main(void)
{
	int n;
	cin >> n;
	AvlNode* root = NULL;
	for (int i = 0; i < n; i++)
	{
		int tmp;
		cin >> tmp;
		root=Insert(tmp, root);
	}
	cout << root->val << endl;
	return 0;
}