AVL树练习

Posted 2020-10-08 Al_X

#ifndef MY_AVLTREE
#define MY_AVLTREE
#include<iostream>
#include<cmath>
#define PRINTS(x) std::cout<<x<<std::ends

struct AvlNode;
typedef AvlNode* AvlTree;
typedef AvlNode* Position;
struct AvlNode {
    int val;
    AvlTree lTree, rTree; 
    int Height;
    AvlNode() :lTree(NULL), rTree(NULL) {}
};

AvlTree MakeEmpty(AvlTree T);
Position Find(AvlTree T,int val);
Position FindMin(AvlTree T);
Position FindMax(AvlTree T);
AvlTree Insert(AvlTree &T, int val);
AvlTree Delete(AvlTree &T, int val);
int Retrieve(Position p);
AvlTree SingleRotateWithLeft(AvlTree T);
AvlTree SingleRotateWithRight(AvlTree T);
AvlTree DoubleRotateWithLeft(AvlTree T);
AvlTree DoubleRotateWithRight(AvlTree T);
void Print(AvlTree T)
{

    if (T == NULL)return;
    Print(T->lTree);
    PRINTS(T->val);
    Print(T->rTree);
}
//用于测试
void InsAndPrint(AvlTree &T, int val)
{
    Insert(T, val);
    Print(T);
    std::cout << std::endl;
}
//用于测试
void DelAndPrint(AvlTree &T, int val)
{
    Delete(T, val);
    Print(T);
    std::cout << std::endl;
}

int main()
{
    //测试
    AvlTree Tree=NULL;
    InsAndPrint(Tree, 1);
    InsAndPrint(Tree, 1);
    InsAndPrint(Tree, 4);
    InsAndPrint(Tree, 5);
    InsAndPrint(Tree, 1);
    InsAndPrint(Tree, 4);
    InsAndPrint(Tree, 8);
    InsAndPrint(Tree, 1);
    InsAndPrint(Tree, 0);
    InsAndPrint(Tree, 1919);
    InsAndPrint(Tree, 810);
    InsAndPrint(Tree, 114514);
    InsAndPrint(Tree, 1551);
    InsAndPrint(Tree, 6655);
    DelAndPrint(Tree, 1);
    DelAndPrint(Tree, 4);
    DelAndPrint(Tree, 1551);
    DelAndPrint(Tree, 6655);
    DelAndPrint(Tree, 114514);
    DelAndPrint(Tree, 810);
    DelAndPrint(Tree, 1919);
    DelAndPrint(Tree, 5);
    DelAndPrint(Tree, 0);
    DelAndPrint(Tree, 8);
    //system("pause");
}

AvlTree MakeEmpty(AvlTree T)
{
    if (T->lTree) MakeEmpty(T->lTree);
    if (T->rTree) MakeEmpty(T->rTree);
    delete(T);
    return NULL;
}

Position Find(AvlTree T, int val)
{
    if (T == NULL)return NULL;
    if (val == T->val) return T;
    if (val < T->val)return Find(T->lTree, val);
    if (val > T->val)return Find(T->rTree, val);
}

Position FindMin(AvlTree T)
{
    if (T->lTree == NULL) return T;
    else return FindMin(T->lTree);
}

Position FindMax(AvlTree T)
{
    if (T->rTree == NULL) return T;
    else return FindMax(T->rTree);
}

int getHeight(AvlTree T)
{
    if (T == NULL) return 0;
    else return T->Height;
}

void UpdateHeight(AvlTree T)
{
    if (T == NULL)return;
    T->Height = (getHeight(T->rTree) > getHeight(T->lTree)) ? (getHeight(T->rTree) + 1) : (getHeight(T->lTree) + 1);
}

AvlTree Insert(AvlTree &T, int val)
{
    if (T == NULL)
    {
        T = new AvlNode;
        T->Height = 1;
        T->val = val;
    }
    else if (val == T->val) return T;
    else if (val < T->val) T->lTree = Insert(T->lTree, val);
    else T->rTree = Insert(T->rTree, val);
    if (abs(getHeight(T->lTree)-getHeight(T->rTree))>=2)
    {
        if (getHeight(T->lTree) > getHeight(T->rTree))
        {
            if (val > T->lTree->val) T = DoubleRotateWithLeft(T);
            else T = SingleRotateWithLeft(T);
        }
        else
        {
            if (val < T->rTree->val) T = DoubleRotateWithRight(T);
            else T = SingleRotateWithRight(T);
        }
    }
    UpdateHeight(T);
    return T;
}

AvlTree Delete(AvlTree &T, int val)
{
    if (T == NULL)return NULL;
    if (val == T->val)
    {
        AvlTree nextT;
        if (T->lTree != NULL) {
            nextT = T->lTree;
            AvlTree i;
            if (nextT->rTree == NULL) nextT->rTree = T->rTree;
            else
            {
                for (i = nextT; i->rTree->rTree; i = i->rTree);
                i->rTree = T->rTree;
            }
        }
        else nextT = T->rTree;
        delete(T);
        T = nextT;
        if (T == NULL)return NULL;
    }
    else if (val < T->val)T->lTree = Delete(T->lTree, val);
    else if (val > T->val)T->rTree = Delete(T->rTree, val);
    if (abs(getHeight(T->lTree) - getHeight(T->rTree)) >= 2)
    {
        if (getHeight(T->lTree) > getHeight(T->rTree))
        {
            if (getHeight(T->lTree->lTree) >= getHeight(T->lTree->rTree)) T = SingleRotateWithLeft(T);
            else T = DoubleRotateWithLeft(T);
        }
        else
        {
            if (getHeight(T->rTree->rTree) >= getHeight(T->rTree->lTree)) T = SingleRotateWithRight(T);
            else T = DoubleRotateWithRight(T);
        }
    }
    UpdateHeight(T);
    return T;
}

int Retrieve(Position p)
{
    return p->val;
}
 
AvlTree SingleRotateWithLeft(AvlTree T)
{
    AvlTree newT = T->lTree;
    T->lTree = newT->rTree;
    newT->rTree = T;
    return newT;
}

AvlTree SingleRotateWithRight(AvlTree T)
{
    AvlTree newT = T->rTree;
    T->rTree = newT->lTree;
    newT->lTree = T;
    return newT;
}

AvlTree DoubleRotateWithLeft(AvlTree T)
{
    T->lTree = SingleRotateWithRight(T->lTree);
    T = SingleRotateWithLeft(T);
    return T;
}

AvlTree DoubleRotateWithRight(AvlTree T)
{
    T->rTree = SingleRotateWithLeft(T->rTree);
    T = SingleRotateWithRight(T);
    return T;
}
#endif

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