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如何在 AVL 树中进行插入操作？

[英]How to make insert operation in AVL Tree?

 原文  2021-11-20 09:37:11  9   1    c/ data-structures/ tree/ avl-tree

问题描述

我需要使用输入 {1,2,3,4,5,6,7,8,9,10,11,12,13} 制作 AVL 树。 但是，我的插入操作有问题。 这是我的代码：

#include<stdio.h>
#include<stdlib.h>
#define MAXNODE 100

typedef struct AvlNode *Position;
typedef struct AvlNode *AvlTree;

struct AvlNode
{
    int Element;
    AvlTree Left;
    AvlTree Right;
    int Height;
};

int Max(int a, int b)
{
    return (a > b)? a:b;

}

AvlTree MakeEmpty(AvlTree T)
{
    if(T != NULL)
    {
        MakeEmpty(T->Left);
        MakeEmpty(T->Right);
        free(T);
    }
    return NULL;
}

int Height(Position P)
{
    if(P == NULL)
    {
        return -1;
    }
    else
    {
        return P->Height;
    }
}

Position SingleRotateWithLeft(Position K2)
{
    Position K1;            //Rotate centered with K1
    K1 = K2->Left;          //Assign K1 as the left subtree of K2
    K2->Left = K1->Right;   //Link Y as left subtree of K2
    K1->Right = K2;
    K2->Height = Max(K2->Left->Height, K2->Right->Height) + 1;
    K1->Height = Max(K1->Left->Height, K2->Height) + 1;
    return K1;
}

Position SingleRotateWithRight(Position K2)
{
    Position K1;
    K1 =  K2->Right;
    K2->Right = K1->Left;
    K1->Left = K2;
    K2->Height = Max(K2->Right->Height, K2->Left->Height) + 1;
    K1->Height = Max(K1->Right->Height, K2->Height) + 1;
    return K1;
}

Position DoubleRotateWithLeft(Position K3)
{
    K3->Left = SingleRotateWithRight(K3->Left);
    return SingleRotateWithLeft(K3);
}

Position DoubleRotateWithRight(Position K3)
{
    K3->Right = SingleRotateWithLeft(K3->Right);
    return SingleRotateWithRight(K3);
}

/*Insert function*/
/*
-perform normal BST insertion
-current node must be one of the ancestors of the newly inserted node
-update height
-get balance factor(left subtree height-right subtree height)
-if balance factor > 1: current node is unbalance(left left case or left right case
-if balance factor < -1: current node is unbalance(right right left or right left case)
*/
AvlTree Insert(int X, AvlTree T)
{
    if(T == NULL)
    {
        T = (AvlTree)malloc(sizeof(struct AvlNode));
        if(T == NULL)
        {
            printf("Out of space!\n");
            return NULL;
        }
        else
        {
            T->Element = X;
            T->Height = 0;
            T->Left = NULL;
            T->Right = NULL;

        }
    }
    else if(X < T->Element)
    {
        T->Left = Insert(X, T->Left);
        if(T->Left->Height - T->Right->Height == 2)
        {
            if(X<T->Left->Element)
            {
                T = SingleRotateWithLeft(T);
            }
            else
            {
                T = DoubleRotateWithLeft(T);
            }
        }
    }
    else if(X > T->Element)
    {
        T->Right = Insert(X, T->Right);
        if(T->Right->Height - T->Left->Height == 2)
        {
            if(X > T->Right->Element)
            {
                T = SingleRotateWithRight(T);
            }
            else
            {
                T = DoubleRotateWithRight(T);
            }
        }
    }
    //X is in the tree already
    T->Height = Max(T->Left->Height, T->Right->Height) + 1;
    return T;
}



//To print the all edges in tree using level order traversal

void PrintTreeEdge(AvlTree T)
{
    AvlTree Queue[MAXNODE];
    int front;
    int rear;
    if(T == NULL)
    {
        return;
    }
    front = -1;
    rear = 0;
    Queue[rear] = T;
    while(front != rear)
    {
        front++;
        printf("%d-> ", Queue[front]->Element);
        if(Queue[front]->Left != NULL)
        {
            rear++;
            Queue[rear] = Queue[front]->Left;
        }
        if(Queue[front]->Right != NULL)
        {
            rear++;
            Queue[rear] = Queue[front]->Right;
        }
    }
}

int main()
{
    struct AvlNode* Tree = NULL;
    Tree = Insert(1, Tree);
    Insert(2, Tree);
    Insert(3, Tree);
    Insert(4, Tree);
    Insert(5, Tree);
    Insert(6, Tree);
    Insert(7, Tree);
    Insert(8, Tree);
    Insert(9, Tree);

    printf("The order is:\n");
    PrintTreeEdge(Tree);
    return 0;
}

PrintTreeEdge() function 用于使用级别顺序遍历来遍历和打印树。 每次运行这段代码都没有output，但是没有报错，所以不知道是哪一部分出错了。 这是 output： 输出

1 个解决方案

解决方案1
 0  2021-11-20 11:38:10

您的代码中基本上存在两个问题：

  1. 有几个地方可以访问NULL参考的->Height成员。 相反，当您需要从可能是NULL的参考中获取该信息时，请始终使用 function Height 。 在单次旋转功能和Insert function 中修复此问题。

  2. Insert function 可能会在根节点上执行旋转，因此它可能会返回不同的根引用。 这意味着调用者必须始终获取返回的值并将其分配给自己的根引用。 您尚未在主程序中执行此操作。

作为旁注，我发现打印 function 以按顺序打印树并带有深度缩进对调试很有用，因此您实际上可以看到它的结构。

这是纠正了 2 个问题的代码，以及附加的打印 function：

#include<stdio.h>
#include<stdlib.h>
#define MAXNODE 100

typedef struct AvlNode *Position;
typedef struct AvlNode *AvlTree;

struct AvlNode
{
    int Element;
    AvlTree Left;
    AvlTree Right;
    int Height;
};

int Max(int a, int b)
{
    return (a > b)? a:b;
}

AvlTree MakeEmpty(AvlTree T)
{
    if(T != NULL)
    {
        MakeEmpty(T->Left);
        MakeEmpty(T->Right);
        free(T);
    }
    return NULL;
}

int Height(Position P)
{
    if(P == NULL)
    {
        return -1;
    }
    else
    {
        return P->Height;
    }
}

Position SingleRotateWithLeft(Position K2)
{
    Position K1;            //Rotate centered with K1
    K1 = K2->Left;          //Assign K1 as the left subtree of K2
    K2->Left = K1->Right;   //Link Y as left subtree of K2
    K1->Right = K2;
    K2->Height = Max(Height(K2->Left), Height(K2->Right)) + 1;
    K1->Height = Max(Height(K1->Left), Height(K2)) + 1;
    return K1;
}

Position SingleRotateWithRight(Position K2)
{
    Position K1;
    K1 =  K2->Right;
    K2->Right = K1->Left;
    K1->Left = K2;
    K2->Height = Max(Height(K2->Right), Height(K2->Left)) + 1;
    K1->Height = Max(Height(K1->Right), Height(K2)) + 1;
    return K1;
}

Position DoubleRotateWithLeft(Position K3)
{
    K3->Left = SingleRotateWithRight(K3->Left);
    return SingleRotateWithLeft(K3);
}

Position DoubleRotateWithRight(Position K3)
{
    K3->Right = SingleRotateWithLeft(K3->Right);
    return SingleRotateWithRight(K3);
}

/*Insert function*/
/*
-perform normal BST insertion
-current node must be one of the ancestors of the newly inserted node
-update height
-get balance factor(left subtree height-right subtree height)
-if balance factor > 1: current node is unbalance(left left case or left right case
-if balance factor < -1: current node is unbalance(right right left or right left case)
*/
AvlTree Insert(int X, AvlTree T)
{
    if(T == NULL)
    {
        T = (AvlTree)malloc(sizeof(struct AvlNode));
        if(T == NULL)
        {
            printf("Out of space!\n");
            return NULL;
        }
        else
        {
            T->Element = X;
            T->Height = 0;
            T->Left = NULL;
            T->Right = NULL;
        }
    }
    else if(X < T->Element)
    {
        T->Left = Insert(X, T->Left);
        if(Height(T->Left) - Height(T->Right) == 2)
        {
            if(X < T->Left->Element)
            {
                T = SingleRotateWithLeft(T);
            }
            else
            {
                T = DoubleRotateWithLeft(T);
            }
        }
    }
    else if(X > T->Element)
    {
        T->Right = Insert(X, T->Right);
        if(Height(T->Right) - Height(T->Left) == 2)
        {
            if(X > T->Right->Element)
            {
                T = SingleRotateWithRight(T);
            }
            else
            {
                T = DoubleRotateWithRight(T);
            }
        }
    }
    //X is in the tree already
    T->Height = Max(Height(T->Left), Height(T->Right)) + 1;
    return T;
}


void printIndent(AvlTree T, int depth) {
    if (T == NULL) return;
    printIndent(T->Right, depth + 2);
    printf("%*d\n", depth + 1, T->Element);
    printIndent(T->Left, depth + 2);
}

//To print the all edges in tree using level order traversal
void PrintTreeEdge(AvlTree T)
{
    AvlTree Queue[MAXNODE];
    int front;
    int rear;
    if(T == NULL)
    {
        return;
    }
    front = -1;
    rear = 0;
    Queue[rear] = T;
    while(front != rear)
    {
        front++;
        printf("%d-> ", Queue[front]->Element);
        if(Queue[front]->Left != NULL)
        {
            rear++;
            Queue[rear] = Queue[front]->Left;
        }
        if(Queue[front]->Right != NULL)
        {
            rear++;
            Queue[rear] = Queue[front]->Right;
        }
    }
}

int main()
{
    struct AvlNode* Tree = NULL;
    Tree = Insert(1, Tree);
    Tree = Insert(2, Tree);
    Tree = Insert(3, Tree);
    Tree = Insert(4, Tree);
    Tree = Insert(5, Tree);
    Tree = Insert(6, Tree);
    Tree = Insert(7, Tree);
    Tree = Insert(8, Tree);
    Tree = Insert(9, Tree);
    printIndent(Tree, 0);
    printf("The order is:\n");
    PrintTreeEdge(Tree);
    return 0;
}

这将产生以下 output：

      9
    8
      7
  6
    5
4
    3
  2
    1
The order is:
4-> 2-> 6-> 1-> 3-> 5-> 8-> 7-> 9->

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