二叉树

最新推荐文章于 2022-08-30 11:29:38 发布

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这篇博客主要探讨了二叉树的递归遍历方法，包括前序、中序和后序遍历。同时，讲解了如何计算二叉树的叶子节点数量以及如何求取二叉树的高度。最后，介绍了二叉树的复制与释放策略，对于理解和操作二叉树结构具有重要价值。

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递归遍历

#include<iostream>
using namespace std;

//二叉树
typedef struct BINARYNODE
{
    char ch;
    struct BINARYNODE* lchaild; //左子树
    struct BINARYNODE* rchaild; //右子树
}BinaryNode;

//递归
void Recursion(BinaryNode* root)
{
    if (root == NULL)
    {
        return;
    }

    //先访问根节点
    cout << root->ch<<" ";

    //在遍历左子树
    Recursion(root->lchaild);

    //在遍历右子树
    Recursion(root->rchaild);


    //前序遍历：根 左 右
    //中序遍历：左 根 右
    //后续遍历：左 右 根
}

void CreateBinaryTree()
{
    //创建节点
    BinaryNode node1 = { 'a',NULL,NULL };
    BinaryNode node2 = { 'b',NULL,NULL };
    BinaryNode node3 = { 'c',NULL,NULL };
    BinaryNode node4 = { 'd',NULL,NULL };
    BinaryNode node5 = { 'e',NULL,NULL };
    BinaryNode node6 = { 'f',NULL,NULL };
    BinaryNode node7 = { 'g',NULL,NULL };
    BinaryNode node8 = { 'h',NULL,NULL };

    //建立节点关系
    node1.lchaild = &node2;             
    node1.rchaild = &node6;             
    node2.rchaild = &node3;
    node3.lchaild = &node4;
    node3.rchaild = &node5;
    node6.rchaild = &node7;
    node7.lchaild = &node8;

    cout << "前序遍历" << endl;
    Recursion(&node1);

}

int main()
{
    CreateBinaryTree();
    return 0;
}

求二叉树叶子节点

//二叉树
typedef struct BINARYNODE
{
    char ch;
    struct BINARYNODE* lchaild; //左子树
    struct BINARYNODE* rchaild; //右子树
}BinaryNode;

void CaculateLeafNum(BinaryNode *root ,int* leafNum )
{
    if (root == NULL)
    {
        return;
    }

    if (root->lchaild == NULL && root->rchaild == NULL)
    {
        (*leafNum)++;
    }

    //左子树叶子节点数目
    CaculateLeafNum(root->lchaild, leafNum);

    //右子树叶子节点数目
    CaculateLeafNum(root->rchaild, leafNum);

}

void CreateBinaryTree()
{
    //创建节点
    BinaryNode node1 = { 'a',NULL,NULL };
    BinaryNode node2 = { 'b',NULL,NULL };
    BinaryNode node3 = { 'c',NULL,NULL };
    BinaryNode node4 = { 'd',NULL,NULL };
    BinaryNode node5 = { 'e',NULL,NULL };
    BinaryNode node6 = { 'f',NULL,NULL };
    BinaryNode node7 = { 'g',NULL,NULL };
    BinaryNode node8 = { 'h',NULL,NULL };

    //建立节点关系
    node1.lchaild = &node2;             
    node1.rchaild = &node6;             
    node2.rchaild = &node3;
    node3.lchaild = &node4;
    node3.rchaild = &node5;
    node6.rchaild = &node7;
    node7.lchaild = &node8;

    int num = 0;
    CaculateLeafNum(&node1, &num);
    cout << "叶子节点的数目" << num;

}

int main()
{
    CreateBinaryTree();




    return 0;
}

求二叉树的高

//二叉树
typedef struct BINARYNODE
{
    char ch;
    struct BINARYNODE* lchaild; //左子树
    struct BINARYNODE* rchaild; //右子树
}BinaryNode;


int CaculateTreeDepth(BinaryNode* root)
{
    if (root == NULL)
    {
        return 0;
    }

    int depth = 0;

    //求左子树的高
    int leftDepth = CaculateTreeDepth(root->lchaild);

    //求右子树的高
    int rightDepth = CaculateTreeDepth(root->rchaild);

    depth = leftDepth > rightDepth ? leftDepth + 1 : rightDepth + 1;
    return depth;
}


void CreateBinaryTree()
{
    //创建节点
    BinaryNode node1 = { 'a',NULL,NULL };
    BinaryNode node2 = { 'b',NULL,NULL };
    BinaryNode node3 = { 'c',NULL,NULL };
    BinaryNode node4 = { 'd',NULL,NULL };
    BinaryNode node5 = { 'e',NULL,NULL };
    BinaryNode node6 = { 'f',NULL,NULL };
    BinaryNode node7 = { 'g',NULL,NULL };
    BinaryNode node8 = { 'h',NULL,NULL };

    //建立节点关系
    node1.lchaild = &node2;
    node1.rchaild = &node6;
    node2.rchaild = &node3;
    node3.lchaild = &node4;
    node3.rchaild = &node5;
    node6.rchaild = &node7;
    node7.lchaild = &node8;


    cout << CaculateTreeDepth(&node1) << endl;


}

int main()
{
    CreateBinaryTree();

    return 0;
}

二叉树拷贝与释放

//二叉树
typedef struct BINARYNODE
{
    char ch;
    struct BINARYNODE* lchaild; //左子树
    struct BINARYNODE* rchaild; //右子树
}BinaryNode;

//遍历二叉树
void Recursion(BinaryNode* root)
{
    if (root == NULL)
    {
        return;
    }

    cout << root->ch;

    //遍历左子树
    Recursion(root->lchaild);

    //遍历右子树
    Recursion(root->rchaild);



}

//拷贝二叉树
BinaryNode* CopyBinaryTree(BinaryNode* root)
{
    if (root == NULL)
    {
        return NULL;
    }

    //拷贝右子树
    BinaryNode* lchild = CopyBinaryTree(root->lchaild);

    //拷贝左子树
    BinaryNode* rchild = CopyBinaryTree(root->rchaild);

    //创建节点
    BinaryNode* newnode = new BinaryNode;
    newnode->ch = root->ch;
    newnode->lchaild = lchild;
    newnode->rchaild = rchild;



    return newnode;
}

//释放二叉树内存
void FreeSpaceBinaryTree(BinaryNode* root)
{
    if (root != NULL)
    {
        return;
    }

    //释放左子树
    FreeSpaceBinaryTree(root->lchaild);

    //释放右子树
    FreeSpaceBinaryTree(root->rchaild);

    //释放当前节点
    delete root;
}


void CreateBinaryTree()
{
    //创建节点
    BinaryNode node1 = { 'a',NULL,NULL };
    BinaryNode node2 = { 'b',NULL,NULL };
    BinaryNode node3 = { 'c',NULL,NULL };
    BinaryNode node4 = { 'd',NULL,NULL };
    BinaryNode node5 = { 'e',NULL,NULL };
    BinaryNode node6 = { 'f',NULL,NULL };
    BinaryNode node7 = { 'g',NULL,NULL };
    BinaryNode node8 = { 'h',NULL,NULL };

    //建立节点关系
    node1.lchaild = &node2;
    node1.rchaild = &node6;
    node2.rchaild = &node3;
    node3.lchaild = &node4;
    node3.rchaild = &node5;
    node6.rchaild = &node7;
    node7.lchaild = &node8;

    BinaryNode* root = CopyBinaryTree(&node1);
    Recursion(root);
    FreeSpaceBinaryTree(root);
}

int main()
{
    CreateBinaryTree();

    return 0;
}