树2-二叉树拷贝, 遍历, 计算叶子结点和高度

树2-二叉树拷贝, 遍历, 计算叶子结点和高度

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二叉树结点

typedef struct BinaryNode{
    char ch;
    struct BinaryNode *lChild;
    struct BinaryNode *rChild;
} BinaryNode;
//叶子结点的数量
int sum;

二叉树遍历

前序

//递归遍历(前序)
void Recursion(BinaryNode *root){
    //中左右
    if(root==NULL) return; //root为空return
    cout << root->ch;
    //左子树
    Recursion(root->lChild);
    //右子树
    Recursion(root->rChild);
}

中序

//递归遍历(中序)
void Recursion2(BinaryNode *root){
    if(root==NULL) return; //root为空return
    //先遍历左子树
    Recursion2(root->lChild);
    //再访问遍历根节点
    cout << root->ch;
    //再遍历右子树 
    Recursion2(root->rChild);
}

后序

//递归遍历(后序)
void Recursion3(BinaryNode *root){
    if(root==NULL) return; //root为空return
    //先遍历左子树
    Recursion3(root->lChild);
    //再遍历右子树 
    Recursion3(root->rChild);
    //再访问遍历根节点
    cout << root->ch;
}

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求叶子节点的数量

//在成员位置定义一个sum
//求叶子节点的数目(没有子结点)
void CalculateLeafNum(BinaryNode *root){
    if(root==NULL) return;
    if(root->lChild==NULL && root->rChild==NULL){
        sum++;
    };
    //先遍历左子树
    CalculateLeafNum(root->lChild);
    //再遍历右子树 
    CalculateLeafNum(root->rChild);    
}

二叉树拷贝

BinaryNode* CopyBinaryTree(BinaryNode *root){
    if(root==NULL){
        return NULL;
    }
    //拷贝左子树
    BinaryNode *lchild = CopyBinaryTree(root->lChild);
    //拷贝右子树
    BinaryNode *rchild = CopyBinaryTree(root->rChild);

    //创建结点
    BinaryNode *newNode = (BinaryNode*)malloc(sizeof(BinaryNode));
    newNode->ch = root->ch;
    newNode->lChild = lchild;
    newNode->rChild = rchild;
    return newNode;
}

释放二叉树

void FreeSpaceBinaryTree(BinaryNode* root){
    if(root==NULL){
        return;
    }
    //释放左子树
    FreeSpaceBinaryTree(root->lChild);
    //释放右子树 
    FreeSpaceBinaryTree(root->rChild);
    //释放当前结点
    free(root);
}

求二叉树高度

//求二叉树高度
int CalculateTreeDepth(BinaryNode *root){
    if(root==NULL) return 0;
    int depth = 0;
    //求左子树高度
    int leftDepth = CalculateTreeDepth(root->lChild);
    //求右子树高度
    int rightDepth = CalculateTreeDepth(root->rChild);
    //比较高度
    depth = leftDepth>rightDepth ? leftDepth+1 : rightDepth+1;
    return depth;
}

---

创建二叉树

二叉树结构

void CreateBinaryTree(){
    //创建结点
    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};
    //建立结点关系
    node1.lChild = &node2;
    node2.rChild = &node3;
    node3.lChild = &node4;
    node3.rChild = &node5;
    node1.rChild = &node6;
    node6.rChild = &node7;
    node7.rChild = &node8;

    //拷贝二叉树
    BinaryNode *root = CopyBinaryTree(&node1);
    //前序遍历
    cout << "前序遍历: ";
    Recursion(root);
    cout << endl;
    //中序遍历
    cout << "中序遍历: ";
    Recursion2(root);
    cout << endl;
    //后序遍历
    cout << "后序遍历: ";
    Recursion3(root);
    cout << endl;

    //计算叶子结点数量
    CalculateLeafNum(root);
    //求二叉树高度
    int depth = CalculateTreeDepth(root);
    cout << endl;
    cout << "树深度为: " << depth << endl;

    FreeSpaceBinaryTree(root);
}

调用

int main(){
    int sum = 0;
    CreateBinaryTree();
    cout << endl;

    system("pause");
    return 0;
}