用c语言建立一个4层完全二叉树，使其具有建立排序二叉树，插入结点和删除节点的功能

首先，我们需要定义一个二叉树结点的数据结构，包括左右子结点指针和数据域。

typedef struct Node {
    int data;
    struct Node *left;
    struct Node *right;
} Node;

然后，我们需要定义一个二叉树的数据结构，包括根节点指针和节点数量。

typedef struct BinaryTree {
    Node *root;
    int size;
} BinaryTree;

接下来，我们可以实现二叉树的初始化函数。

void init(BinaryTree *tree) {
    tree->root = NULL;
    tree->size = 0;
}

接着，我们可以实现二叉树的插入函数。在插入节点时，我们需要比较当前节点的值和插入节点的值，并根据大小关系递归地插入到左子树或右子树。

void insert(BinaryTree *tree, int value) {
    Node *newNode = (Node*)malloc(sizeof(Node));
    newNode->data = value;
    newNode->left = NULL;
    newNode->right= NULL;
    
    if (tree->root == NULL) {
        tree->root = newNode;
        tree->size++;
        return;
    }
    
    Node *current = tree->root;
    while (1) {
        if (value < current->data) {
            if (current->left == NULL) {
                current->left = newNode;
                tree->size++;
                break;
            }
            current = current->left;
        } else {
            if (current->right == NULL) {
                current->right = newNode;
                tree->size++;
                break;
            }
            current = current->right;
        }
    }
}

最后，我们可以实现二叉树的删除函数。在删除节点时，我们需要递归地找到要删除的节点，并根据其子节点的情况进行删除操作。

Node* delete(Node *root, int value) {
    if (root == NULL) {
        return NULL;
    }
    
    if (value < root->data) {
        root->left = delete(root->left, value);
    } else if (value > root->data) {
        root->right = delete(root->right, value);
    } else {
        if (root->left == NULL) {
            Node *temp = root->right;
            free(root);
            return temp;
        } else if (root->right == NULL) {
            Node *temp = root->left;
            free(root);
            return temp;
        }
        
        Node *temp = root->right;
        while (temp->left != NULL) {
            temp = temp->left;
        }
        
        root->data = temp->data;
        root->right = delete(root->right, temp->data);
    }
    
    return root;
}

void remove(BinaryTree *tree, int value) {
    tree->root = delete(tree->root, value);
    tree->size--;
}

完整代码如下：

#include <stdio.h>
#include <stdlib.h>

typedef struct Node {
    int data;
    struct Node *left;
    struct Node *right;
} Node;

typedef struct BinaryTree {
    Node *root;
    int size;
} BinaryTree;

void init(BinaryTree *tree) {
    tree->root = NULL;
    tree->size = 0;
}

void insert(BinaryTree *tree, int value) {
    Node *newNode = (Node*)malloc(sizeof(Node));
    newNode->data = value;
    newNode->left = NULL;
    newNode->right= NULL;
    
    if (tree->root == NULL) {
        tree->root = newNode;
        tree->size++;
        return;
    }
    
    Node *current = tree->root;
    while (1) {
        if (value < current->data) {
            if (current->left == NULL) {
                current->left = newNode;
                tree->size++;
                break;
            }
            current = current->left;
        } else {
            if (current->right == NULL) {
                current->right = newNode;
                tree->size++;
                break;
            }
            current = current->right;
        }
    }
}

Node* delete(Node *root, int value) {
    if (root == NULL) {
        return NULL;
    }
    
    if (value < root->data) {
        root->left = delete(root->left, value);
    } else if (value > root->data) {
        root->right = delete(root->right, value);
    } else {
        if (root->left == NULL) {
            Node *temp = root->right;
            free(root);
            return temp;
        } else if (root->right == NULL) {
            Node *temp = root->left;
            free(root);
            return temp;
        }
        
        Node *temp = root->right;
        while (temp->left != NULL) {
            temp = temp->left;
        }
        
        root->data = temp->data;
        root->right = delete(root->right, temp->data);
    }
    
    return root;
}

void remove(BinaryTree *tree, int value) {
    tree->root = delete(tree->root, value);
    tree->size--;
}

void printInorder(Node *root) {
    if (root == NULL) {
        return;
    }
    printInorder(root->left);
    printf("%d ", root->data);
    printInorder(root->right);
}

int main() {
    BinaryTree tree;
    init(&tree);
    
    insert(&tree, 5);
    insert(&tree, 2);
    insert(&tree, 8);
    insert(&tree, 1);
    insert(&tree, 3);
    insert(&tree, 6);
    insert(&tree, 9);
    insert(&tree, 4);
    insert(&tree, 7);
    
    printf("Inorder traversal: ");
    printInorder(tree.root);
    printf("\n");
    
    remove(&tree, 3);
    
    printf("Inorder traversal: ");
    printInorder(tree.root);
    printf("\n");

    return 0;
}