多叉树转二叉树

CPP代码

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#include <iostream>
#include <queue>
#include <stack>

using namespace std;

// 多叉树节点
struct Node {
	string name; // 节点名称
	vector<Node*> nodes; //子节点指针数组
	//	构造函数
	Node(string name, vector<Node*> nodes) : name(name), nodes(nodes) {}
};

// 二叉树节点
struct BinaryNode {
	string name; // 节点名称
	BinaryNode *left; // 左子节点指针
	BinaryNode *right; // 右子节点指针
//	构造函数
	BinaryNode(string name, BinaryNode *left, BinaryNode *right) : name(name), left(left), right(right) {}
};

// 按照题意初始化多叉树，返回多叉树的根节点
Node* init() {
	// 第四层节点
	Node* n31 = new Node("神经系统用药", {});
	Node* n32 = new Node("消化系统用药", {});
	Node* n33 = new Node("呼吸系统用药", {});
	Node* n34 = new Node("心脑血管系统用药", {});
	Node* n35 = new Node("抗感染药", {});
	Node* n36 = new Node("其他用药", {});
	// 第三层节点
	vector<Node*> ns1 = {n31, n32, n33, n34, n35, n36};
	Node* n21 = new Node("中成药", {});
	Node* n22 = new Node("化学药品", ns1);
	// 第二层节点
	vector<Node*> ns2 = {n21, n22};
	Node* n11 = new Node("双规制处方药", ns2);
	Node* n12 = new Node("单规制处方药", {});
	// 第一层节点
	Node* root = new Node("药品信息", {n11, n12}); // 根节点
	return root;
}

// 队列实现层序遍历（BFS）
void LevelOrderByQueue(Node* root) {
	queue<Node*> q;
	q.push(root);
	cout << "队列实现层序遍历:" << endl;
	while (!q.empty()) {
		Node* t = q.front(); // 取出队首节点
		q.pop(); // 队首节点出队
		cout << t->name << " "; // 输出节点名称
		for (Node* node : t->nodes) {
			q.push(node); // 将子节点加入队列
		}
	}
}

// 二叉树的非递归遍历(栈)
void InOrder(BinaryNode* root) {
	stack<BinaryNode*> s;
	BinaryNode* t = root;
	cout << endl;
	cout << "二叉树的中序遍历:" << endl;
	while (t != nullptr || !s.empty()) {
		if (t != nullptr) {
			s.push(t);
			t = t->left; // 移动到左子节点
		} else {
			t = s.top(); // 弹出栈顶节点
			s.pop();
			cout << t->name << " "; // 输出节点名称
			t = t->right; // 移动到右子节点
		}
	}
}

// 多叉树转二叉树
//root：多叉树的根节点
//broot：二叉树的根节点
void createBinaryTree(Node* root, BinaryNode* broot) {
	if (root == nullptr)//判空 
		return;
	
	broot->name = root->name; // 转换节点名称
	vector<Node*> nodes = root->nodes;//nodes存的是当前多叉树的子树
	if (nodes.empty()) {
		return;
	}
	// 左儿子右兄弟
	BinaryNode* left = new BinaryNode("", nullptr, nullptr);
	// 递归构建左子树
	createBinaryTree(nodes[0], left);
	BinaryNode* t = left;// t 是当前孩子中最右的孩子
	for (int i = 1; i < nodes.size(); i++) {
		Node* node = nodes[i];
		BinaryNode* right = new BinaryNode(node->name, nullptr, nullptr); // 构建右子树
		// 递归构建右子树
		createBinaryTree(nodes[i], right);
		t->right = right; // 连接右兄弟节点
		t = right;
	}
	broot->left = left; // 连接左子树
}

// 多叉树的先序遍历
void preOrder(Node* root) {
	if (root == nullptr) {
		return;
	}
	cout << root->name << " "; // 输出节点名称
	for (Node* n : root->nodes) {
		preOrder(n); // 递归遍历子节点
	}
}

// 多叉树的后序遍历
void postOrder(Node* root) {
	if (root == nullptr) {
		return;
	}
	for (Node* n : root->nodes) {
		postOrder(n); // 递归遍历子节点
	}
	cout << root->name << " "; // 输出节点名称
}

int main() {
	Node* root = init();
	// 打印先后序遍历
	cout << "多叉树的先序遍历:" << endl;
	preOrder(root); // 先序遍历
	cout << "\n多叉树的后序遍历:" << endl;
	postOrder(root); // 后序遍历
	cout << endl;
	LevelOrderByQueue(root); // 层序遍历
	BinaryNode* broot = new BinaryNode("", nullptr, nullptr);
	createBinaryTree(root, broot); // 多叉树转二叉树
	InOrder(broot); // 中序遍历二叉树
	return 0;
}

C语言代码

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

struct Node {
	char* name;                 // 结点名称
	struct Node** nodes;        // 子结点数组
	int num_nodes;              // 子结点数量
};

struct BinaryNode {
	char* name;                 // 结点名称
	struct BinaryNode* left;    // 左子结点
	struct BinaryNode* right;   // 右子结点
};

// 创建多叉树结点
struct Node* createNode(char* name, struct Node** nodes, int num_nodes) {
	struct Node* new_node = (struct Node*)malloc(sizeof(struct Node));
	new_node->name = name;
	new_node->nodes = nodes;
	new_node->num_nodes = num_nodes;
	return new_node;
}

// 创建二叉树结点
struct BinaryNode* createBinaryNode(char* name, struct BinaryNode* left, struct BinaryNode* right) {
	struct BinaryNode* new_node = (struct BinaryNode*)malloc(sizeof(struct BinaryNode));
	new_node->name = name;
	new_node->left = left;
	new_node->right = right;
	return new_node;
}

// 多叉树的层序遍历
void levelOrder(struct Node* root) {
	struct Node** queue = (struct Node**)malloc(sizeof(struct Node*) * 1000);
	int front = 0;
	int rear = 0;
	queue[rear++] = root;
	
	printf("队列实现层序遍历:\n");
	while (front < rear) {
		struct Node* temp = queue[front++];
		printf("%s ", temp->name);
		for (int i = 0; i < temp->num_nodes; i++) {
			queue[rear++] = temp->nodes[i];
		}
	}
	printf("\n");
}

// 二叉树的中序遍历
void inOrder(struct BinaryNode* root) {
	struct BinaryNode** stack = (struct BinaryNode**)malloc(sizeof(struct BinaryNode*) * 1000);
	int top = -1;
	struct BinaryNode* temp = root;
	
	printf("\n二叉树的中序遍历:\n");
	while (temp != NULL || top != -1) {
		if (temp != NULL) {
			stack[++top] = temp;
			temp = temp->left;
		}
		else {
			temp = stack[top--];
			printf("%s ", temp->name);
			temp = temp->right;
		}
	}
}

// 创建二叉树
void createBinaryTree(struct Node* root, struct BinaryNode* broot) {
	broot->name = root->name;
	struct Node** nodes = root->nodes;
	int num_nodes = root->num_nodes;
	if (num_nodes == 0) {
		return;
	}
	struct BinaryNode* left = createBinaryNode("", NULL, NULL);
	createBinaryTree(nodes[0], left);
	struct BinaryNode* temp = left;
	for (int i = 1; i < num_nodes; i++) {
		struct Node* node = nodes[i];
		struct BinaryNode* right = createBinaryNode(node->name, NULL, NULL);
		createBinaryTree(nodes[i], right);
		temp->right = right;
		temp = right;
	}
	broot->left = left;
}

// 多叉树的先序遍历
void preOrder(struct Node* root) {
	if (root == NULL) {
		return;
	}
	printf("%s ", root->name);
	for (int i = 0; i < root->num_nodes; i++) {
		preOrder(root->nodes[i]);
	}
}

// 多叉树的后序遍历
void postOrder(struct Node* root) {
	if (root == NULL) {
		return;
	}
	for (int i = 0; i < root->num_nodes; i++) {
		postOrder(root->nodes[i]);
	}
	printf("%s ", root->name);
}

int main() {
	// 创建多叉树结点
	struct Node* n31 = createNode("神经系统用药", NULL, 0);
	struct Node* n32 = createNode("消化系统用药", NULL, 0);
	struct Node* n33 = createNode("呼吸系统用药", NULL, 0);
	struct Node* n34 = createNode("心脑血管系统用药", NULL, 0);
	struct Node* n35 = createNode("抗感染药", NULL, 0);
	struct Node* n36 = createNode("其他用药", NULL, 0);
	struct Node* ns1[] = { n31, n32, n33, n34, n35, n36 };
	struct Node* n21 = createNode("中成药", NULL, 0);
	struct Node* n22 = createNode("化学药品", ns1, 6);
	struct Node* ns2[] = { n21, n22 };
	struct Node* n11 = createNode("双规制处方药", ns2, 2);
	struct Node* n12 = createNode("单规制处方药", NULL, 0);
	struct Node* nodes[] = { n11, n12 };
	struct Node* root = createNode("药品信息", nodes, 2);
	
	printf("多叉树的先序遍历:\n");
	preOrder(root);
	printf("\n多叉树的后序遍历:\n");
	postOrder(root);
	printf("\n");
	levelOrder(root);
	
	// 创建二叉树
	struct BinaryNode* broot = createBinaryNode("", NULL, NULL);
	createBinaryTree(root, broot);
	inOrder(broot);
	
	return 0;
}