# 滿二叉樹 > 原文： [https://www.programiz.com/dsa/full-binary-tree](https://www.programiz.com/dsa/full-binary-tree) #### 在本教程中，您將學習滿二叉樹及其不同的定理。 此外，您還將找到一些工作示例，以檢查 C，C++ ，Java 和 Python 中的完整二進制樹。 滿二叉樹是二叉樹的一種特殊類型，其中每個父節點/內部節點都有兩個或沒有子節點。 **也稱為適當的二叉樹。**  滿二叉樹 * * * ## 滿二叉樹定理 ``` Let, i = the number of internal nodes n = be the total number of nodes l = number of leaves λ = number of levels ``` 1. 葉子數為`i + 1`。 2. 節點總數為`2i + 1`。 3. 內部節點數為`(n – 1) / 2`。 4. 葉子數為`(n + 1) / 2`。 5. 節點總數為`2l – 1`。 6. 內部節點數為`l – 1`。 7. 葉子數最多為`2^(λ - 1)`。 * * * ## Python，Java 和 C/C++ 示例 以下代碼用于檢查樹是否為滿二叉樹。 ```py # Checking if a binary tree is a full binary tree in Python # Creating a node class Node: def __init__(self, item): self.item = item self.leftChild = None self.rightChild = None # Checking full binary tree def isFullTree(root): # Tree empty case if root is None: return True # Checking whether child is present if root.leftChild is None and root.rightChild is None: return True if root.leftChild is not None and root.rightChild is not None: return (isFullTree(root.leftChild) and isFullTree(root.rightChild)) return False root = Node(1) root.rightChild = Node(3) root.leftChild = Node(2) root.leftChild.leftChild = Node(4) root.leftChild.rightChild = Node(5) root.rightChild.leftChild.leftChild = Node(6) root.rightChild.leftChild.rightChild = Node(7) if isFullTree(root): print("The tree is a full binary tree") else: print("The tree is not a full binary full") ``` ```java // Checking if a binary tree is a full binary tree in Java class Node { int data; Node leftChild, rightChild; Node(int item) { data = item; leftChild = rightChild = null; } } class BinaryTree { Node root; // Check for Full Binary Tree boolean isFullBinaryTree(Node node) { // Checking tree emptiness if (node == null) return true; // Checking the children if (node.leftChild == null && node.rightChild == null) return true; if ((node.leftChild != null) && (node.rightChild != null)) return (isFullBinaryTree(node.leftChild) && isFullBinaryTree(node.rightChild)); return false; } public static void main(String args[]) { BinaryTree tree = new BinaryTree(); tree.root = new Node(1); tree.root.leftChild = new Node(2); tree.root.rightChild = new Node(3); tree.root.leftChild.leftChild = new Node(4); tree.root.leftChild.rightChild = new Node(5); tree.root.rightChild.leftChild = new Node(6); tree.root.rightChild.rightChild = new Node(7); if (tree.isFullBinaryTree(tree.root)) System.out.print("The tree is a full binary tree"); else System.out.print("The tree is not a full binary tree"); } } ``` ```c // Checking if a binary tree is a full binary tree in C #include <stdbool.h> #include <stdio.h> #include <stdlib.h> struct Node { int item; struct Node *left, *right; }; // Creation of new Node struct Node *createNewNode(char k) { struct Node *node = (struct Node *)malloc(sizeof(struct Node)); node->item = k; node->right = node->left = NULL; return node; } bool isFullBinaryTree(struct Node *root) { // Checking tree emptiness if (root == NULL) return true; // Checking the presence of children if (root->left == NULL && root->right == NULL) return true; if ((root->left) && (root->right)) return (isFullBinaryTree(root->left) && isFullBinaryTree(root->right)); return false; } int main() { struct Node *root = NULL; root = createNewNode(1); root->left = createNewNode(2); root->right = createNewNode(3); root->left->left = createNewNode(4); root->left->right = createNewNode(5); root->right->left->left = createNewNode(6); root->right->left->right = createNewNode(7); if (isFullBinaryTree(root)) printf("The tree is a full binary tree\n"); else printf("The tree is not a full binary full\n"); } ``` ```cpp // Checking if a binary tree is a full binary tree in C++ #include <iostream> using namespace std; struct Node { int key; struct Node *left, *right; }; // New node creation struct Node *newNode(char k) { struct Node *node = (struct Node *)malloc(sizeof(struct Node)); node->key = k; node->right = node->left = NULL; return node; } bool isFullBinaryTree(struct Node *root) { // Checking for emptiness if (root == NULL) return true; // Checking for the presence of children if (root->left == NULL && root->right == NULL) return true; if ((root->left) && (root->right)) return (isFullBinaryTree(root->left) && isFullBinaryTree(root->right)); return false; } int main() { struct Node *root = NULL; root = newNode(1); root->left = newNode(2); root->right = newNode(3); root->left->left = newNode(4); root->left->right = newNode(5); root->right->left->left = newNode(6); root->right->left->right = newNode(7); if (isFullBinaryTree(root)) cout << "The tree is a full binary tree\n"; else cout << "The tree is not a full binary full\n"; } ```