Ideaalne kahendpuu

Lang L: none (table-of-contents)

Pythoni, Java ja C / C ++ näited
Täiuslikud binaarpuu teoreemid

Selles õpetuses saate teada täiusliku binaarse puu kohta. Samuti leiate toimivaid näiteid täiusliku binaarpuu kontrollimiseks C, C ++, Java ja Python.

Täiuslik binaarne puu on kahendpuu tüüp, milles igal sisesõlmel on täpselt kaks lapsesõlme ja kõik lehesõlmed on samal tasemel.

Ideaalne kahendpuu

Kõigi sisemiste sõlmede aste on 2.

Rekursiivselt võib täiusliku binaarse puu määratleda järgmiselt:

Kui ühel sõlmel pole lapsi, on see täiuslik binaarne puu h = 0,
Kui sõlmel on h> 0, on see ideaalne kahendpuu, kui selle mõlemad alampuud on kõrged h - 1ja kattuvad.

Ideaalne kahendpuu (rekursiivne esitus)

Pythoni, Java ja C / C ++ näited

Järgmine kood on mõeldud selleks, et kontrollida, kas puu on täiuslik binaarne puu.

Python Java C C ++

 # Checking if a binary tree is a perfect binary tree in Python class newNode: def __init__(self, k): self.key = k self.right = self.left = None # Calculate the depth def calculateDepth(node): d = 0 while (node is not None): d += 1 node = node.left return d # Check if the tree is perfect binary tree def is_perfect(root, d, level=0): # Check if the tree is empty if (root is None): return True # Check the presence of trees if (root.left is None and root.right is None): return (d == level + 1) if (root.left is None or root.right is None): return False return (is_perfect(root.left, d, level + 1) and is_perfect(root.right, d, level + 1)) root = None root = newNode(1) root.left = newNode(2) root.right = newNode(3) root.left.left = newNode(4) root.left.right = newNode(5) if (is_perfect(root, calculateDepth(root))): print("The tree is a perfect binary tree") else: print("The tree is not a perfect binary tree")

 // Checking if a binary tree is a perfect binary tree in Java class PerfectBinaryTree ( static class Node ( int key; Node left, right; ) // Calculate the depth static int depth(Node node) ( int d = 0; while (node != null) ( d++; node = node.left; ) return d; ) // Check if the tree is perfect binary tree static boolean is_perfect(Node root, int d, int level) ( // Check if the tree is empty if (root == null) return true; // If for children if (root.left == null && root.right == null) return (d == level + 1); if (root.left == null || root.right == null) return false; return is_perfect(root.left, d, level + 1) && is_perfect(root.right, d, level + 1); ) // Wrapper function static boolean is_Perfect(Node root) ( int d = depth(root); return is_perfect(root, d, 0); ) // Create a new node static Node newNode(int k) ( Node node = new Node(); node.key = k; node.right = null; node.left = null; return node; ) public static void main(String args()) ( Node root = null; root = newNode(1); root.left = newNode(2); root.right = newNode(3); root.left.left = newNode(4); root.left.right = newNode(5); if (is_Perfect(root) == true) System.out.println("The tree is a perfect binary tree"); else System.out.println("The tree is not a perfect binary tree"); ) )

 // Checking if a binary tree is a perfect binary tree in C #include #include #include struct node ( int data; struct node *left; struct node *right; ); // Creating a new node struct node *newnode(int data) ( struct node *node = (struct node *)malloc(sizeof(struct node)); node->data = data; node->left = NULL; node->right = NULL; return (node); ) // Calculate the depth int depth(struct node *node) ( int d = 0; while (node != NULL) ( d++; node = node->left; ) return d; ) // Check if the tree is perfect bool is_perfect(struct node *root, int d, int level) ( // Check if the tree is empty if (root == NULL) return true; // Check the presence of children if (root->left == NULL && root->right == NULL) return (d == level + 1); if (root->left == NULL || root->right == NULL) return false; return is_perfect(root->left, d, level + 1) && is_perfect(root->right, d, level + 1); ) // Wrapper function bool is_Perfect(struct node *root) ( int d = depth(root); return is_perfect(root, d, 0); ) 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 = newnode(6); if (is_Perfect(root)) printf("The tree is a perfect binary tree"); else printf("The tree is not a perfect binary tree"); )

 // Checking if a binary tree is a perfect binary tree in C++ #include using namespace std; struct Node ( int key; struct Node *left, *right; ); int depth(Node *node) ( int d = 0; while (node != NULL) ( d++; node = node->left; ) return d; ) bool isPerfectR(struct Node *root, int d, int level = 0) ( if (root == NULL) return true; if (root->left == NULL && root->right == NULL) return (d == level + 1); if (root->left == NULL || root->right == NULL) return false; return isPerfectR(root->left, d, level + 1) && isPerfectR(root->right, d, level + 1); ) bool isPerfect(Node *root) ( int d = depth(root); return isPerfectR(root, d); ) struct Node *newNode(int k) ( struct Node *node = new Node; node->key = k; node->right = node->left = NULL; return node; ) 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 = newNode(6); if (isPerfect(root)) cout << "The tree is a perfect binary tree"; else cout << "The tree is not a perfect binary tree"; )