Perfekt binært tre

Innholdsfortegnelse

Python, Java og C / C ++ eksempler
Perfekte Binary Tree-teoremer

I denne veiledningen vil du lære om det perfekte binære treet. Du finner også arbeidseksempler for å sjekke et perfekt binært tre i C, C ++, Java og Python.

Et perfekt binært tre er en type binært tre der hver intern node har nøyaktig to underordnede noder, og alle bladnodene er på samme nivå.

Perfekt binært tre

Alle interne noder har en grad på 2.

Rekursivt kan et perfekt binært tre defineres som:

Hvis en enkelt node ikke har barn, er det et perfekt binært høydetre h = 0,
Hvis en node har h> 0det, er det et perfekt binært tre hvis begge undertrærne er av høyde h - 1og ikke er overlappende.

Perfekt binært tre (rekursiv representasjon)

Python, Java og C / C ++ eksempler

Følgende kode er for å sjekke om et tre er et perfekt binært tre.

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"; )