Pohon Biner Seimbang

Dalam tutorial ini, Anda akan belajar tentang pohon biner yang seimbang dan berbagai jenisnya. Selain itu, Anda akan menemukan contoh kerja pohon biner yang seimbang di C, C ++, Java dan Python.

Pohon biner yang seimbang, juga disebut sebagai pohon biner dengan keseimbangan tinggi, didefinisikan sebagai pohon biner di mana ketinggian subpohon kiri dan kanan dari setiap simpul berbeda tidak lebih dari 1.

Untuk mempelajari lebih lanjut tentang ketinggian pohon / node, kunjungi Tree Data Structure. Berikut adalah ketentuan untuk pohon biner dengan keseimbangan tinggi:

  1. perbedaan antara subtree kiri dan kanan untuk setiap node tidak lebih dari satu
  2. subtree kiri seimbang
  3. subtree kanan seimbang
Balanced Binary Tree dengan kedalaman di setiap level Unbalanced Binary Tree dengan kedalaman di setiap level

Contoh Python, Java dan C / C ++

Kode berikut untuk memeriksa apakah pohon memiliki ketinggian yang seimbang.

Python Java C ++ 
 # Checking if a binary tree is CalculateHeight balanced in Python # CreateNode creation class CreateNode: def __init__(self, item): self.item = item self.left = self.right = None # Calculate height class CalculateHeight: def __init__(self): self.CalculateHeight = 0 # Check height balance def is_height_balanced(root, CalculateHeight): left_height = CalculateHeight() right_height = CalculateHeight() if root is None: return True l = is_height_balanced(root.left, left_height) r = is_height_balanced(root.right, right_height) CalculateHeight.CalculateHeight = max( left_height.CalculateHeight, right_height.CalculateHeight) + 1 if abs(left_height.CalculateHeight - right_height.CalculateHeight) <= 1: return l and r return False CalculateHeight = CalculateHeight() root = CreateNode(1) root.left = CreateNode(2) root.right = CreateNode(3) root.left.left = CreateNode(4) root.left.right = CreateNode(5) if is_height_balanced(root, CalculateHeight): print('The tree is balanced') else: print('The tree is not balanced') 
 // Checking if a binary tree is height balanced in Java // Node creation class Node ( int data; Node left, right; Node(int d) ( data = d; left = right = null; ) ) // Calculate height class Height ( int height = 0; ) class BinaryTree ( Node root; // Check height balance boolean checkHeightBalance(Node root, Height height) ( // Check for emptiness if (root == null) ( height.height = 0; return true; ) Height leftHeighteight = new Height(), rightHeighteight = new Height(); boolean l = checkHeightBalance(root.left, leftHeighteight); boolean r = checkHeightBalance(root.right, rightHeighteight); int leftHeight = leftHeighteight.height, rightHeight = rightHeighteight.height; height.height = (leftHeight> rightHeight ? leftHeight : rightHeight) + 1; if ((leftHeight - rightHeight>= 2) || (rightHeight - leftHeight>= 2)) return false; else return l && r; ) public static void main(String args()) ( Height height = new Height(); BinaryTree tree = new BinaryTree(); tree.root = new Node(1); tree.root.left = new Node(2); tree.root.right = new Node(3); tree.root.left.left = new Node(4); tree.root.left.right = new Node(5); if (tree.checkHeightBalance(tree.root, height)) System.out.println("The tree is balanced"); else System.out.println("The tree is not balanced"); ) )
 // Checking if a binary tree is height balanced in C #include #include #define bool int // Node creation struct node ( int item; struct node *left; struct node *right; ); // Create a new node struct node *newNode(int item) ( struct node *node = (struct node *)malloc(sizeof(struct node)); node->item = item; node->left = NULL; node->right = NULL; return (node); ) // Check for height balance bool checkHeightBalance(struct node *root, int *height) ( // Check for emptiness int leftHeight = 0, rightHeight = 0; int l = 0, r = 0; if (root == NULL) ( *height = 0; return 1; ) l = checkHeightBalance(root->left, &leftHeight); r = checkHeightBalance(root->right, &rightHeight); *height = (leftHeight> rightHeight ? leftHeight : rightHeight) + 1; if ((leftHeight - rightHeight>= 2) || (rightHeight - leftHeight>= 2)) return 0; else return l && r; ) int main() ( int height = 0; struct node *root = newNode(1); root->left = newNode(2); root->right = newNode(3); root->left->left = newNode(4); root->left->right = newNode(5); if (checkHeightBalance(root, &height)) printf("The tree is balanced"); else printf("The tree is not balanced"); )
 // Checking if a binary tree is height balanced in C++ #include using namespace std; #define bool int class node ( public: int item; node *left; node *right; ); // Create anew node node *newNode(int item) ( node *Node = new node(); Node->item = item; Node->left = NULL; Node->right = NULL; return (Node); ) // Check height balance bool checkHeightBalance(node *root, int *height) ( // Check for emptiness int leftHeight = 0, rightHeight = 0; int l = 0, r = 0; if (root == NULL) ( *height = 0; return 1; ) l = checkHeightBalance(root->left, &leftHeight); r = checkHeightBalance(root->right, &rightHeight); *height = (leftHeight> rightHeight ? leftHeight : rightHeight) + 1; if ((leftHeight - rightHeight>= 2) || (rightHeight - leftHeight>= 2)) return 0; else return l && r; ) int main() ( int height = 0; node *root = newNode(1); root->left = newNode(2); root->right = newNode(3); root->left->left = newNode(4); root->left->right = newNode(5); if (checkHeightBalance(root, &height)) cout << "The tree is balanced"; else cout << "The tree is not balanced"; )

Aplikasi Balanced Binary Tree

  • Pohon AVL
  • Pohon Pencarian Biner Seimbang

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