logo

Trova l'altezza di un albero binario speciale i cui nodi foglia sono collegati

Dato un albero binario speciale di chi nodi fogliari sono collegati per formare a elenco circolare doppiamente concatenato il compito è trovare il altezza dell'albero.

Esempi:



Ingresso:

Trova l'altezza-di-un-albero-binario-speciale-i-cui-nodi-foglia-sono-connessi-2' title=

Produzione: 2
Spiegazione: L'altezza dell'albero binario dopo aver riconosciuto i nodi foglia è 2. Nell'albero binario sopra 6, 5 e 4 sono nodi foglia e formano una lista circolare doppiamente collegata. Qui il puntatore sinistro del nodo foglia fungerà da puntatore precedente della lista circolare doppiamente collegata e il suo puntatore destro fungerà da puntatore successivo della lista circolare doppiamente collegata. 

Ingresso:



Trova l'altezza-di-un-albero-binario-speciale-i-cui-nodi-foglia-sono-connessi-1' loading='lazy' title=

Produzione: 1
Spiegazione: L'altezza dell'albero binario dopo aver riconosciuto i nodi foglia è 1. Nell'albero binario sopra 2 e 3 sono nodi foglia e formano un elenco circolare doppiamente collegato.

Approccio :

L'idea è seguire approccio simile come facciamo per trovare l'altezza di un normale albero binario . Noi ricorsivamente calcolare altezza Di sinistra e destra sottoalberi di un nodo e assegnare altezza al nodo come massimo delle altezze di due bambini più 1. Ma figlio sinistro e destro di a nodo fogliare sono nulli per i normali alberi binari. Ma qui il nodo foglia è un nodo circolare di elenco doppiamente collegato. Quindi affinché un nodo sia un nodo foglia controlliamo se il nodo è sinistro, destro sta indicando il nodo e il suo la destra è sinistra sta anche indicando il nodo si.



C++
// C++ program to calculate height of a special tree // whose leaf nodes forms a circular doubly linked list #include    using namespace std; class Node { public:  int data;  Node *left *right;  Node(int x) {  data = x;  left = nullptr;  right = nullptr;  } }; // function to check if given  // node is a leaf node or node bool isLeaf(Node* node) {    // For a node to be a leaf node it should  // satisfy the following two conditions:  // 1. Node's left's right pointer should be   // current node.  // 2. Node's right's left pointer should be   // current node.    // If one condition is met it is guaranteed  // that the other consition is also true.  return node->left && node->left->right == node  && node->right && node->right->left == node; } // Compute the height of a tree  int findTreeHeight(Node* node) {    // if node is NULL return -1.  if (node == nullptr)  return -1;  // if node is a leaf node return 0  if (isLeaf(node))  return 0;  // compute the depth of each subtree  // and take maximum  return 1 + max(findTreeHeight(node->left)   findTreeHeight(node->right)); } int main() {    Node* root = new Node(1);  root->left = new Node(2);  root->right = new Node(3);  root->left->left = new Node(4);  root->left->right = new Node(5);  root->left->left->left = new Node(6);  // Given tree contains 3 leaf nodes  Node* l1 = root->left->left->left;  Node* l2 = root->left->right;  Node* l3 = root->right;  // create circular doubly linked list out of  // leaf nodes of the tree  // set next pointer of linked list  l1->right = l2 l2->right = l3 l3->right = l1;  // set prev pointer of linked list  l3->left = l2 l2->left = l1 l1->left = l3;  cout << findTreeHeight(root);  return 0; } 
C
// C program to calculate height of a special tree // whose leaf nodes forms a circular doubly linked list #include  #include  struct Node {  int data;  struct Node *left *right; }; // function to check if given  // node is a leaf node or node int isLeaf(struct Node* node) {    // For a node to be a leaf node it should  // satisfy the following two conditions:  // 1. Node's left's right pointer should be   // current node.  // 2. Node's right's left pointer should be   // current node.    // If one condition is met it is guaranteed  // that the other condition is also true.  return node->left && node->left->right == node  && node->right && node->right->left == node; } // Compute the height of a tree  int findTreeHeight(struct Node* node) {    // if node is NULL return -1.  if (node == NULL)  return -1;  // if node is a leaf node return 0  if (isLeaf(node))  return 0;  // compute the depth of each subtree and take maximum  int leftDepth = findTreeHeight(node->left);  int rightDepth = findTreeHeight(node->right);  return 1 + (leftDepth > rightDepth ? leftDepth : rightDepth); } struct Node* createNode(int data) {  struct Node* newNode =   (struct Node*)malloc(sizeof(struct Node));  newNode->data = data;  newNode->left = NULL;  newNode->right = NULL;  return newNode; } int main() {    struct Node* root = createNode(1);  root->left = createNode(2);  root->right = createNode(3);  root->left->left = createNode(4);  root->left->right = createNode(5);  root->left->left->left = createNode(6);  // Given tree contains 3 leaf nodes  struct Node* l1 = root->left->left->left;  struct Node* l2 = root->left->right;  struct Node* l3 = root->right;  // create circular doubly linked list out of  // leaf nodes of the tree  // set next pointer of linked list  l1->right = l2 l2->right = l3 l3->right = l1;  // set prev pointer of linked list  l3->left = l2 l2->left = l1 l1->left = l3;  printf('%d' findTreeHeight(root));  return 0; } 
Java
// Java program to calculate height of a special tree // whose leaf nodes forms a circular doubly linked list class Node {  int data;  Node left right;  Node(int x) {  data = x;  left = null;  right = null;  } } class GfG {  // function to check if given   // node is a leaf node or node  static boolean isLeaf(Node node) {    // For a node to be a leaf node it should  // satisfy the following two conditions:  // 1. Node's left's right pointer should be   // current node.  // 2. Node's right's left pointer should be   // current node.    // If one condition is met it is guaranteed  // that the other condition is also true.  return node.left != null && node.left.right == node  && node.right != null && node.right.left == node;  }  // Compute the height of a tree   static int findTreeHeight(Node node) {    // if node is NULL return -1.  if (node == null)  return -1;  // if node is a leaf node return 0  if (isLeaf(node))  return 0;  // compute the depth of each subtree and take maximum  return 1 + Math.max(findTreeHeight(node.left)   findTreeHeight(node.right));  }  public static void main(String[] args) {  Node root = new Node(1);  root.left = new Node(2);  root.right = new Node(3);  root.left.left = new Node(4);  root.left.right = new Node(5);  root.left.left.left = new Node(6);  // Given tree contains 3 leaf nodes  Node l1 = root.left.left.left;  Node l2 = root.left.right;  Node l3 = root.right;  // create circular doubly linked list out of  // leaf nodes of the tree  // set next pointer of linked list  l1.right = l2;  l2.right = l3;  l3.right = l1;  // set prev pointer of linked list  l3.left = l2;  l2.left = l1;  l1.left = l3;  System.out.println(findTreeHeight(root));  } } 
Python
# Python program to calculate height of a special tree # whose leaf nodes forms a circular doubly linked list class Node: def __init__(self data): self.data = data self.left = None self.right = None # function to check if given  # node is a leaf node or node def isLeaf(node): # For a node to be a leaf node it should # satisfy the following two conditions: # 1. Node's left's right pointer should be  # current node. # 2. Node's right's left pointer should be  # current node. # If one condition is met it is guaranteed # that the other condition is also true. return (node.left and node.left.right == node and node.right and node.right.left == node) # Compute the height of a tree  def findTreeHeight(node): # if node is NULL return -1. if node is None: return -1 # if node is a leaf node return 0 if isLeaf(node): return 0 # compute the depth of each subtree and take maximum return 1 + max(findTreeHeight(node.left) findTreeHeight(node.right)) if __name__ == '__main__': root = Node(1) root.left = Node(2) root.right = Node(3) root.left.left = Node(4) root.left.right = Node(5) root.left.left.left = Node(6) # Given tree contains 3 leaf nodes l1 = root.left.left.left l2 = root.left.right l3 = root.right # create circular doubly linked list out of # leaf nodes of the tree # set next pointer of linked list l1.right = l2 l2.right = l3 l3.right = l1 # set prev pointer of linked list l3.left = l2 l2.left = l1 l1.left = l3 print(findTreeHeight(root)) 
C#
// C# program to calculate height of a special tree // whose leaf nodes forms a circular doubly linked list using System; class Node {  public int data;  public Node left right;  public Node(int x) {  data = x;  left = null;  right = null;  } } class GfG {  // function to check if given   // node is a leaf node or node  static bool isLeaf(Node node) {    // For a node to be a leaf node it should  // satisfy the following two conditions:  // 1. Node's left's right pointer should be   // current node.  // 2. Node's right's left pointer should be   // current node.    // If one condition is met it is guaranteed  // that the other condition is also true.  return node.left != null && node.left.right == node  && node.right != null && node.right.left == node;  }  // Compute the height of a tree   static int findTreeHeight(Node node) {    // if node is NULL return -1.  if (node == null)  return -1;  // if node is a leaf node return 0  if (isLeaf(node))  return 0;  // compute the depth of each subtree and take maximum  return 1 + Math.Max(findTreeHeight(node.left) findTreeHeight(node.right));  }  static void Main(string[] args) {  Node root = new Node(1);  root.left = new Node(2);  root.right = new Node(3);  root.left.left = new Node(4);  root.left.right = new Node(5);  root.left.left.left = new Node(6);  // Given tree contains 3 leaf nodes  Node l1 = root.left.left.left;  Node l2 = root.left.right;  Node l3 = root.right;  // create circular doubly linked list out of  // leaf nodes of the tree  // set next pointer of linked list  l1.right = l2;  l2.right = l3;  l3.right = l1;  // set prev pointer of linked list  l3.left = l2;  l2.left = l1;  l1.left = l3;  Console.WriteLine(findTreeHeight(root));  } } 
JavaScript
// JavaScript program to calculate height of a special tree // whose leaf nodes forms a circular doubly linked list class Node {  constructor(data) {  this.data = data;  this.left = null;  this.right = null;  } } // function to check if given  // node is a leaf node or node function isLeaf(node) {    // For a node to be a leaf node it should  // satisfy the following two conditions:  // 1. Node's left's right pointer should be   // current node.  // 2. Node's right's left pointer should be   // current node.    // If one condition is met it is guaranteed  // that the other condition is also true.  return node.left && node.left.right === node  && node.right && node.right.left === node; } // Compute the height of a tree  function findTreeHeight(node) {    // if node is NULL return -1.  if (node === null)  return -1;  // if node is a leaf node return 0  if (isLeaf(node))  return 0;  // compute the depth of each subtree and take maximum  return 1 + Math.max(findTreeHeight(node.left) findTreeHeight(node.right)); } const root = new Node(1); root.left = new Node(2); root.right = new Node(3); root.left.left = new Node(4); root.left.right = new Node(5); root.left.left.left = new Node(6); // Given tree contains 3 leaf nodes const l1 = root.left.left.left; const l2 = root.left.right; const l3 = root.right; // create circular doubly linked list out of // leaf nodes of the tree // set next pointer of linked list l1.right = l2; l2.right = l3; l3.right = l1; // set prev pointer of linked list l3.left = l2; l2.left = l1; l1.left = l3; console.log(findTreeHeight(root)); 

Produzione
3

Complessità temporale: O(n) dove N è il numero di nodi.
Spazio ausiliario: OH)