logo

Didžiausias iš eilės didėjančio kelio ilgis dvejetainiame medyje

Atsižvelgiant į dvejetainį medį, suraskite ilgiausio kelio, kurį sudaro mazgai su iš eilės reikšmėmis didėjančia tvarka, ilgį. Kiekvienas mazgas laikomas 1 ilgio keliu. 

Pavyzdžiai: 



 10 /  /  11 9 /  / /  /  13 12 13 8 Maximum Consecutive Path Length is 3 (10 11 12)   Note  : 10 9 8 is NOT considered since the nodes should be in increasing order. 5 /  /  8 11 /  /  9 10 / / / / 6 15 Maximum Consecutive Path Length is 2 (8 9).

Kiekvienas dvejetainio medžio mazgas gali tapti kelio dalimi, kuri prasideda nuo vieno iš pirminio mazgo, arba naujas kelias gali prasidėti nuo paties mazgo. Svarbiausia yra rekursyviai rasti kairiojo ir dešiniojo pomedžio kelio ilgį ir grąžinti maksimalų skaičių. Keliaujant per medį reikia atsižvelgti į kai kuriuos atvejus, kurie aptariami toliau.

  • ankstesnė : saugo pagrindinio mazgo vertę. Inicijuoti ankstesnį su vienu mažesne nei šakninio mazgo reikšmė, kad kelias, prasidedantis nuo šaknies, būtų bent 1 ilgio. 
  • tik : Išsaugo kelio ilgį, kuris baigiasi šiuo metu lankomo mazgo pirminiu elementu.

1 atvejis : Dabartinio mazgo vertė yra ankstesnė +1 
Tokiu atveju padidinkite kelio ilgį 1, tada rekursyviai suraskite kairiojo ir dešiniojo antrinio medžio kelio ilgį, tada grąžinkite didžiausią tarp dviejų ilgių.

2 atvejis : Dabartinio mazgo reikšmė NĖRA ankstesnė+1 
Naujas kelias gali prasidėti nuo šio mazgo, todėl rekursyviai raskite kairiojo ir dešiniojo antrinio medžio kelio ilgį. Kelias, kuris baigiasi dabartinio mazgo pirminiame mazge, gali būti didesnis už kelią, kuris prasideda nuo šio mazgo. Taigi naudokite maksimalų kelią, kuris prasideda nuo šio mazgo ir baigiasi ankstesniame mazge.



Žemiau yra aukščiau pateiktos idėjos įgyvendinimas.

C++
// C++ Program to find Maximum Consecutive // Path Length in a Binary Tree #include    using namespace std; // To represent a node of a Binary Tree struct Node {  Node *left *right;  int val; }; // Create a new Node and return its address Node *newNode(int val) {  Node *temp = new Node();  temp->val = val;  temp->left = temp->right = NULL;  return temp; } // Returns the maximum consecutive Path Length int maxPathLenUtil(Node *root int prev_val int prev_len) {  if (!root)  return prev_len;  // Get the value of Current Node  // The value of the current node will be  // prev Node for its left and right children  int cur_val = root->val;  // If current node has to be a part of the  // consecutive path then it should be 1 greater  // than the value of the previous node  if (cur_val == prev_val+1)  {  // a) Find the length of the Left Path  // b) Find the length of the Right Path  // Return the maximum of Left path and Right path  return max(maxPathLenUtil(root->left cur_val prev_len+1)  maxPathLenUtil(root->right cur_val prev_len+1));  }  // Find length of the maximum path under subtree rooted with this  // node (The path may or may not include this node)  int newPathLen = max(maxPathLenUtil(root->left cur_val 1)  maxPathLenUtil(root->right cur_val 1));  // Take the maximum previous path and path under subtree rooted  // with this node.  return max(prev_len newPathLen); } // A wrapper over maxPathLenUtil(). int maxConsecutivePathLength(Node *root) {  // Return 0 if root is NULL  if (root == NULL)  return 0;  // Else compute Maximum Consecutive Increasing Path  // Length using maxPathLenUtil.  return maxPathLenUtil(root root->val-1 0); } //Driver program to test above function int main() {  Node *root = newNode(10);  root->left = newNode(11);  root->right = newNode(9);  root->left->left = newNode(13);  root->left->right = newNode(12);  root->right->left = newNode(13);  root->right->right = newNode(8);  cout << 'Maximum Consecutive Increasing Path Length is '  << maxConsecutivePathLength(root);  return 0; } 
Java
// Java Program to find Maximum Consecutive  // Path Length in a Binary Tree  import java.util.*; class GfG { // To represent a node of a Binary Tree  static class Node  {   Node left right;   int val;  } // Create a new Node and return its address  static Node newNode(int val)  {   Node temp = new Node();   temp.val = val;   temp.left = null;  temp.right = null;   return temp;  }  // Returns the maximum consecutive Path Length  static int maxPathLenUtil(Node root int prev_val int prev_len)  {   if (root == null)   return prev_len;   // Get the value of Current Node   // The value of the current node will be   // prev Node for its left and right children   int cur_val = root.val;   // If current node has to be a part of the   // consecutive path then it should be 1 greater   // than the value of the previous node   if (cur_val == prev_val+1)   {   // a) Find the length of the Left Path   // b) Find the length of the Right Path   // Return the maximum of Left path and Right path   return Math.max(maxPathLenUtil(root.left cur_val prev_len+1)   maxPathLenUtil(root.right cur_val prev_len+1));   }   // Find length of the maximum path under subtree rooted with this   // node (The path may or may not include this node)   int newPathLen = Math.max(maxPathLenUtil(root.left cur_val 1)   maxPathLenUtil(root.right cur_val 1));   // Take the maximum previous path and path under subtree rooted   // with this node.   return Math.max(prev_len newPathLen);  }  // A wrapper over maxPathLenUtil().  static int maxConsecutivePathLength(Node root)  {   // Return 0 if root is NULL   if (root == null)   return 0;   // Else compute Maximum Consecutive Increasing Path   // Length using maxPathLenUtil.   return maxPathLenUtil(root root.val-1 0);  }  //Driver program to test above function  public static void main(String[] args)  {   Node root = newNode(10);   root.left = newNode(11);   root.right = newNode(9);   root.left.left = newNode(13);   root.left.right = newNode(12);   root.right.left = newNode(13);   root.right.right = newNode(8);   System.out.println('Maximum Consecutive Increasing Path Length is '+maxConsecutivePathLength(root));  }  }  
Python3
# Python program to find Maximum consecutive  # path length in binary tree # A binary tree node class Node: # Constructor to create a new node def __init__(self val): self.val = val self.left = None self.right = None # Returns the maximum consecutive path length def maxPathLenUtil(root prev_val prev_len): if root is None: return prev_len # Get the value of current node # The value of the current node will be  # prev node for its left and right children curr_val = root.val # If current node has to be a part of the  # consecutive path then it should be 1 greater # than the value of the previous node if curr_val == prev_val +1 : # a) Find the length of the left path  # b) Find the length of the right path # Return the maximum of left path and right path return max(maxPathLenUtil(root.left curr_val prev_len+1) maxPathLenUtil(root.right curr_val prev_len+1)) # Find the length of the maximum path under subtree  # rooted with this node newPathLen = max(maxPathLenUtil(root.left curr_val 1) maxPathLenUtil(root.right curr_val 1)) # Take the maximum previous path and path under subtree # rooted with this node return max(prev_len  newPathLen) # A Wrapper over maxPathLenUtil() def maxConsecutivePathLength(root): # Return 0 if root is None if root is None: return 0 # Else compute maximum consecutive increasing path  # length using maxPathLenUtil return maxPathLenUtil(root root.val -1  0) # Driver program to test above function root = Node(10) root.left = Node(11) root.right = Node(9) root.left.left = Node(13) root.left.right = Node(12) root.right.left = Node(13) root.right.right = Node(8) print ('Maximum Consecutive Increasing Path Length is') print (maxConsecutivePathLength(root)) # This code is contributed by Nikhil Kumar Singh(nickzuck_007) 
C#
// C# Program to find Maximum Consecutive  // Path Length in a Binary Tree using System; class GfG  {  // To represent a node of a Binary Tree   class Node   {   public Node left right;   public int val;   }  // Create a new Node and return its address   static Node newNode(int val)   {   Node temp = new Node();   temp.val = val;   temp.left = null;  temp.right = null;   return temp;   }   // Returns the maximum consecutive Path Length   static int maxPathLenUtil(Node root   int prev_val int prev_len)   {   if (root == null)   return prev_len;   // Get the value of Current Node   // The value of the current node will be   // prev Node for its left and right children   int cur_val = root.val;   // If current node has to be a part of the   // consecutive path then it should be 1 greater   // than the value of the previous node   if (cur_val == prev_val+1)   {   // a) Find the length of the Left Path   // b) Find the length of the Right Path   // Return the maximum of Left path and Right path   return Math.Max(maxPathLenUtil(root.left cur_val prev_len+1)   maxPathLenUtil(root.right cur_val prev_len+1));   }   // Find length of the maximum path under subtree rooted with this   // node (The path may or may not include this node)   int newPathLen = Math.Max(maxPathLenUtil(root.left cur_val 1)   maxPathLenUtil(root.right cur_val 1));   // Take the maximum previous path and path under subtree rooted   // with this node.   return Math.Max(prev_len newPathLen);   }   // A wrapper over maxPathLenUtil().   static int maxConsecutivePathLength(Node root)   {   // Return 0 if root is NULL   if (root == null)   return 0;   // Else compute Maximum Consecutive Increasing Path   // Length using maxPathLenUtil.   return maxPathLenUtil(root root.val - 1 0);   }   // Driver code  public static void Main(String[] args)   {   Node root = newNode(10);   root.left = newNode(11);   root.right = newNode(9);   root.left.left = newNode(13);   root.left.right = newNode(12);   root.right.left = newNode(13);   root.right.right = newNode(8);   Console.WriteLine('Maximum Consecutive' +  ' Increasing Path Length is '+  maxConsecutivePathLength(root));   }  }  // This code has been contributed by 29AjayKumar 
JavaScript
<script> // Javascript Program to find Maximum Consecutive  // Path Length in a Binary Tree  // To represent a node of a Binary Tree  class Node  {  constructor(val)  {  this.val = val;  this.left = this.right = null;  } } // Returns the maximum consecutive Path Length  function maxPathLenUtil(rootprev_valprev_len) {  if (root == null)   return prev_len;     // Get the value of Current Node   // The value of the current node will be   // prev Node for its left and right children   let cur_val = root.val;     // If current node has to be a part of the   // consecutive path then it should be 1 greater   // than the value of the previous node   if (cur_val == prev_val+1)   {     // a) Find the length of the Left Path   // b) Find the length of the Right Path   // Return the maximum of Left path and Right path   return Math.max(maxPathLenUtil(root.left cur_val prev_len+1)   maxPathLenUtil(root.right cur_val prev_len+1));   }     // Find length of the maximum path under subtree rooted with this   // node (The path may or may not include this node)   let newPathLen = Math.max(maxPathLenUtil(root.left cur_val 1)   maxPathLenUtil(root.right cur_val 1));     // Take the maximum previous path and path under subtree rooted   // with this node.   return Math.max(prev_len newPathLen);  } // A wrapper over maxPathLenUtil().  function maxConsecutivePathLength(root) {  // Return 0 if root is NULL   if (root == null)   return 0;     // Else compute Maximum Consecutive Increasing Path   // Length using maxPathLenUtil.   return maxPathLenUtil(root root.val-1 0);  } // Driver program to test above function  let root = new Node(10);  root.left = new Node(11);  root.right = new Node(9);  root.left.left = new Node(13);  root.left.right = new Node(12);  root.right.left = new Node(13);  root.right.right = new Node(8);  document.write('Maximum Consecutive Increasing Path Length is '+  maxConsecutivePathLength(root)+'  
'
); // This code is contributed by rag2127 </script>

Išvestis
Maximum Consecutive Increasing Path Length is 3

Laiko sudėtingumas: O(n^2), kur n yra mazgų skaičius duotame dvejetainiame medyje.
Pagalbinė erdvė: O(log(n))