בהינתן עץ בינארי מצא את אורך הנתיב הארוך ביותר הכולל צמתים עם ערכים עוקבים בסדר הולך וגדל. כל צומת נחשב כנתיב באורך 1.
דוגמאות:
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).
כל צומת בעץ הבינארי יכול להפוך לחלק מהנתיב שמתחיל מאחד מצומת האב שלו או שמסלול חדש יכול להתחיל מהצומת הזה עצמו. המפתח הוא למצוא באופן רקורסיבי את אורך הנתיב עבור עץ המשנה השמאלי והימני ולאחר מכן להחזיר את המקסימום. יש לשקול מקרים מסוימים בעת חציית העץ, עליהם נדון להלן.
- הקודם : מאחסן את הערך של צומת האב. אתחול הקודם עם אחד פחות מהערך של צומת השורש כך שהנתיב שמתחיל בשורש יכול להיות באורך של לפחות 1.
- רַק : מאחסן את אורך הנתיב שמסתיים באב של הצומת הנוכחי שביקר בו.
מקרה 1 : הערך של הצומת הנוכחי הוא הקודם +1
במקרה זה הגדל את אורך הנתיב ב-1 ואז מצא באופן רקורסיבי את אורך הנתיב עבור עץ המשנה השמאלי והימני ואז החזר את המקסימום בין שני אורכים.
מקרה 2 : הערך של הצומת הנוכחי אינו prev+1
נתיב חדש יכול להתחיל מהצומת הזה, כך שמצא באופן רקורסיבי את אורך הנתיב עבור עץ המשנה השמאלי והימני. הנתיב שמסתיים בצומת האב של הצומת הנוכחי עשוי להיות גדול יותר מהנתיב שמתחיל מהצומת הזה. אז קח את המקסימום של הנתיב שמתחיל מהצומת הזה ומסתיים בצומת הקודם.
להלן יישום הרעיון לעיל.
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>
תְפוּקָה
Maximum Consecutive Increasing Path Length is 3
מורכבות זמן: O(n^2) כאשר n הוא מספר הצמתים בעץ הבינארי הנתון.
רווח עזר: O(log(n))