Construct a special tree from given preorder traversal
Given an array ‘pre[]’ that represents Preorder traversal of a spacial binary tree where every node has either 0 or 2 children. One more array ‘preLN[]’ is given which has only two possible values ‘L’ and ‘N’. The value ‘L’ in ‘preLN[]’ indicates that the corresponding node in Binary Tree is a leaf node and value ‘N’ indicates that the corresponding node is non-leaf node. Write a function to construct the tree from the given two arrays.
Example:
Input: pre[] = {10, 30, 20, 5, 15}, preLN[] = {'N', 'N', 'L', 'L', 'L'}
Output: Root of following tree
10
/ \
30 15
/ \
20 5
The first element in pre[] will always be root. So we can easily figure out root. If left subtree is empty, the right subtree must also be empty and preLN[] entry for root must be ‘L’. We can simply create a node and return it. If left and right subtrees are not empty, then recursively call for left and right subtrees and link the returned nodes to root.
C++
/* A program to construct Binary Tree from preorder traversal */#include<bits/stdc++.h> /* A binary tree node structure */struct node { int data; struct node *left; struct node *right; }; /* Utility function to create a new Binary Tree node */struct node* newNode (int data) { struct node *temp = new struct node; temp->data = data; temp->left = NULL; temp->right = NULL; return temp; } /* A recursive function to create a Binary Tree from given pre[] preLN[] arrays. The function returns root of tree. index_ptr is used to update index values in recursive calls. index must be initially passed as 0 */struct node *constructTreeUtil(int pre[], char preLN[], int *index_ptr, int n) { int index = *index_ptr; // store the current value of index in pre[] // Base Case: All nodes are constructed if (index == n) return NULL; // Allocate memory for this node and increment index for // subsequent recursive calls struct node *temp = newNode ( pre[index] ); (*index_ptr)++; // If this is an internal node, construct left and right subtrees and link the subtrees if (preLN[index] == 'N') { temp->left = constructTreeUtil(pre, preLN, index_ptr, n); temp->right = constructTreeUtil(pre, preLN, index_ptr, n); } return temp; } // A wrapper over constructTreeUtil() struct node *constructTree(int pre[], char preLN[], int n) { // Initialize index as 0. Value of index is used in recursion to maintain // the current index in pre[] and preLN[] arrays. int index = 0; return constructTreeUtil (pre, preLN, &index, n); } /* This function is used only for testing */void printInorder (struct node* node) { if (node == NULL) return; /* first recur on left child */ printInorder (node->left); /* then print the data of node */ printf("%d ", node->data); /* now recur on right child */ printInorder (node->right); } /* Driver function to test above functions */int main() { struct node *root = NULL; /* Constructing tree given in the above figure 10 / \ 30 15 / \ 20 5 */ int pre[] = {10, 30, 20, 5, 15}; char preLN[] = {'N', 'N', 'L', 'L', 'L'}; int n = sizeof(pre)/sizeof(pre[0]); // construct the above tree root = constructTree (pre, preLN, n); // Test the constructed tree printf("Following is Inorder Traversal of the Constructed Binary Tree: \n"); printInorder (root); return 0; } |
Java
// Java program to construct a binary tree from preorder traversal // A Binary Tree node class Node { int data; Node left, right; Node(int item) { data = item; left = right = null; } } class Index { int index = 0; } class BinaryTree { Node root; Index myindex = new Index(); /* A recursive function to create a Binary Tree from given pre[] preLN[] arrays. The function returns root of tree. index_ptr is used to update index values in recursive calls. index must be initially passed as 0 */ Node constructTreeUtil(int pre[], char preLN[], Index index_ptr, int n, Node temp) { // store the current value of index in pre[] int index = index_ptr.index; // Base Case: All nodes are constructed if (index == n) return null; // Allocate memory for this node and increment index for // subsequent recursive calls temp = new Node(pre[index]); (index_ptr.index)++; // If this is an internal node, construct left and right subtrees // and link the subtrees if (preLN[index] == 'N') { temp.left = constructTreeUtil(pre, preLN, index_ptr, n, temp.left); temp.right = constructTreeUtil(pre, preLN, index_ptr, n, temp.right); } return temp; } // A wrapper over constructTreeUtil() Node constructTree(int pre[], char preLN[], int n, Node node) { // Initialize index as 0. Value of index is used in recursion to // maintain the current index in pre[] and preLN[] arrays. int index = 0; return constructTreeUtil(pre, preLN, myindex, n, node); } /* This function is used only for testing */ void printInorder(Node node) { if (node == null) return; /* first recur on left child */ printInorder(node.left); /* then print the data of node */ System.out.print(node.data + " "); /* now recur on right child */ printInorder(node.right); } // driver function to test the above functions public static void main(String args[]) { BinaryTree tree = new BinaryTree(); int pre[] = new int[]{10, 30, 20, 5, 15}; char preLN[] = new char[]{'N', 'N', 'L', 'L', 'L'}; int n = pre.length; // construct the above tree Node mynode = tree.constructTree(pre, preLN, n, tree.root); // Test the constructed tree System.out.println("Following is Inorder Traversal of the" + "Constructed Binary Tree: "); tree.printInorder(mynode); } } // This code has been contributed by Mayank Jaiswal |
Python3
# A program to construct Binary # Tree from preorder traversal # Utility function to create a # new Binary Tree node class newNode: def __init__(self, data): self.data = data self.left = None self.right = None # A recursive function to create a # Binary Tree from given pre[] preLN[] # arrays. The function returns root of # tree. index_ptr is used to update # index values in recursive calls. index # must be initially passed as 0 def constructTreeUtil(pre, preLN, index_ptr, n): index = index_ptr[0] # store the current value # of index in pre[] # Base Case: All nodes are constructed if index == n: return None # Allocate memory for this node and # increment index for subsequent # recursive calls temp = newNode(pre[index]) index_ptr[0] += 1 # If this is an internal node, construct left # and right subtrees and link the subtrees if preLN[index] == 'N': temp.left = constructTreeUtil(pre, preLN, index_ptr, n) temp.right = constructTreeUtil(pre, preLN, index_ptr, n) return temp # A wrapper over constructTreeUtil() def constructTree(pre, preLN, n): # Initialize index as 0. Value of index is # used in recursion to maintain the current # index in pre[] and preLN[] arrays. index = [0] return constructTreeUtil(pre, preLN, index, n) # This function is used only for testing def printInorder (node): if node == None: return # first recur on left child printInorder (node.left) # then print the data of node print(node.data,end=" ") # now recur on right child printInorder (node.right) # Driver Code if __name__ == '__main__': root = None # Constructing tree given in # the above figure # 10 # / \ # 30 15 # / \ # 20 5 pre = [10, 30, 20, 5, 15] preLN = ['N', 'N', 'L', 'L', 'L'] n = len(pre) # construct the above tree root = constructTree (pre, preLN, n) # Test the constructed tree print("Following is Inorder Traversal of", "the Constructed Binary Tree:") printInorder (root) # This code is contributed by PranchalK |
C#
// C# program to construct a binary // tree from preorder traversal using System; // A Binary Tree node public class Node { public int data; public Node left, right; public Node(int item) { data = item; left = right = null; } } public class Index { public int index = 0; } class GFG { public Node root; public Index myindex = new Index(); /* A recursive function to create a Binary Tree from given pre[] preLN[] arrays. The function returns root of tree. index_ptr is used to update index values in recursive calls. index must be initially passed as 0 */public virtual Node constructTreeUtil(int[] pre, char[] preLN, Index index_ptr, int n, Node temp) { // store the current value of index in pre[] int index = index_ptr.index; // Base Case: All nodes are constructed if (index == n) { return null; } // Allocate memory for this node // and increment index for // subsequent recursive calls temp = new Node(pre[index]); (index_ptr.index)++; // If this is an internal node, // construct left and right subtrees // and link the subtrees if (preLN[index] == 'N') { temp.left = constructTreeUtil(pre, preLN, index_ptr, n, temp.left); temp.right = constructTreeUtil(pre, preLN, index_ptr, n, temp.right); } return temp; } // A wrapper over constructTreeUtil() public virtual Node constructTree(int[] pre, char[] preLN, int n, Node node) { // Initialize index as 0. Value of // index is used in recursion to // maintain the current index in // pre[] and preLN[] arrays. int index = 0; return constructTreeUtil(pre, preLN, myindex, n, node); } /* This function is used only for testing */public virtual void printInorder(Node node) { if (node == null) { return; } /* first recur on left child */ printInorder(node.left); /* then print the data of node */ Console.Write(node.data + " "); /* now recur on right child */ printInorder(node.right); } // Driver Code public static void Main(string[] args) { GFG tree = new GFG(); int[] pre = new int[]{10, 30, 20, 5, 15}; char[] preLN = new char[]{'N', 'N', 'L', 'L', 'L'}; int n = pre.Length; // construct the above tree Node mynode = tree.constructTree(pre, preLN, n, tree.root); // Test the constructed tree Console.WriteLine("Following is Inorder Traversal of the" + "Constructed Binary Tree: "); tree.printInorder(mynode); } } // This code is contributed by Shrikant13 |
Output:
Following is Inorder Traversal of the Constructed Binary Tree: 20 30 5 10 15
Time Complexity: O(n)
Construct the full k-ary tree from its preorder traversal
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