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Construct a special tree from given preorder traversal

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  • Difficulty Level : Hard
  • Last Updated : 17 Jun, 2022

Given an array ‘pre[]’ that represents Preorder traversal of a special 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 a 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

Approach: The first element in pre[] will always be root. So we can easily figure out the root. If the left subtree is empty, the right subtree must also be empty, and the preLN[] entry for root must be ‘L’. We can simply create a node and return it. If the left and right subtrees are not empty, then recursively call for left and right subtrees and link the returned nodes to root.  
Below is the implementation of the above approach: 

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);
 
    // Print the data of node
    printf("%d ", node->data);
 
    // Now recur on right child
    printInorder (node->right);
}
 
// Driver code
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("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

Javascript




<script>
  
 
// JavaScript program to construct a binary
// tree from preorder traversal
 
// A Binary Tree node
class Node
{
    constructor(item)
    {
        this.data = item;
        this.left = null;
        this.right = null;
    }
}
 
class Index
{
    constructor()
    {
        this.index = 0;
    }
}
 
 
var root = null;
var 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 */
function constructTreeUtil(pre, preLN, index_ptr, n, temp)
{
    // store the current value of index in pre[]
    var 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()
function constructTree(pre, preLN, n, node)
{
    // Initialize index as 0. Value of
    // index is used in recursion to
    // maintain the current index in
    // pre[] and preLN[] arrays.
    var index = 0;
 
    return constructTreeUtil(pre, preLN,
                             myindex, n, node);
}
 
/* This function is used only for testing */
function printInorder( node)
{
    if (node == null)
    {
        return;
    }
 
    /* first recur on left child */
    printInorder(node.left);
 
    /* then print the data of node */
    document.write(node.data + " ");
 
    /* now recur on right child */
    printInorder(node.right);
}
 
// Driver Code
var pre = [10, 30, 20, 5, 15];
var preLN = ['N', 'N', 'L', 'L', 'L'];
var n = pre.length;
// construct the above tree
var mynode = constructTree(pre, preLN,
                                 n, root);
// Test the constructed tree
document.write("Following is Inorder Traversal of the" +
                              "Constructed Binary Tree:<br>");
printInorder(mynode);
 
 
 
</script>

Output

Inorder Traversal of the Constructed Binary Tree: 
20 30 5 10 15 

Time Complexity: O(n)
Auxiliary Space: O(n)

Method 2: Using Stack without recursion

Approach: 

  • As the Pre-order Traversal is given so we first make a root and insert the first value into it.
  • Traverse the given pre-order traversal.
    • Check the left of stack’s top
      • If it  NULL then we add the present node on left
      • Otherwise, Add into right if right is NULL.
    • If left and right both are not NULL, it means that the node have both left and right so we pop out the nodes until we won’t get any node whose left or right is NULL.
    • If the present node is not a leaf node, push node into the stack.
  • Finally return the root of the constructed tree.

Below is the implementation of the above approach: 

C++




// A program to construct Binary Tree from preorder
// traversal
#include <bits/stdc++.h>
using namespace std;
 
// A binary tree node structure
struct node {
    int data;
    struct node* left;
    struct node* right;
    node(int x)
    {
        data = x;
        left = right = NULL;
    }
};
 
struct node* constructTree(int pre[], char preLN[], int n)
{
    // Taking an empty Stack
    stack<node*> st;
 
    // Setting up root node
    node* root = new node(pre[0]);
    // Checking if root is not leaf node
    if (preLN[0] != 'L')
        st.push(root);
 
    // Iterating over the given node values
    for (int i = 1; i < n; i++) {
        node* temp = new node(pre[i]);
 
        // Checking if the left position is NULL or not
        if (!st.top()->left) {
            st.top()->left = temp;
 
            // Checking for leaf node
            if (preLN[i] != 'L')
                st.push(temp);
        }
 
        // Checking if the right position is NULL or not
        else if (!st.top()->right) {
            st.top()->right = temp;
            if (preLN[i] != 'L')
 
                // Checking for leaf node
                st.push(temp);
        }
 
        // If left and right of top node is already filles
        else {
            while (st.top()->left && st.top()->right)
                st.pop();
            st.top()->right = temp;
 
            // Checking for leaf node
            if (preLN[i] != 'L')
                st.push(temp);
        }
    }
 
    // Returning the root of tree
    return root;
}
 
// This function is used only for testing
void printInorder(struct node* node)
{
    if (node == NULL)
        return;
 
    // First recur on left child
    printInorder(node->left);
 
    // Print the data of node
    printf("%d ", node->data);
 
    // Now recur on right child
    printInorder(node->right);
}
 
// Driver code
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("Inorder Traversal of the Constructed Binary Tree: \n");
    printInorder(root);
 
    return 0;
}
 
// This code is contributed by shubhamrajput6156

Java




// Java program to construct Binary Tree from preorder
// traversal
 
// A Binary Tree node
import java.util.*;
 
class GFG
{
static class node {
    int data;
    node left, right;
 
    node(int item)
    {
        data = item;
        left = right = null;
    }
}
 
 public static node constructTree(int []pre, char []preLN, int n)
{
    // Taking an empty Stack
    Stack<node> st = new Stack<node>();
 
    // Setting up root node
    node root = new node(pre[0]);
    // Checking if root is not leaf node
    if (preLN[0] != 'L')
        st.push(root);
 
    // Iterating over the given node values
    for (int i = 1; i < n; i++) {
        node temp = new node(pre[i]);
 
        // Checking if the left position is NULL or not
        if (st.peek().left==null) {
            st.peek().left = temp;
 
            // Checking for leaf node
            if (preLN[i] != 'L')
                st.push(temp);
        }
 
        // Checking if the right position is NULL or not
        else if (st.peek().right==null) {
            st.peek().right = temp;
             
            // Checking for leaf node
            if (preLN[i] != 'L')
                st.push(temp);
        }
 
        // If left and right of top node is already filles
        else {
            while (st.peek().left!=null && st.peek().right!=null)
                st.pop();
            st.peek().right = temp;
 
            // Checking for leaf node
            if (preLN[i] != 'L')
                st.push(temp);
        }
    }
 
    // Returning the root of tree
    return root;
}
 
// This function is used only for testing
public static void printInorder( node temp)
{
    if (temp == null)
        return;
 
    // First recur on left child
    printInorder(temp.left);
 
    // Print the data of node
    System.out.println(temp.data);
 
    // Now recur on right child
    printInorder(temp.right);
}
 
    // driver function to test the above functions
    public static void main(String args[])
    {
    //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 = pre.length;
 
    // construct the above tree
    node root = constructTree(pre, preLN, n);
 
    // Test the constructed tree
    System.out.println("Inorder Traversal of the Constructed Binary Tree: ");
    printInorder(root);
    }
}
 
// This code is contributed by jana_sayantan.

Output

Inorder Traversal of the Constructed Binary Tree: 
20 30 5 10 15 

Time Complexity: O(n)
Auxiliary Space: O(n)

Construct the full k-ary tree from its preorder traversal


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