Construct Binary Tree from given Parent Array representation

Given an array that represents a tree in such a way that array indexes are values in tree nodes and array values give the parent node of that particular index (or node). The value of the root node index would always be -1 as there is no parent for root. Construct the standard linked representation of given Binary Tree from this given representation.

Examples:

Input: parent[] = {1, 5, 5, 2, 2, -1, 3}
Output: root of below tree
          5
        /  \
       1    2
      /    / \
     0    3   4
         /
        6 
Explanation: 
Index of -1 is 5.  So 5 is root.  
5 is present at indexes 1 and 2.  So 1 and 2 are
children of 5.  
1 is present at index 0, so 0 is child of 1.
2 is present at indexes 3 and 4.  So 3 and 4 are
children of 2.  
3 is present at index 6, so 6 is child of 3.


Input: parent[] = {-1, 0, 0, 1, 1, 3, 5};
Output: root of below tree
         0
       /   \
      1     2
     / \
    3   4
   /
  5 
 /
6

Expected time complexity is O(n) where n is number of elements in given array.

We strongly recommend to minimize your browser and try this yourself first.

A Simple Solution to recursively construct by first searching the current root, then recurring for the found indexes (there can be at most two indexes) and making them left and right subtrees of root. This solution takes O(n²) as we have to linearly search for every node.

An Efficient Solution can solve the above problem in O(n) time. The idea is to use extra space. An array created[0..n-1] is used to keep track of created nodes. 
createTree(parent[], n)

1. Create an array of pointers say created[0..n-1]. The value of created[i] is NULL if node for index i is not created, else value is pointer to the created node.
2. Do following for every index i of given array 
   createNode(parent, i, created)

createNode(parent[], i, created[])

1. If created[i] is not NULL, then node is already created. So return.
2. Create a new node with value ‘i’.
3. If parent[i] is -1 (i is root), make created node as root and return.
4. Check if parent of ‘i’ is created (We can check this by checking if created[parent[i]] is NULL or not.
5. If parent is not created, recur for parent and create the parent first.
6. Let the pointer to parent be p. If p->left is NULL, then make the new node as left child. Else make the new node as right child of parent.

Following is C++ implementation of above idea. 

C++14

// C++ program to construct a Binary Tree from parent array
#include<bits/stdc++.h>
using namespace std;

// A tree node
struct Node
{
    int key;
    struct Node *left, *right;
};

// Utility function to create new Node
Node *newNode(int key)
{
    Node *temp = new Node;
    temp->key  = key;
    temp->left  = temp->right = NULL;
    return (temp);
}

// Creates a node with key as 'i'.  If i is root, then it changes
// root.  If parent of i is not created, then it creates parent first
void createNode(int parent[], int i, Node *created[], Node **root)
{
    // If this node is already created
    if (created[i] != NULL)
        return;

    // Create a new node and set created[i]
    created[i] = newNode(i);

    // If 'i' is root, change root pointer and return
    if (parent[i] == -1)
    {
        *root = created[i];
        return;
    }

    // If parent is not created, then create parent first
    if (created[parent[i]] == NULL)
        createNode(parent, parent[i], created, root);

    // Find parent pointer
    Node *p = created[parent[i]];

    // If this is first child of parent
    if (p->left == NULL)
        p->left = created[i];
    else // If second child
        p->right = created[i];
}

// Creates tree from parent[0..n-1] and returns root of the created tree
Node *createTree(int parent[], int n)
{
    // Create an array created[] to keep track
    // of created nodes, initialize all entries
    // as NULL
    Node *created[n];
    for (int i=0; i<n; i++)
        created[i] = NULL;

    Node *root = NULL;
    for (int i=0; i<n; i++)
        createNode(parent, i, created, &root);

    return root;
}

//For adding new line in a program
inline void newLine(){
    cout << "\n";
}

// Utility function to do inorder traversal
void inorder(Node *root)
{
    if (root != NULL)
    {
        inorder(root->left);
        cout << root->key << " ";
        inorder(root->right);
    }
}

// Driver method
int main()
{
    int parent[] =  {-1, 0, 0, 1, 1, 3, 5};
    int n = sizeof parent / sizeof parent[0];
    Node *root = createTree(parent, n);
    cout << "Inorder Traversal of constructed tree\n";
    inorder(root);
    newLine();
}

Java

// Java program to construct a binary tree from parent array

// A binary tree node
class Node
{
    int key;
    Node left, right;

    public Node(int key)
    {
        this.key = key;
        left = right = null;
    }
}

class BinaryTree
{
    Node root;

    // Creates a node with key as 'i'.  If i is root, then it changes
    // root.  If parent of i is not created, then it creates parent first
    void createNode(int parent[], int i, Node created[])
    {
        // If this node is already created
        if (created[i] != null)
            return;

        // Create a new node and set created[i]
        created[i] = new Node(i);

        // If 'i' is root, change root pointer and return
        if (parent[i] == -1)
        {
            root = created[i];
            return;
        }

        // If parent is not created, then create parent first
        if (created[parent[i]] == null)
            createNode(parent, parent[i], created);

        // Find parent pointer
        Node p = created[parent[i]];

        // If this is first child of parent
        if (p.left == null)
            p.left = created[i];
        else // If second child

            p.right = created[i];
    }

    /* Creates tree from parent[0..n-1] and returns root of
       the created tree */
    Node createTree(int parent[], int n)
    {
        // Create an array created[] to keep track
        // of created nodes, initialize all entries
        // as NULL
        Node[] created = new Node[n];
        for (int i = 0; i < n; i++)
            created[i] = null;

        for (int i = 0; i < n; i++)
            createNode(parent, i, created);

        return root;
    }

    //For adding new line in a program
    void newLine()
    {
        System.out.println("");
    }

    // Utility function to do inorder traversal
    void inorder(Node node)
    {
        if (node != null)
        {
            inorder(node.left);
            System.out.print(node.key + " ");
            inorder(node.right);
        }
    }

    // Driver method
    public static void main(String[] args)
    {

        BinaryTree tree = new BinaryTree();
        int parent[] = new int[]{-1, 0, 0, 1, 1, 3, 5};
        int n = parent.length;
        Node node = tree.createTree(parent, n);
        System.out.println("Inorder traversal of constructed tree ");
        tree.inorder(node);
        tree.newLine();
    }
}

// This code has been contributed by Mayank Jaiswal(mayank_24)

Python3

# Python implementation to construct a Binary Tree from
# parent array

# A node structure
class Node:
    # A utility function to create a new node
    def __init__(self, key):
        self.key = key
        self.left = None
        self.right = None

""" Creates a node with key as 'i'. If i is root,then
    it changes root. If parent of i is not created, then
    it creates parent first
"""
def createNode(parent, i, created, root):

    # If this node is already created
    if created[i] is not None:
        return

    # Create a new node and set created[i]
    created[i] = Node(i)

    # If 'i' is root, change root pointer and return
    if parent[i] == -1:
        root[0] = created[i] # root[0] denotes root of the tree
        return

    # If parent is not created, then create parent first
    if created[parent[i]] is None:
        createNode(parent, parent[i], created, root )

    # Find parent pointer
    p = created[parent[i]]

    # If this is first child of parent
    if p.left is None:
        p.left = created[i]
    # If second child
    else:
        p.right = created[i]


# Creates tree from parent[0..n-1] and returns root of the
# created tree
def createTree(parent):
    n = len(parent)

    # Create and array created[] to keep track
    # of created nodes, initialize all entries as None
    created = [None for i in range(n+1)]

    root = [None]
    for i in range(n):
        createNode(parent, i, created, root)

    return root[0]

#Inorder traversal of tree
def inorder(root):
    if root is not None:
        inorder(root.left)
        print (root.key,end=" ")
        inorder(root.right)

# Driver Method
parent = [-1, 0, 0, 1, 1, 3, 5]
root = createTree(parent)
print ("Inorder Traversal of constructed tree")
inorder(root)

# This code is contributed by Nikhil Kumar Singh(nickzuck_007)

C#

// C# program to construct a binary
// tree from parent array
using System;

// A binary tree node
public class Node
{
    public int key;
    public Node left, right;

    public Node(int key)
    {
        this.key = key;
        left = right = null;
    }
}

class GFG
{
public Node root;

// Creates a node with key as 'i'.
// If i is root, then it changes
// root. If parent of i is not created,
// then it creates parent first
public virtual void createNode(int[] parent,
                               int i, Node[] created)
{
    // If this node is already created
    if (created[i] != null)
    {
        return;
    }

    // Create a new node and set created[i]
    created[i] = new Node(i);

    // If 'i' is root, change root
    // pointer and return
    if (parent[i] == -1)
    {
        root = created[i];
        return;
    }

    // If parent is not created, then
    // create parent first
    if (created[parent[i]] == null)
    {
        createNode(parent, parent[i], created);
    }

    // Find parent pointer
    Node p = created[parent[i]];

    // If this is first child of parent
    if (p.left == null)
    {
        p.left = created[i];
    }
    else // If second child
    {

        p.right = created[i];
    }
}

/* Creates tree from parent[0..n-1]
and returns root of the created tree */
public virtual Node createTree(int[] parent, int n)
{
    // Create an array created[] to
    // keep track of created nodes,
    // initialize all entries as NULL
    Node[] created = new Node[n];
    for (int i = 0; i < n; i++)
    {
        created[i] = null;
    }

    for (int i = 0; i < n; i++)
    {
        createNode(parent, i, created);
    }

    return root;
}

// For adding new line in a program
public virtual void newLine()
{
    Console.WriteLine("");
}

// Utility function to do inorder traversal
public virtual void inorder(Node node)
{
    if (node != null)
    {
        inorder(node.left);
        Console.Write(node.key + " ");
        inorder(node.right);
    }
}

// Driver Code
public static void Main(string[] args)
{
    GFG tree = new GFG();
    int[] parent = new int[]{-1, 0, 0, 1, 1, 3, 5};
    int n = parent.Length;
    Node node = tree.createTree(parent, n);
    Console.WriteLine("Inorder traversal of " +
                          "constructed tree ");
    tree.inorder(node);
    tree.newLine();
}
}

// This code is contributed by Shrikant13

Javascript

<script>

// Javascript program to construct a binary
// tree from parent array

// A binary tree node
class Node
{
  constructor(key)
  {
    this.key = key;
    this.left = null;
    this.right = null;
  }
}


var root = null;

// Creates a node with key as 'i'.
// If i is root, then it changes
// root. If parent of i is not created,
// then it creates parent first
function createNode(parent, i, created)
{
    // If this node is already created
    if (created[i] != null)
    {
        return;
    }

    // Create a new node and set created[i]
    created[i] = new Node(i);

    // If 'i' is root, change root
    // pointer and return
    if (parent[i] == -1)
    {
        root = created[i];
        return;
    }

    // If parent is not created, then
    // create parent first
    if (created[parent[i]] == null)
    {
        createNode(parent, parent[i], created);
    }

    // Find parent pointer
    var p = created[parent[i]];

    // If this is first child of parent
    if (p.left == null)
    {
        p.left = created[i];
    }
    else // If second child
    {

        p.right = created[i];
    }
}

/* Creates tree from parent[0..n-1]
and returns root of the created tree */
function createTree(parent, n)
{
    // Create an array created[] to
    // keep track of created nodes,
    // initialize all entries as NULL
    var created = Array(n);
    for (var i = 0; i < n; i++)
    {
        created[i] = null;
    }

    for (var i = 0; i < n; i++)
    {
        createNode(parent, i, created);
    }

    return root;
}

// For adding new line in a program
function newLine()
{
    document.write("");
}

// Utility function to do inorder traversal
function inorder(node)
{
    if (node != null)
    {
        inorder(node.left);
        document.write(node.key + " ");
        inorder(node.right);
    }
}

// Driver Code
var parent = [-1, 0, 0, 1, 1, 3, 5];
var n = parent.length;
var node = createTree(parent, n);
document.write("Inorder traversal of " +
                      "constructed tree<br>");
inorder(node);
newLine();

// This code is contributed by rrrtnx.

</script>

Output

Inorder Traversal of constructed tree
6 5 3 1 4 0 2 

Time Complexity: O(n^2)

In this approach, we iterate over the parent array, and in the worst case, we need to create a node for every element in the array. And in the createNode() function, the main time complexity is due to the recursive calls that depend on the height of the tree, which can be n. So, the overall time complexity of the algorithm is O(n^2).

Space Complexity: O(n)

The space complexity of the algorithm is linear, i.e., O(n), since we need to create a node for every element of the parent array.

Another Efficient Solution:

The idea is to first create all n new tree nodes, each having values from 0 to n – 1, where n is the size of parent array, and store them in any data structure like map, array etc to keep track of which node is created for which value. Then traverse the given parent array and build the tree by setting the parent-child relationship.

Following is the C++ implementation of the above idea.

C++

// C++ program to construct a Binary Tree from parent array
#include <bits/stdc++.h>
using namespace std;


struct Node {
    int data;
    struct Node* left = NULL;
    struct Node* right = NULL;
    Node() {}

    Node(int x) { data = x; }
};

// Function to construct binary tree from parent array.
Node* createTree(int parent[], int n)
{
    // Create an array to store the reference
    // of all newly created nodes corresponding
    // to node value
    vector<Node*> ref;

    // This root represent the root of the
    // newly constructed tree
    Node* root = new Node();

    // Create n new tree nodes, each having
    // a value from 0 to n-1, and store them
    // in ref
    for (int i = 0; i < n; i++) {
        Node* temp = new Node(i);
        ref.push_back(temp);
    }

    // Traverse the parent array and build the tree
    for (int i = 0; i < n; i++) {

        // If the parent is -1, set the root
        // to the current node having
        // the value i which is stored in ref[i]
        if (parent[i] == -1) {
            root = ref[i];
        }
        else {
            // Check if the parent's left child
            // is NULL then map the left child
            // to its parent.
            if (ref[parent[i]]->left == NULL)
                ref[parent[i]]->left = ref[i];
            else
                ref[parent[i]]->right = ref[i];
        }
    }

    // Return the root of the newly constructed tree
    return root;
}

// Function for inorder traversal
void inorder(Node* root)
{
    if (root != NULL) {
        inorder(root->left);
        cout << root->data << " ";
        inorder(root->right);
    }
}

// Driver code
int main()
{
    int parent[] = { -1, 0, 0, 1, 1, 3, 5 };
    int n = sizeof parent / sizeof parent[0];
    Node* root = createTree(parent, n);
    cout << "Inorder Traversal of constructed tree\n";
    inorder(root);
    return 0;
}

Java

// Java program to construct a Binary Tree from parent array

// A binary tree node
class Node {
    int key;
    Node left, right;
    public Node() {}
    public Node(int key)
    {
        this.key = key;
        left = right = null;
    }
}

class BinaryTree {
    Node root;

    // Function to construct binary tree from parent array.
    Node createTree(int parent[], int n)
    {
        // Create an array to store the reference
        // of all newly created nodes corresponding
        // to node value
        Node[] ref = new Node[n];

        // This root represent the root of the
        // newly constructed tree
        Node root = new Node();

        // Create n new tree nodes, each having
        // a value from 0 to n-1, and store them
        // in ref
        for (int i = 0; i < n; i++) {
            Node temp = new Node(i);
            ref[i] = temp;
        }

        // Traverse the parent array and build the tree
        for (int i = 0; i < n; i++) {

            // If the parent is -1, set the root
            // to the current node having
            // the value i which is stored in ref[i]
            if (parent[i] == -1) {
                root = ref[i];
            }
            else {
                // Check if the parent's left child
                // is NULL then map the left child
                // to its parent.
                if (ref[parent[i]].left == null)
                    ref[parent[i]].left = ref[i];
                else
                    ref[parent[i]].right = ref[i];
            }
        }

        // Return the root of the newly constructed tree
        return root;
    }

    // function for inorder traversal
    void inorder(Node node)
    {
        if (node != null) {
            inorder(node.left);
            System.out.print(node.key + " ");
            inorder(node.right);
        }
    }

    // Driver code
    public static void main(String[] args)
    {

        BinaryTree tree = new BinaryTree();
        int parent[] = new int[] { -1, 0, 0, 1, 1, 3, 5 };
        int n = parent.length;
        Node node = tree.createTree(parent, n);
        System.out.println(
            "Inorder traversal of constructed tree ");
        tree.inorder(node);
    }
}

// This code has been contributed by Abhijeet Kumar(abhijeet19403)

Python3

# Python program to construct a Binary Tree from parent array
class Node:
    def __init__(self, x):
        self.data = x
        self.left = None
        self.right = None


# Function to construct binary tree from parent array
def createTree(parent, n):
    # Create an array to store the reference
    # of all newly created nodes corresponding
    # to node value
    ref = []

    # This root refpresent the roof of the
    # newly constructed tree

    # create n new tree nodes, each having
    # a value from 0 to n-1, and store them in ref
    for i in range(0, n):
        temp = Node(i)
        ref.append(temp)

    # Traverse the parent array and build the tree
    for i in range(0, n):
        # If the parent is -1, set the root
        # to the current node having
        # the value i which is stored in ref[i]
        if parent[i] == -1:
            root = ref[i]

        else:
            # check if the parent's left child
            # is NULL then map the left child
            # to its parent.
            if ref[parent[i]].left is None:
                ref[parent[i]].left = ref[i]
            else:
                ref[parent[i]].right = ref[i]

    # return the root of the newly constructed tree
    return root


# Function for inorder traversal
def inorder(root):
    if root is not None:
        inorder(root.left)
        print(root.data, end=" ")
        inorder(root.right)


# Driver code
parent = [-1, 0, 0, 1, 1, 3, 5]
n = 7
root = createTree(parent, n)
print("Inorder traversal of constructed tree")
inorder(root)

# This code is contributed by Kirti Agarwal

C#

// C# program to construct a Binary Tree from parent array
using System;

// A binary tree node
class Node {
  public int key;
  public Node left, right;
  public Node() {}
  public Node(int key)
  {
    this.key = key;
    left = right = null;
  }
}

class BinaryTree {
  public Node root;

  // Function to construct binary tree from parent array.
  public Node createTree(int[] parent, int n)
  {
    // Create an array to store the reference
    // of all newly created nodes corresponding
    // to node value
    Node[] refi = new Node[n];

    // This root represent the root of the
    // newly constructed tree
    Node root = new Node();

    // Create n new tree nodes, each having
    // a value from 0 to n-1, and store them
    // in ref
    for (int i = 0; i < n; i++) {
      Node temp = new Node(i);
      refi[i] = temp;
    }

    // Traverse the parent array and build the tree
    for (int i = 0; i < n; i++) {

      // If the parent is -1, set the root
      // to the current node having
      // the value i which is stored in ref[i]
      if (parent[i] == -1) {
        root = refi[i];
      }
      else {
        // Check if the parent's left child
        // is NULL then map the left child
        // to its parent.
        if (refi[parent[i]].left == null)
          refi[parent[i]].left = refi[i];
        else
          refi[parent[i]].right = refi[i];
      }
    }

    // Return the root of the newly constructed tree
    return root;
  }

  // function for inorder traversal
  public void inorder(Node node)
  {
    if (node != null) {
      inorder(node.left);
      Console.Write(node.key + " ");
      inorder(node.right);
    }
  }

  // Driver code
  public static void Main(String[] args)
  {

    BinaryTree tree = new BinaryTree();

    int[] parent = new int[] { -1, 0, 0, 1, 1, 3, 5 };
    int n = parent.Length;
    Node node = tree.createTree(parent, n);
    Console.WriteLine(
      "Inorder traversal of constructed tree ");
    tree.inorder(node);
  }
}

// This code is contributed by lokeshpotta20.

Javascript

// JavaScript Program to construct a Binary tree from parent array
class Node{
    constructor(x){
        this.data = x;
        this.left = null;
        this.right = null;
    }
}

// Functiont to construct binary tree from parent array
function createTree(parent, n){
    // create an array to store the reference
    // of all newly created nodes corresponding
    // to node value
    let ref = [];

    // This root represent the root of the
    // newly constructed tree
    let root = new Node();

    // create a new treenodes, each having
    // a value from 1 to n-1, and store them
    // in ref
    for(let i = 0; i<n; i++){
        let temp = new Node(i);
        ref.push(temp);
    }

    // Traverse the parent array and build the tree
    for(let i = 0; i<n; i++){
        // If the parent is -1, set the root
        // to the current node having
        // the value i which is stored in ref[i]
        if(parent[i] == -1){
            root = ref[i];
        }else{
            // check if the parent's left child
            // is NULL then map the left child
            // to its parent.
            if(ref[parent[i]].left == null){
                ref[parent[i]].left = ref[i];
            }else{
                ref[parent[i]].right = ref[i];
            }
        }
    }
    return root;
}

// Function for Inorder Traversal
function inorder(root){
    if(root != null){
        inorder(root.left);
        console.log(root.data + " ");
        inorder(root.right);
    }
}

// Driver Code
let parent = [-1, 0, 0, 1, 1, 3, 5];
let n = parent.length;
let root = createTree(parent, n);
console.log("Inorder Traversal of constructed tree ");
inorder(root);

// This code is contributed by Yash Agarwal(yashagarwal2852002)

Output

Inorder Traversal of constructed tree
6 5 3 1 4 0 2 

Time Complexity: O(n), where n is the size of parent array
Auxiliary Space: O(n)

Similar Problem: Find Height of Binary Tree represented by Parent array
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