🏆 Live Soccer TV: dsa/check if given preorder inorder and postorder traversals are of same tree

Given the Preorder, Inorder, and Postorder traversal sequences of a binary tree. Determine whether these three traversal sequences can belong to the same binary tree.

Return true if all three traversals represent the same tree; otherwise, return false.

Examples:

Input: pre[] = [1, 2, 4, 5, 3], in[] = [4, 2, 5, 1, 3], post[] = [4, 5, 2, 3, 1]
Output: true
Explanation: All of the above three traversal sequences are of the same binary tree.

Input: pre[] = [1, 5, 4, 2, 3], in[] = [4, 2, 5, 1, 3], post[] = [4, 1, 2, 3, 5]
Output: false
Explanation: First element in preorder and the last element in postorder must be same, but here they are different (1 and 5). Hence, answer is false.

Try It Yourself

Table of Content

[Naive Approach] Tree Construction Using Inorder and Preorder - O(n ^ 2) Time and O(n) Space
[Better Approach] Tree Construction With Hash Map - O(n) Time and O(n) Space
[Expected Approach] Without Constructing Tree - O(n) Time and O(n) Space

[Naive Approach] Tree Construction Using Inorder and Preorder - O(n ^ 2) Time and O(n) Space

The idea is to use the inorder and preorder (inorder and postorder can also be used) traversals(refer to this post) to build the tree. After constructing the tree, generate its postorder traversal and compare it with the given postorder traversal. If both traversals match, all three traversals belong to the same tree; otherwise, they do not.

Check whether the sizes of the preorder, inorder, and postorder traversals are equal. If not, return false.
Construct a binary tree using the given inorder and preorder traversals.
Pick the current node from preorder and locate its position in the inorder traversal.
Recursively construct the left and right subtrees using the inorder boundaries.
Generate the postorder traversal of the constructed tree and compare it with the given postorder traversal.
If the generated and given postorder traversals match completely, return true; otherwise, return false.

C++

#include <bits/stdc++.h>
using namespace std;

class Node
{
  public:
    int data;
    Node *left, *right;

    Node(int val)
    {
        data = val;
        left = right = nullptr;
    }
};

/* Search value in inorder vector */
int search(vector<int> &in, int start, int end, int value)
{
    for (int i = start; i <= end; i++)
    {
        if (in[i] == value)
            return i;
    }

    return -1;
}

/* Build tree using inorder and preorder */
Node *buildTree(vector<int> &in, vector<int> &pre, int inStart, int inEnd, int &preIndex)
{
    if (inStart > inEnd)
        return nullptr;

    // Traversal exhausted
    if (preIndex >= pre.size())
        return nullptr;

    // Find current root in inorder
    // before creating node
    int inIndex = search(in, inStart, inEnd, pre[preIndex]);

    // Invalid traversal
    if (inIndex == -1)
        return nullptr;

    // Create current node
    Node *root = new Node(pre[preIndex++]);

    // Leaf node
    if (inStart == inEnd)
        return root;

    // Construct left subtree
    root->left = buildTree(in, pre, inStart, inIndex - 1, preIndex);

    // Construct right subtree
    root->right = buildTree(in, pre, inIndex + 1, inEnd, preIndex);

    return root;
}

/* Compare generated postorder with given postorder */
int checkPostorder(Node *root, vector<int> &post, int index)
{
    if (root == nullptr)
        return index;

    index = checkPostorder(root->left, post, index);

    if (index == -1)
        return -1;

    index = checkPostorder(root->right, post, index);

    if (index == -1)
        return -1;

    // Compare current node
    if (root->data == post[index])
        return index + 1;

    return -1;
}

bool checktree(vector<int> &pre, vector<int> &in, vector<int> &post)
{
    int n = in.size();

    // Traversals must have same size
    if (pre.size() != n || post.size() != n)
        return false;

    int preIndex = 0;

    // Build tree from inorder
    // and preorder
    Node *root = buildTree(in, pre, 0, n - 1, preIndex);

    // Invalid tree construction
    if (root == nullptr && n > 0)
        return false;

    // Compare generated postorder
    // with given postorder
    int index = checkPostorder(root, post, 0);

    return (index == n);
}

int main()
{
    vector<int> in = {4, 2, 5, 1, 3};
    vector<int> pre = {1, 2, 4, 5, 3};
    vector<int> post = {4, 5, 2, 3, 1};

    cout << (checktree(pre, in, post) ? "true" : "false");

    return 0;
}

Java

import java.util.*;

class Node {
    public int data;
    public Node left, right;

    Node(int val)
    {
        data = val;
        left = right = null;
    }
}

public class GFG {
    /* Search value in inorder vector */
    static int search(int[] in, int start, int end,
                      int value)
    {
        for (int i = start; i <= end; i++) {
            if (in[i] == value)
                return i;
        }

        return -1;
    }

    /* Build tree using inorder and preorder */
    static Node buildTree(int[] in, int[] pre, int inStart,
                          int inEnd, int[] preIndex)
    {
        if (inStart > inEnd)
            return null;

        // Traversal exhausted
        if (preIndex[0] >= pre.length)
            return null;

        // Find current root in inorder
        // before creating node
        int inIndex
            = search(in, inStart, inEnd, pre[preIndex[0]]);

        // Invalid traversal
        if (inIndex == -1)
            return null;

        // Create current node
        Node root = new Node(pre[preIndex[0]++]);

        // Leaf node
        if (inStart == inEnd)
            return root;

        // Construct left subtree
        root.left = buildTree(in, pre, inStart, inIndex - 1,
                              preIndex);

        // Construct right subtree
        root.right = buildTree(in, pre, inIndex + 1, inEnd,
                               preIndex);

        return root;
    }

    /* Compare generated postorder with given postorder */
    static int checkPostorder(Node root, int[] post,
                              int index)
    {
        if (root == null)
            return index;

        index = checkPostorder(root.left, post, index);

        if (index == -1)
            return -1;

        index = checkPostorder(root.right, post, index);

        if (index == -1)
            return -1;

        // Compare current node
        if (root.data == post[index])
            return index + 1;

        return -1;
    }

    static boolean checktree(int[] pre, int[] in,
                             int[] post)
    {
        int n = in.length;

        // Traversals must have same size
        if (pre.length != n || post.length != n)
            return false;

        int[] preIndex = { 0 };

        // Build tree from inorder
        // and preorder
        Node root = buildTree(in, pre, 0, n - 1, preIndex);

        // Invalid tree construction
        if (root == null && n > 0)
            return false;

        // Compare generated postorder
        // with given postorder
        int index = checkPostorder(root, post, 0);

        return (index == n);
    }

    public static void main(String[] args)
    {
        int[] in = { 4, 2, 5, 1, 3 };
        int[] pre = { 1, 2, 4, 5, 3 };
        int[] post = { 4, 5, 2, 3, 1 };

        System.out.println(
            checktree(pre, in, post) ? "true" : "false");
    }
}

Python

class Node:

    def __init__(self, val):
        self.data = val
        self.left = None
        self.right = None


""" Search value in inorder vector """
def search(inorder, start, end, value):

    for i in range(start, end + 1):
        if inorder[i] == value:
            return i

    return -1


""" Build tree using inorder and preorder """
def buildTree(inorder, pre, inStart, inEnd, preIndex):

    if inStart > inEnd:
        return None

    # Traversal exhausted
    if preIndex[0] >= len(pre):
        return None

    # Find current root in inorder
    # before creating node
    inIndex = search(inorder, inStart, inEnd, pre[preIndex[0]])

    # Invalid traversal
    if inIndex == -1:
        return None

    # Create current node
    root = Node(pre[preIndex[0]])
    preIndex[0] += 1

    # Leaf node
    if inStart == inEnd:
        return root

    # Construct left subtree
    root.left = buildTree(inorder, pre, inStart, inIndex - 1, preIndex)

    # Construct right subtree
    root.right = buildTree(inorder, pre, inIndex + 1, inEnd, preIndex)

    return root


""" Compare generated postorder with given postorder """
def checkPostorder(root, post, index):

    if root is None:
        return index

    index = checkPostorder(root.left, post, index)

    if index == -1:
        return -1

    index = checkPostorder(root.right, post, index)

    if index == -1:
        return -1

    # Compare current node
    if root.data == post[index]:
        return index + 1

    return -1


def checktree(pre, inorder, post):

    n = len(inorder)

    # Traversals must have same size
    if len(pre) != n or len(post) != n:
        return False

    preIndex = [0]

    # Build tree from inorder
    # and preorder
    root = buildTree(inorder, pre, 0, n - 1, preIndex)

    # Invalid tree construction
    if root is None and n > 0:
        return False

    # Compare generated postorder
    # with given postorder
    index = checkPostorder(root, post, 0)

    return index == n

# Driver Code

if __name__ == "__main__":
    inorder = [4, 2, 5, 1, 3]
    pre = [1, 2, 4, 5, 3]
    post = [4, 5, 2, 3, 1]

    print(str(checktree(pre, inorder, post)).lower())

using System;

class Node {
    public int data;
    public Node left, right;

    public Node(int val)
    {
        data = val;
        left = right = null;
    }
}

class GFG {
    /* Search value in inorder vector */
    static int search(int[] inOrder, int start, int end,
                      int value)
    {
        for (int i = start; i <= end; i++) {
            if (inOrder[i] == value)
                return i;
        }

        return -1;
    }

    /* Build tree using inorder and preorder */
    static Node buildTree(int[] inOrder, int[] pre,
                          int inStart, int inEnd,
                          ref int preIndex)
    {
        if (inStart > inEnd)
            return null;

        // Traversal exhausted
        if (preIndex >= pre.Length)
            return null;

        // Find current root in inorder
        // before creating node
        int inIndex
            = search(inOrder, inStart, inEnd, pre[preIndex]);

        // Invalid traversal
        if (inIndex == -1)
            return null;

        // Create current node
        Node root = new Node(pre[preIndex++]);

        // Leaf node
        if (inStart == inEnd)
            return root;

        // Construct left subtree
        root.left = buildTree(inOrder, pre, inStart,
                              inIndex - 1, ref preIndex);

        // Construct right subtree
        root.right = buildTree(inOrder, pre, inIndex + 1,
                               inEnd, ref preIndex);

        return root;
    }

    /* Compare generated postorder with given postorder */
    static int checkPostorder(Node root, int[] post,
                              int index)
    {
        if (root == null)
            return index;

        index = checkPostorder(root.left, post, index);

        if (index == -1)
            return -1;

        index = checkPostorder(root.right, post, index);

        if (index == -1)
            return -1;

        // Compare current node
        if (root.data == post[index])
            return index + 1;

        return -1;
    }

    static bool checktree(int[] pre, int[] inOrder,
                          int[] post)
    {
        int n = inOrder.Length;

        // Traversals must have same size
        if (pre.Length != n || post.Length != n)
            return false;

        int preIndex = 0;

        // Build tree from inorder
        // and preorder
        Node root
            = buildTree(inOrder, pre, 0, n - 1, ref preIndex);

        // Invalid tree construction
        if (root == null && n > 0)
            return false;

        // Compare generated postorder
        // with given postorder
        int index = checkPostorder(root, post, 0);

        return (index == n);
    }

    static void Main()
    {
        int[] inOrder = { 4, 2, 5, 1, 3 };
        int[] pre = { 1, 2, 4, 5, 3 };
        int[] post = { 4, 5, 2, 3, 1 };

        Console.WriteLine(
            checktree(pre, inOrder, post) ? "true" : "false");
    }
}

JavaScript

class Node {
    constructor(val)
    {
        this.data = val;
        this.left = null;
        this.right = null;
    }
}

/* Search value in inorder vector */
function search(inOrder, start, end, value)
{
    for (let i = start; i <= end; i++) {
        if (inOrder[i] === value)
            return i;
    }

    return -1;
}

/* Build tree using inorder and preorder */
function buildTree(inOrder, pre, inStart, inEnd, preIndex)
{
    if (inStart > inEnd)
        return null;

    // Traversal exhausted
    if (preIndex.value >= pre.length)
        return null;

    // Find current root in inorder
    // before creating node
    let inIndex = search(inOrder, inStart, inEnd,
                         pre[preIndex.value]);

    // Invalid traversal
    if (inIndex === -1)
        return null;

    // Create current node
    let root = new Node(pre[preIndex.value++]);

    // Leaf node
    if (inStart === inEnd)
        return root;

    // Construct left subtree
    root.left = buildTree(inOrder, pre, inStart, inIndex - 1,
                          preIndex);

    // Construct right subtree
    root.right = buildTree(inOrder, pre, inIndex + 1, inEnd,
                           preIndex);

    return root;
}

/* Compare generated postorder with given postorder */
function checkPostorder(root, post, index)
{
    if (root === null)
        return index;

    index = checkPostorder(root.left, post, index);

    if (index === -1)
        return -1;

    index = checkPostorder(root.right, post, index);

    if (index === -1)
        return -1;

    // Compare current node
    if (root.data === post[index])
        return index + 1;

    return -1;
}

function checktree(pre, inOrder, post)
{
    let n = inOrder.length;

    // Traversals must have same size
    if (pre.length !== n || post.length !== n)
        return false;

    let preIndex = {value : 0};

    // Build tree from inorder
    // and preorder
    let root = buildTree(inOrder, pre, 0, n - 1, preIndex);

    // Invalid tree construction
    if (root === null && n > 0)
        return false;

    // Compare generated postorder
    // with given postorder
    let index = checkPostorder(root, post, 0);

    return index === n;
}

// Driver Code
let inOrder = [ 4, 2, 5, 1, 3 ];
let pre = [ 1, 2, 4, 5, 3 ];
let post = [ 4, 5, 2, 3, 1 ];

console.log(checktree(pre, inOrder, post) ? "true" : "false");

Output

true

[Better Approach] Tree Construction With Hash Map - O(n) Time and O(n) Space

The idea is to construct the binary tree using the given inorder and preorder traversals (inorder and postorder can also be used) similar to the first approach. To avoid repeatedly searching for the root in the inorder traversal, store the indices of inorder elements in a hash map for constant-time lookup. This will reduce complexity from quadratic to linear.

Check whether the sizes of preorder, inorder, and postorder traversals are equal.
Store the index of each element of the inorder traversal in a hash map.
Construct the binary tree using preorder traversal and use the hash map to directly locate the root index in inorder.
Recursively build the left and right subtrees.
Generate and compare the postorder traversal of the constructed tree with the given postorder traversal.
Return true if both match; otherwise return false.

C++

#include <bits/stdc++.h>
using namespace std;

class Node
{
  public:
    int data;
    Node *left, *right;

    Node(int val)
    {
        data = val;
        left = right = nullptr;
    }
};

/* Build tree using inorder and preorder */
Node *buildTree(vector<int> &in, vector<int> &pre, unordered_map<int, int> &mp, int inStart, int inEnd,
                int &preIndex)
{
    if (inStart > inEnd)
        return nullptr;

    // Traversal exhausted
    if (preIndex >= pre.size())
        return nullptr;

    int rootVal = pre[preIndex];

    // Root not present
    if (mp.find(rootVal) == mp.end())
        return nullptr;

    int inIndex = mp[rootVal];

    // Root index does not belong
    // to current subtree
    if (inIndex < inStart || inIndex > inEnd)
        return nullptr;

    // Create current node
    Node *root = new Node(pre[preIndex++]);

    // Leaf node
    if (inStart == inEnd)
        return root;

    // Construct left subtree
    root->left = buildTree(in, pre, mp, inStart, inIndex - 1, preIndex);

    // Construct right subtree
    root->right = buildTree(in, pre, mp, inIndex + 1, inEnd, preIndex);

    return root;
}

/* Compare generated postorder with given postorder */
int checkPostorder(Node *root, vector<int> &post, int index)
{
    if (root == nullptr)
        return index;

    index = checkPostorder(root->left, post, index);

    if (index == -1)
        return -1;

    index = checkPostorder(root->right, post, index);

    if (index == -1)
        return -1;

    // Compare current node
    if (index < post.size() && root->data == post[index])
        return index + 1;

    return -1;
}

bool checktree(vector<int> &pre, vector<int> &in, vector<int> &post)
{
    int n = in.size();

    // Traversals must have same size
    if (pre.size() != n || post.size() != n)
        return false;

    /* Build hash map to store
       indices of inorder elements */
    unordered_map<int, int> mp;

    for (int i = 0; i < n; i++)
    {
        mp[in[i]] = i;
    }

    int preIndex = 0;

    // Build tree from inorder
    // and preorder
    Node *root = buildTree(in, pre, mp, 0, n - 1, preIndex);

    // Invalid tree construction
    if (root == nullptr && n > 0)
        return false;

    // Compare generated postorder
    // with given postorder
    int index = checkPostorder(root, post, 0);

    return (index == n);
}

int main()
{
    vector<int> in = {4, 2, 5, 1, 3};
    vector<int> pre = {1, 2, 4, 5, 3};
    vector<int> post = {4, 5, 2, 3, 1};

    cout << (checktree(pre, in, post) ? "true" : "false");

    return 0;
}

Java

import java.util.*;

class Node {
    public int data;
    public Node left, right;

    Node(int val)
    {
        data = val;
        left = right = null;
    }
}

public class GFG {
    /* Build tree using inorder and preorder */
    static Node buildTree(int[] in, int[] pre,
                          HashMap<Integer, Integer> mp,
                          int inStart, int inEnd,
                          int[] preIndex)
    {
        if (inStart > inEnd)
            return null;

        // Traversal exhausted
        if (preIndex[0] >= pre.length)
            return null;

        int rootVal = pre[preIndex[0]];

        // Root not present
        if (!mp.containsKey(rootVal))
            return null;

        int inIndex = mp.get(rootVal);

        // Root index does not belong
        // to current subtree
        if (inIndex < inStart || inIndex > inEnd)
            return null;

        // Create current node
        Node root = new Node(pre[preIndex[0]++]);

        // Leaf node
        if (inStart == inEnd)
            return root;

        // Construct left subtree
        root.left = buildTree(in, pre, mp, inStart,
                              inIndex - 1, preIndex);

        // Construct right subtree
        root.right = buildTree(in, pre, mp, inIndex + 1,
                               inEnd, preIndex);

        return root;
    }

    /* Compare generated postorder with given postorder */
    static int checkPostorder(Node root, int[] post,
                              int index)
    {
        if (root == null)
            return index;

        index = checkPostorder(root.left, post, index);

        if (index == -1)
            return -1;

        index = checkPostorder(root.right, post, index);

        if (index == -1)
            return -1;

        // Compare current node
        if (index < post.length && root.data == post[index])
            return index + 1;

        return -1;
    }

    static boolean checktree(int[] pre, int[] in,
                             int[] post)
    {
        int n = in.length;

        // Traversals must have same size
        if (pre.length != n || post.length != n)
            return false;

        /* Build hash map to store
           indices of inorder elements */
        HashMap<Integer, Integer> mp = new HashMap<>();

        for (int i = 0; i < n; i++) {
            mp.put(in[i], i);
        }

        int[] preIndex = { 0 };

        // Build tree from inorder
        // and preorder
        Node root
            = buildTree(in, pre, mp, 0, n - 1, preIndex);

        // Invalid tree construction
        if (root == null && n > 0)
            return false;

        // Compare generated postorder
        // with given postorder
        int index = checkPostorder(root, post, 0);

        return (index == n);
    }

    public static void main(String[] args)
    {
        int[] in = { 4, 2, 5, 1, 3 };
        int[] pre = { 1, 2, 4, 5, 3 };
        int[] post = { 4, 5, 2, 3, 1 };

        System.out.println(
            checktree(pre, in, post) ? "true" : "false");
    }
}

Python

class Node:

    def __init__(self, val):
        self.data = val
        self.left = None
        self.right = None


""" Build tree using inorder and preorder """
def buildTree(inorder, pre, mp, inStart, inEnd, preIndex):

    if inStart > inEnd:
        return None

    # Traversal exhausted
    if preIndex[0] >= len(pre):
        return None

    rootVal = pre[preIndex[0]]

    # Root not present
    if rootVal not in mp:
        return None

    inIndex = mp[rootVal]

    # Root index does not belong
    # to current subtree
    if inIndex < inStart or inIndex > inEnd:
        return None

    # Create current node
    root = Node(pre[preIndex[0]])
    preIndex[0] += 1

    # Leaf node
    if inStart == inEnd:
        return root

    # Construct left subtree
    root.left = buildTree(inorder, pre, mp, inStart, inIndex - 1, preIndex)

    # Construct right subtree
    root.right = buildTree(inorder, pre, mp, inIndex + 1, inEnd, preIndex)

    return root


""" Compare generated postorder with given postorder """
def checkPostorder(root, post, index):

    if root is None:
        return index

    index = checkPostorder(root.left, post, index)

    if index == -1:
        return -1

    index = checkPostorder(root.right, post, index)

    if index == -1:
        return -1

    # Compare current node
    if index < len(post) and root.data == post[index]:
        return index + 1

    return -1


def checktree(pre, inorder, post):

    n = len(inorder)

    # Traversals must have same size
    if len(pre) != n or len(post) != n:
        return False

    """ Build hash map to store indices of inorder elements """
    mp = {}

    for i in range(n):
        mp[inorder[i]] = i

    preIndex = [0]

    # Build tree from inorder
    # and preorder
    root = buildTree(inorder, pre, mp, 0, n - 1, preIndex)

    # Invalid tree construction
    if root is None and n > 0:
        return False

    # Compare generated postorder
    # with given postorder
    index = checkPostorder(root, post, 0)

    return index == n

# Driver Code
if __name__ == "__main__":
    inorder = [4, 2, 5, 1, 3]
    pre = [1, 2, 4, 5, 3]
    post = [4, 5, 2, 3, 1]

    print(str(checktree(pre, inorder, post)).lower())

using System;
using System.Collections.Generic;

class Node {
    public int data;
    public Node left, right;

    public Node(int val)
    {
        data = val;
        left = right = null;
    }
}

class GFG {
    /* Build tree using inorder and preorder */
    static Node buildTree(int[] inOrder, int[] pre,
                          Dictionary<int, int> mp,
                          int inStart, int inEnd,
                          ref int preIndex)
    {
        if (inStart > inEnd)
            return null;

        // Traversal exhausted
        if (preIndex >= pre.Length)
            return null;

        int rootVal = pre[preIndex];

        // Root not present
        if (!mp.ContainsKey(rootVal))
            return null;

        int inIndex = mp[rootVal];

        // Root index does not belong
        // to current subtree
        if (inIndex < inStart || inIndex > inEnd)
            return null;

        // Create current node
        Node root = new Node(pre[preIndex++]);

        // Leaf node
        if (inStart == inEnd)
            return root;

        // Construct left subtree
        root.left = buildTree(inOrder, pre, mp, inStart,
                              inIndex - 1, ref preIndex);

        // Construct right subtree
        root.right = buildTree(inOrder, pre, mp, inIndex + 1,
                               inEnd, ref preIndex);

        return root;
    }

    /* Compare generated postorder with given postorder */
    static int checkPostorder(Node root, int[] post,
                              int index)
    {
        if (root == null)
            return index;

        index = checkPostorder(root.left, post, index);

        if (index == -1)
            return -1;

        index = checkPostorder(root.right, post, index);

        if (index == -1)
            return -1;

        // Compare current node
        if (index < post.Length && root.data == post[index])
            return index + 1;

        return -1;
    }

    static bool checktree(int[] pre, int[] inOrder,
                          int[] post)
    {
        int n = inOrder.Length;

        // Traversals must have same size
        if (pre.Length != n || post.Length != n)
            return false;

        /* Build hash map to store
           indices of inorder elements */
        Dictionary<int, int> mp
            = new Dictionary<int, int>();

        for (int i = 0; i < n; i++) {
            mp[inOrder[i]] = i;
        }

        int preIndex = 0;

        // Build tree from inorder
        // and preorder
        Node root = buildTree(inOrder, pre, mp, 0, n - 1,
                              ref preIndex);

        // Invalid tree construction
        if (root == null && n > 0)
            return false;

        // Compare generated postorder
        // with given postorder
        int index = checkPostorder(root, post, 0);

        return (index == n);
    }

    static void Main()
    {
        int[] inOrder = { 4, 2, 5, 1, 3 };
        int[] pre = { 1, 2, 4, 5, 3 };
        int[] post = { 4, 5, 2, 3, 1 };

        Console.WriteLine(
            checktree(pre, inOrder, post) ? "true" : "false");
    }
}

JavaScript

class Node {
    constructor(val)
    {
        this.data = val;
        this.left = null;
        this.right = null;
    }
}

/* Build tree using inorder and preorder */
function buildTree(inOrder, pre, mp, inStart, inEnd, preIndex)
{
    if (inStart > inEnd)
        return null;

    // Traversal exhausted
    if (preIndex.value >= pre.length)
        return null;

    let rootVal = pre[preIndex.value];

    // Root not present
    if (!mp.has(rootVal))
        return null;

    let inIndex = mp.get(rootVal);

    // Root index does not belong
    // to current subtree
    if (inIndex < inStart || inIndex > inEnd)
        return null;

    // Create current node
    let root = new Node(pre[preIndex.value++]);

    // Leaf node
    if (inStart === inEnd)
        return root;

    // Construct left subtree
    root.left = buildTree(inOrder, pre, mp, inStart,
                          inIndex - 1, preIndex);

    // Construct right subtree
    root.right = buildTree(inOrder, pre, mp, inIndex + 1,
                           inEnd, preIndex);

    return root;
}

/* Compare generated postorder with given postorder */
function checkPostorder(root, post, index)
{
    if (root === null)
        return index;

    index = checkPostorder(root.left, post, index);

    if (index === -1)
        return -1;

    index = checkPostorder(root.right, post, index);

    if (index === -1)
        return -1;

    // Compare current node
    if (index < post.length && root.data === post[index])
        return index + 1;

    return -1;
}

function checktree(pre, inOrder, post)
{
    let n = inOrder.length;

    // Traversals must have same size
    if (pre.length !== n || post.length !== n)
        return false;

    /* Build hash map to store
       indices of inorder elements */
    let mp = new Map();

    for (let i = 0; i < n; i++) {
        mp.set(inOrder[i], i);
    }

    let preIndex = {value : 0};

    // Build tree from inorder
    // and preorder
    let root
        = buildTree(inOrder, pre, mp, 0, n - 1, preIndex);

    // Invalid tree construction
    if (root === null && n > 0)
        return false;

    // Compare generated postorder
    // with given postorder
    let index = checkPostorder(root, post, 0);

    return index === n;
}

// Driver Code
let inOrder = [ 4, 2, 5, 1, 3 ];
let pre = [ 1, 2, 4, 5, 3 ];
let post = [ 4, 5, 2, 3, 1 ];

console.log(checktree(pre, inOrder, post) ? "true" : "false");

Output

true

[Expected Approach] Without Constructing Tree - O(n) Time and O(n) Space

The idea is to avoid constructing the binary tree explicitly. Since the first element of preorder is the root, locate it in the inorder traversal to determine the left and right subtree boundaries. Using these boundaries, recursively verify the corresponding parts of preorder, inorder, and postorder traversals. If every subtree satisfies the conditions, then all three traversals belong to the same tree.

Check if the sizes of preorder, inorder, and postorder traversals are equal. If not, return false.
Store the indices of all elements from the inorder traversal in a hash map for constant-time lookup.
Take the first element of the current preorder range as the root of the subtree.
Find the root position in inorder using the hash map and determine the size of the left subtree.
Verify whether the root matches the last element of the current postorder range, then recursively validate the left and right subtrees.
If all recursive checks succeed, return true; otherwise return false.

C++

#include <bits/stdc++.h>
using namespace std;

bool solve(vector<int> &pre, vector<int> &in, vector<int> &post, unordered_map<int, int> &mp,
           int ps, int pe, int is, int ie, int pos, int poe)
{
    // if the array lengths are 0,
    // then all of them are obviously equal
    if (ps > pe)
        return true;

    // if array lengths are 1,
    // then check if all of them are equal
    if (ps == pe)
    {
        return (pre[ps] == in[is]) && (in[is] == post[pos]);
    }

    // Root of current subtree
    int root = pre[ps];

    // Check whether root exists
    // in inorder traversal
    if (mp.find(root) == mp.end())
        return false;

    // Find root index in O(1)
    int idx = mp[root];

    // Root index should belong
    // to current subtree
    if (idx < is || idx > ie)
        return false;

    // Check whether root exists
    // at the current postorder root position
    if (root != post[poe])
        return false;

    // Calculate left subtree size
    int leftSize = idx - is;

    // check for the left subtree
    bool ret1 =
        solve(pre, in, post, mp, ps + 1, ps + leftSize, is, idx - 1, pos, pos + leftSize - 1);

    // check for the right subtree
    bool ret2 =
        solve(pre, in, post, mp, ps + leftSize + 1, pe, idx + 1, ie, pos + leftSize, poe - 1);

    // return true only if both are correct
    return (ret1 && ret2);
}

bool checktree(vector<int> &pre, vector<int> &in, vector<int> &post)
{
    int n = in.size();

    // Check if all the array lengths are equal
    if (pre.size() != n || post.size() != n)
        return false;

    /* Build hash map to store
       indices of inorder elements */
    unordered_map<int, int> mp;

    for (int i = 0; i < n; i++)
    {
        mp[in[i]] = i;
    }

    return solve(pre, in, post, mp, 0, n - 1, 0, n - 1, 0, n - 1);
}

int main()
{
    // Traversal Arrays
    vector<int> in = {4, 2, 5, 1, 3};
    vector<int> pre = {1, 2, 4, 5, 3};
    vector<int> post = {4, 5, 2, 3, 1};

    cout << (checktree(pre, in, post) ? "true" : "false");

    return 0;
}

Java

import java.util.*;

class GFG {

    static boolean solve(int[] pre, int[] in,
                         int[] post,
                         HashMap<Integer, Integer> mp,
                         int ps, int pe, int is, int ie,
                         int pos, int poe)
    {
        // if the array lengths are 0,
        // then all of them are obviously equal
        if (ps > pe)
            return true;

        // if array lengths are 1,
        // then check if all of them are equal
        if (ps == pe) {
            return (pre[ps] == in[is])
                && (in[is] == post[pos]);
        }

        // Root of current subtree
        int root = pre[ps];

        // Check whether root exists
        // in inorder traversal
        if (!mp.containsKey(root))
            return false;

        // Find root index in O(1)
        int idx = mp.get(root);

        // Root index should belong
        // to current subtree
        if (idx < is || idx > ie)
            return false;

        // Check whether root exists
        // at the current postorder root position
        if (root != post[poe])
            return false;

        // Calculate left subtree size
        int leftSize = idx - is;

        // check for the left subtree
        boolean ret1
            = solve(pre, in, post, mp,
                    ps + 1, ps + leftSize, is, idx - 1, pos,
                    pos + leftSize - 1);

        // check for the right subtree
        boolean ret2
            = solve(pre, in, post, mp,
                    ps + leftSize + 1, pe, idx + 1, ie,
                    pos + leftSize, poe - 1);

        // return true only if both are correct
        return (ret1 && ret2);
    }

    static boolean checktree(int[] pre, int[] in,
                             int[] post)
    {
        int n = in.length;

        // Check if all the array lengths are equal
        if (pre.length != n || post.length != n)
            return false;

        /* Build hash map to store
           indices of inorder elements */
        HashMap<Integer, Integer> mp = new HashMap<>();

        for (int i = 0; i < n; i++) {
            mp.put(in[i], i);
        }

        return solve(pre, in, post, mp, 0,
                     n - 1, 0, n - 1, 0, n - 1);
    }

    public static void main(String[] args)
    {
        // Traversal Arrays
        int[] in = { 4, 2, 5, 1, 3 };
        int[] pre = { 1, 2, 4, 5, 3 };
        int[] post = { 4, 5, 2, 3, 1 };

        System.out.println(
            checktree(pre, in, post)
                ? "true"
                : "false");
    }
}

Python

def solve(pre, inorder, post,
          mp, ps, pe, is_, ie,
          pos, poe):

    # if the array lengths are 0,
    # then all of them are obviously equal
    if ps > pe:
        return True

    # if array lengths are 1,
    # then check if all of them are equal
    if ps == pe:
        return (pre[ps] == inorder[is_]
                and inorder[is_] == post[pos])

    # Root of current subtree
    root = pre[ps]

    # Check whether root exists
    # in inorder traversal
    if root not in mp:
        return False

    # Find root index in O(1)
    idx = mp[root]

    # Root index should belong
    # to current subtree
    if idx < is_ or idx > ie:
        return False

    # Check whether root exists
    # at the current postorder root position
    if root != post[poe]:
        return False

    # Calculate left subtree size
    leftSize = idx - is_

    # check for the left subtree
    ret1 = solve(pre, inorder, post, mp, ps + 1, ps + leftSize,
        is_, idx - 1, pos, pos + leftSize - 1)

    # check for the right subtree
    ret2 = solve(pre, inorder, post, mp, ps + leftSize + 1, pe,
        idx + 1, ie, pos + leftSize, poe - 1)

    # return true only if both are correct
    return ret1 and ret2


def checktree(pre, inorder, post):

    n = len(inorder)

    # Check if all the array lengths are equal
    if len(pre) != n or len(post) != n:
        return False

    """ Build hash map to store indices of inorder elements """
    mp = {}

    for i in range(n):
        mp[inorder[i]] = i

    return solve(pre, inorder, post, mp, 0, n - 1, 0, n - 1, 0, n - 1)


# Driver Code
if __name__ == "__main__":
    inorder = [4, 2, 5, 1, 3]
    pre = [1, 2, 4, 5, 3]
    post = [4, 5, 2, 3, 1]

    print("true" if checktree(
        pre, inorder, post)
        else "false")

using System;
using System.Collections.Generic;

class GFG {
    static bool solve(int[] pre, int[] inorder,
                      int[] post,
                      Dictionary<int, int> mp, int ps,
                      int pe, int is_, int ie, int pos,
                      int poe)
    {
        // if the array lengths are 0,
        // then all of them are obviously equal
        if (ps > pe)
            return true;

        // if array lengths are 1,
        // then check if all of them are equal
        if (ps == pe) {
            return (pre[ps] == inorder[is_])
                && (inorder[is_] == post[pos]);
        }

        // Root of current subtree
        int root = pre[ps];

        // Check whether root exists
        // in inorder traversal
        if (!mp.ContainsKey(root))
            return false;

        // Find root index in O(1)
        int idx = mp[root];

        // Root index should belong
        // to current subtree
        if (idx < is_ || idx > ie)
            return false;

        // Check whether root exists
        // at the current postorder root position
        if (root != post[poe])
            return false;

        // Calculate left subtree size
        int leftSize = idx - is_;

        // check for the left subtree
        bool ret1 = solve(pre, inorder, post, mp,
                          ps + 1, ps + leftSize, is_,
                          idx - 1, pos, pos + leftSize - 1);

        // check for the right subtree
        bool ret2 = solve(pre, inorder, post, mp,
                          ps + leftSize + 1, pe, idx + 1,
                          ie, pos + leftSize, poe - 1);

        // return true only if both are correct
        return (ret1 && ret2);
    }

    static bool checktree(int[] pre, int[] inorder,
                          int[] post)
    {
        int n = inorder.Length;

        // Check if all the array lengths are equal
        if (pre.Length != n || post.Length != n)
            return false;

        /* Build hash map to store
           indices of inorder elements */
        Dictionary<int, int> mp
            = new Dictionary<int, int>();

        for (int i = 0; i < n; i++) {
            mp[inorder[i]] = i;
        }

        return solve(pre, inorder, post, mp, 0,
                     n - 1, 0, n - 1, 0, n - 1);
    }

    static void Main()
    {
        // Traversal Arrays
        int[] inorder = { 4, 2, 5, 1, 3 };
        int[] pre = { 1, 2, 4, 5, 3 };
        int[] post = { 4, 5, 2, 3, 1 };

        Console.WriteLine(
            checktree(pre, inorder, post)
                ? "true"
                : "false");
    }
}

JavaScript

function solve(pre, inorder, post, mp, ps, pe,
               is_, ie, pos, poe)
{
    // if the array lengths are 0,
    // then all of them are obviously equal
    if (ps > pe)
        return true;

    // if array lengths are 1,
    // then check if all of them are equal
    if (ps === pe) {
        return (pre[ps] === inorder[is_])
               && (inorder[is_] === post[pos]);
    }

    // Root of current subtree
    let root = pre[ps];

    // Check whether root exists
    // in inorder traversal
    if (!mp.has(root))
        return false;

    // Find root index in O(1)
    let idx = mp.get(root);

    // Root index should belong
    // to current subtree
    if (idx < is_ || idx > ie)
        return false;

    // Check whether root exists
    // at the current postorder root position
    if (root !== post[poe])
        return false;

    // Calculate left subtree size
    let leftSize = idx - is_;

    // check for the left subtree
    let ret1 = solve(pre, inorder, post, mp,
                     ps + 1, ps + leftSize, is_, idx - 1,
                     pos, pos + leftSize - 1);

    // check for the right subtree
    let ret2 = solve(pre, inorder, post, mp,
                     ps + leftSize + 1, pe, idx + 1, ie,
                     pos + leftSize, poe - 1);

    // return true only if both are correct
    return (ret1 && ret2);
}

function checktree(pre, inorder, post)
{
    let n = inorder.length;

    // Check if all the array lengths are equal
    if (pre.length !== n || post.length !== n)
        return false;

    /* Build hash map to store
       indices of inorder elements */
    let mp = new Map();

    for (let i = 0; i < n; i++) {
        mp.set(inorder[i], i);
    }

    return solve(pre, inorder, post, mp, 0, n - 1,
                 0, n - 1, 0, n - 1);
}

// Driver Code
let inorder = [ 4, 2, 5, 1, 3 ];
let pre = [ 1, 2, 4, 5, 3 ];
let post = [ 4, 5, 2, 3, 1 ];

console.log(checktree(pre, inorder, post)
                ? "true"
                : "false");

Output

true

Check if given Preorder, Inorder and Postorder traversals are of same binary tree

[Naive Approach] Tree Construction Using Inorder and Preorder - O(n ^ 2) Time and O(n) Space

[Better Approach] Tree Construction With Hash Map - O(n) Time and O(n) Space

[Expected Approach] Without Constructing Tree - O(n) Time and O(n) Space

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