Two nodes of a BST are swapped, correct the BST

Two of the nodes of a Binary Search Tree (BST) are swapped. Fix (or correct) the BST. 

Input: x = 20, y = 8 
         10
        /  \
      5    8
    / \
  2   20
Output:
         10
        /  \
     5    20
   / \
 2   8

Input: x = 10 y = 5 
         10
        /  \
      5    8
    / \
  2   20
Output:
         5
        /  \
     10   20
   / \
 2   8

Approach:

The in-order traversal of a BST produces a sorted array. So a simple method is to store inorder traversal of the input tree in an auxiliary array. Sort the auxiliary array. Finally, insert the auxiliary array elements back to the BST, keeping the structure of the BST same. 

Time complexity: O(N * logN) 
Auxiliary Space: O(N).

We can solve this in O(n) time and with a single traversal of the given BST. 

Two nodes of a BST are swapped, correct the BST using recursion:

Since in-order traversal of BST is always a sorted array, the problem can be reduced to a problem where two elements of a sorted array are swapped. 

There are two cases that to handle:

Maintain three-pointers, first, middle, and last. When the first point where the current node value is smaller than the previous node value is found, update the first with the previous node & the middle with the current node. 
When we find the second point where the current node value is smaller than the previous node value, we update the last with the current node. If the last node value is null, then two swapped nodes of BST are adjacent i.e. first and middle otherwise first and last

Illustration:

1. The swapped nodes are not adjacent in the in-order traversal of the BST. 

 For example, Nodes 5 and 25 are swapped in {3 5 7 8 10 15 20 25}. 
 The inorder traversal of the given tree is 3 25 7 8 10 15 20 5 

Observe carefully, during inorder traversal, find node 7 is smaller than the previously visited node 25. Here save the context of node 25 (previous node). Again, find that node 5 is smaller than the previous node 20. This time, save the context of node 5 (the current node ). Finally, swap the two node’s values.

2. The swapped nodes are adjacent in the inorder traversal of BST.

  For example, Nodes 7 and 8 are swapped in {3 5 7 8 10 15 20 25}. 
  The inorder traversal of the given tree is 3 5 8 7 10 15 20 25 

Here only one point exists where a node value is smaller than the previous node value. e.g. node 7 is smaller than node 8. 

Follow the below steps to implement the idea:

• Initialize pointers prev, first, middle, and last as Null pointers.
• Traverse the Binary search tree in in-order form 
  • Make a recursive call for root -> left.
  • If *prev != null and root -> data < (*prev)->data) then 
    • If first = Null then set first = prev and middle = root.
    • Else last = root.
  • Make a recursive call for root -> right.
  • Store the current node as prev.
• If last != Null swap last and first pointer.
• Else swap first and middle pointer

Below is the implementation of the above approach. 

C++

// Two nodes in the BST's swapped, correct the BST.
#include <bits/stdc++.h>
using namespace std;

/* A binary tree node has data, pointer to left child
   and a pointer to right child */
struct node
{
    int data;
    struct node *left, *right;
};

// A utility function to swap two integers
void swap( int* a, int* b )
{
    int t = *a;
    *a = *b;
    *b = t;
}

/* Helper function that allocates a new node with the
   given data and NULL left and right pointers. */
struct node* newNode(int data)
{
    struct node* node = (struct node *)malloc(sizeof(struct node));
    node->data = data;
    node->left = NULL;
    node->right = NULL;
    return(node);
}

// This function does inorder traversal to find out the two swapped nodes.
// It sets three pointers, first, middle and last.  If the swapped nodes are
// adjacent to each other, then first and middle contain the resultant nodes
// Else, first and last contain the resultant nodes
void correctBSTUtil( struct node* root, struct node** first,
                     struct node** middle, struct node** last,
                     struct node** prev )
{
    if( root )
    {
        // Recur for the left subtree
        correctBSTUtil( root->left, first, middle, last, prev );

        // If this node is smaller than the previous node, it's violating
        // the BST rule.
        if (*prev && root->data < (*prev)->data)
        {

            // If this is first violation, mark these two nodes as
            // 'first' and 'middle'
            if ( !*first )
            {
                *first = *prev;
                *middle = root;
            }

            // If this is second violation, mark this node as last
            else
                *last = root;
        }

        // Mark this node as previous
        *prev = root;

        // Recur for the right subtree
        correctBSTUtil( root->right, first, middle, last, prev );
    }
}

// A function to fix a given BST where two nodes are swapped.  This
// function uses correctBSTUtil() to find out two nodes and swaps the
// nodes to fix the BST
void correctBST( struct node* root )
{

    // Initialize pointers needed for correctBSTUtil()
    struct node *first, *middle, *last, *prev;
    first = middle = last = prev = NULL;

    // Set the pointers to find out two nodes
    correctBSTUtil( root, &first, &middle, &last, &prev );

    // Fix (or correct) the tree
    if( first && last )
        swap( &(first->data), &(last->data) );
    else if( first && middle ) // Adjacent nodes swapped
        swap( &(first->data), &(middle->data) );

    // else nodes have not been swapped, passed tree is really BST.
}

/* A utility function to print Inorder traversal */
void printInorder(struct node* node)
{
    if (node == NULL)
        return;
    printInorder(node->left);
    cout <<"  "<< node->data;
    printInorder(node->right);
}

/* Driver program to test above functions*/
int main()
{
    /*   6
        /  \
       10    2
      / \   / \
     1   3 7  12
     10 and 2 are swapped
    */

    struct node *root = newNode(6);
    root->left        = newNode(10);
    root->right       = newNode(2);
    root->left->left  = newNode(1);
    root->left->right = newNode(3);
    root->right->right = newNode(12);
    root->right->left = newNode(7);

    cout <<"Inorder Traversal of the original tree \n";
    printInorder(root);

    correctBST(root);

    cout <<"\nInorder Traversal of the fixed tree \n";
    printInorder(root);

    return 0;
}

// This code is contributed by shivanisinghss2110

C

// Two nodes in the BST's swapped, correct the BST.
#include <stdio.h>
#include <stdlib.h>

/* A binary tree node has data, pointer to left child
   and a pointer to right child */
struct node
{
    int data;
    struct node *left, *right;
};

// A utility function to swap two integers
void swap( int* a, int* b )
{
    int t = *a;
    *a = *b;
    *b = t;
}

/* Helper function that allocates a new node with the
   given data and NULL left and right pointers. */
struct node* newNode(int data)
{
    struct node* node = (struct node *)malloc(sizeof(struct node));
    node->data = data;
    node->left = NULL;
    node->right = NULL;
    return(node);
}

// This function does inorder traversal to find out the two swapped nodes.
// It sets three pointers, first, middle and last.  If the swapped nodes are
// adjacent to each other, then first and middle contain the resultant nodes
// Else, first and last contain the resultant nodes
void correctBSTUtil( struct node* root, struct node** first,
                     struct node** middle, struct node** last,
                     struct node** prev )
{
    if( root )
    {
        // Recur for the left subtree
        correctBSTUtil( root->left, first, middle, last, prev );

        // If this node is smaller than the previous node, it's violating
        // the BST rule.
        if (*prev && root->data < (*prev)->data)
        {
            // If this is first violation, mark these two nodes as
            // 'first' and 'middle'
            if ( !*first )
            {
                *first = *prev;
                *middle = root;
            }

            // If this is second violation, mark this node as last
            else
                *last = root;
        }

        // Mark this node as previous
        *prev = root;

        // Recur for the right subtree
        correctBSTUtil( root->right, first, middle, last, prev );
    }
}

// A function to fix a given BST where two nodes are swapped.  This
// function uses correctBSTUtil() to find out two nodes and swaps the
// nodes to fix the BST
void correctBST( struct node* root )
{
    // Initialize pointers needed for correctBSTUtil()
    struct node *first, *middle, *last, *prev;
    first = middle = last = prev = NULL;

    // Set the pointers to find out two nodes
    correctBSTUtil( root, &first, &middle, &last, &prev );

    // Fix (or correct) the tree
    if( first && last )
        swap( &(first->data), &(last->data) );
    else if( first && middle ) // Adjacent nodes swapped
        swap( &(first->data), &(middle->data) );

    // else nodes have not been swapped, passed tree is really BST.
}

/* A utility function to print Inorder traversal */
void printInorder(struct node* node)
{
    if (node == NULL)
        return;
    printInorder(node->left);
    printf("%d ", node->data);
    printInorder(node->right);
}

/* Driver program to test above functions*/
int main()
{
    /*   6
        /  \
       10    2
      / \   / \
     1   3 7  12
     10 and 2 are swapped
    */

    struct node *root = newNode(6);
    root->left        = newNode(10);
    root->right       = newNode(2);
    root->left->left  = newNode(1);
    root->left->right = newNode(3);
    root->right->right = newNode(12);
    root->right->left = newNode(7);

    printf("Inorder Traversal of the original tree \n");
    printInorder(root);

    correctBST(root);

    printf("\nInorder Traversal of the fixed tree \n");
    printInorder(root);

    return 0;
}

Java

// Java program to correct the BST
// if two nodes are swapped
import java.util.*;
import java.lang.*;
import java.io.*;

class Node {

    int data;
    Node left, right;

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

class BinaryTree
{
    Node first, middle, last, prev;

    // This function does inorder traversal
    // to find out the two swapped nodes.
    // It sets three pointers, first, middle
    // and last. If the swapped nodes are
    // adjacent to each other, then first
    // and middle contain the resultant nodes
    // Else, first and last contain the
    // resultant nodes
    void correctBSTUtil( Node root)
    {
        if( root != null )
        {
            // Recur for the left subtree
            correctBSTUtil( root.left);

            // If this node is smaller than
            // the previous node, it's
            // violating the BST rule.
            if (prev != null && root.data <
                                prev.data)
            {
                // If this is first violation,
                // mark these two nodes as
                // 'first' and 'middle'
                if (first == null)
                {
                    first = prev;
                    middle = root;
                }

                // If this is second violation,
                // mark this node as last
                else
                    last = root;
            }

            // Mark this node as previous
            prev = root;

            // Recur for the right subtree
            correctBSTUtil( root.right);
        }
    }

    // A function to fix a given BST where
    // two nodes are swapped. This function
    // uses correctBSTUtil() to find out
    // two nodes and swaps the nodes to
    // fix the BST
    void correctBST( Node root )
    {
        // Initialize pointers needed
        // for correctBSTUtil()
        first = middle = last = prev = null;

        // Set the pointers to find out
        // two nodes
        correctBSTUtil( root );

        // Fix (or correct) the tree
        if( first != null && last != null )
        {
            int temp = first.data;
            first.data = last.data;
            last.data = temp;
        }
        // Adjacent nodes swapped
        else if( first != null && middle !=
                                    null )
        {
            int temp = first.data;
            first.data = middle.data;
            middle.data = temp;
        }

        // else nodes have not been swapped,
        // passed tree is really BST.
    }

    /* A utility function to print
     Inorder traversal */
    void printInorder(Node node)
    {
        if (node == null)
            return;
        printInorder(node.left);
        System.out.print(" " + node.data);
        printInorder(node.right);
    }


    // Driver program to test above functions
    public static void main (String[] args)
    {
        /*   6
            / \
           10  2
          / \ / \
         1  3 7 12

        10 and 2 are swapped
        */

        Node root = new Node(6);
        root.left = new Node(10);
        root.right = new Node(2);
        root.left.left = new Node(1);
        root.left.right = new Node(3);
        root.right.right = new Node(12);
        root.right.left = new Node(7);

        System.out.println("Inorder Traversal"+
                        " of the original tree");
        BinaryTree tree = new BinaryTree();
        tree.printInorder(root);

        tree.correctBST(root);

        System.out.println("\nInorder Traversal"+
                          " of the fixed tree");
        tree.printInorder(root);
    }
}
// This code is contributed by Chhavi

Python3

# Python3 program to correct the BST
# if two nodes are swapped
class Node:

    # Constructor to create a new node
    def __init__(self, data):

        self.key = data
        self.left = None
        self.right = None

# Utility function to track the nodes
# that we have to swap
def correctBstUtil(root, first, middle,
                   last, prev):

    if(root):

        # Recur for the left sub tree
        correctBstUtil(root.left, first,
                       middle, last, prev)

        # If this is the first violation, mark these
        # two nodes as 'first and 'middle'
        if(prev[0] and root.key < prev[0].key):
            if(not first[0]):
                first[0] = prev[0]
                middle[0] = root
            else:

                # If this is the second violation,
                # mark this node as last
                last[0] = root

        prev[0] = root

        # Recur for the right subtree
        correctBstUtil(root.right, first,
                       middle, last, prev)

# A function to fix a given BST where
# two nodes are swapped. This function
# uses correctBSTUtil() to find out two
# nodes and swaps the nodes to fix the BST
def correctBst(root):

    # Followed four lines just for forming
    # an array with only index 0 filled
    # with None and we will update it accordingly.
    # we made it null so that we can fill
    # node data in them.
    first = [None]
    middle = [None]
    last = [None]
    prev = [None]

    # Setting arrays (having zero index only)
    # for capturing the required node
    correctBstUtil(root, first, middle,
                   last, prev)

    # Fixing the two nodes
    if(first[0] and last[0]):

        # Swapping for first and last key values
        first[0].key, last[0].key = (last[0].key,
                                    first[0].key)

    elif(first[0] and middle[0]):

        # Swapping for first and middle key values
        first[0].key, middle[0].key = (middle[0].key,
                                        first[0].key)

    # else tree will be fine

# Function to print inorder
# traversal of tree
def PrintInorder(root):

    if(root):
        PrintInorder(root.left)
        print(root.key, end = " ")
        PrintInorder(root.right)

    else:
        return

# Driver code

#      6
#     /   \
#   10    2
#  / \   / \
# 1   3 7   12

# Following 7 lines are for tree formation
root = Node(6)
root.left = Node(10)
root.right = Node(2)
root.left.left = Node(1)
root.left.right = Node(3)
root.right.left = Node(7)
root.right.right = Node(12)

# Printing inorder traversal of normal tree
print("inorder traversal of normal tree")
PrintInorder(root)
print("")

# Function call to do the task
correctBst(root)

# Printing inorder for corrected Bst tree
print("")
print("inorder for corrected BST")

PrintInorder(root)

# This code is contributed by rajutkarshai

C#

// C# program to correct the BST
// if two nodes are swapped
using System;
class Node{

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

class BinaryTree
{
  Node first, middle,
       last, prev;

// This function does inorder traversal
// to find out the two swapped nodes.
// It sets three pointers, first, middle
// and last. If the swapped nodes are
// adjacent to each other, then first
// and middle contain the resultant nodes
// Else, first and last contain the
// resultant nodes
void correctBSTUtil( Node root)
{
  if( root != null )
  {
    // Recur for the
    // left subtree
    correctBSTUtil(root.left);

    // If this node is smaller than
    // the previous node, it's
    // violating the BST rule.
    if (prev != null && root.data <
        prev.data)
    {
      // If this is first violation,
      // mark these two nodes as
      // 'first' and 'middle'
      if (first == null)
      {
        first = prev;
        middle = root;
      }

      // If this is second violation,
      // mark this node as last
      else
        last = root;
    }

    // Mark this node
    // as previous
    prev = root;

    // Recur for the
    // right subtree
    correctBSTUtil(root.right);
  }
}

// A function to fix a given BST where
// two nodes are swapped. This function
// uses correctBSTUtil() to find out
// two nodes and swaps the nodes to
// fix the BST
void correctBST( Node root )
{
  // Initialize pointers needed
  // for correctBSTUtil()
  first = middle = last =
          prev = null;

  // Set the pointers to
  // find out two nodes
  correctBSTUtil(root);

  // Fix (or correct)
  // the tree
  if(first != null &&
     last != null)
  {
    int temp = first.data;
    first.data = last.data;
    last.data = temp;
  }

  // Adjacent nodes swapped
  else if(first != null &&
          middle != null)
  {
    int temp = first.data;
    first.data = middle.data;
    middle.data = temp;
  }

  // else nodes have not been
  // swapped, passed tree is
  // really BST.
}

// A utility function to print
// Inorder traversal
void printInorder(Node node)
{
  if (node == null)
    return;
  printInorder(node.left);
  Console.Write(" " + node.data);
  printInorder(node.right);
}

// Driver code
public static void Main(String[] args)
{
  /*         6
            / \
           10  2
          / \ / \
         1  3 7 12

        10 and 2 are swapped
        */

  Node root = new Node(6);
  root.left = new Node(10);
  root.right = new Node(2);
  root.left.left = new Node(1);
  root.left.right = new Node(3);
  root.right.right = new Node(12);
  root.right.left = new Node(7);

  Console.WriteLine("Inorder Traversal" +
                    " of the original tree");
  BinaryTree tree = new BinaryTree();
  tree.printInorder(root);
  tree.correctBST(root);
  Console.WriteLine("\nInorder Traversal" +
                    " of the fixed tree");
  tree.printInorder(root);
}
}

// This code is contributed by gauravrajput1

Javascript

<script>

// JavaScript program to correct the BST
// if two nodes are swapped

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


    var first, middle, last, prev;

    // This function does inorder traversal
    // to find out the two swapped nodes.
    // It sets three pointers, first, middle
    // and last. If the swapped nodes are
    // adjacent to each other, then first
    // and middle contain the resultant nodes
    // Else, first and last contain the
    // resultant nodes
    function correctBSTUtil(root) {
        if (root != null) {
            // Recur for the left subtree
            correctBSTUtil(root.left);

            // If this node is smaller than
            // the previous node, it's
            // violating the BST rule.
            if (prev != null && root.data < prev.data) {
                // If this is first violation,
                // mark these two nodes as
                // 'first' and 'middle'
                if (first == null) {
                    first = prev;
                    middle = root;
                }

                // If this is second violation,
                // mark this node as last
                else
                    last = root;
            }

            // Mark this node as previous
            prev = root;

            // Recur for the right subtree
            correctBSTUtil(root.right);
        }
    }

    // A function to fix a given BST where
    // two nodes are swapped. This function
    // uses correctBSTUtil() to find out
    // two nodes and swaps the nodes to
    // fix the BST
    function correctBST(root) {
        // Initialize pointers needed
        // for correctBSTUtil()
        first = middle = last = prev = null;

        // Set the pointers to find out
        // two nodes
        correctBSTUtil(root);

        // Fix (or correct) the tree
        if (first != null && last != null) {
            var temp = first.data;
            first.data = last.data;
            last.data = temp;
        }
        // Adjacent nodes swapped
        else if (first != null && middle != null) {
            var temp = first.data;
            first.data = middle.data;
            middle.data = temp;
        }

        // else nodes have not been swapped,
        // passed tree is really BST.
    }

    /*
     * A utility function to print Inorder traversal
     */
    function printInorder(node) {
        if (node == null)
            return;
        printInorder(node.left);
        document.write(" " + node.data);
        printInorder(node.right);
    }

    // Driver program to test above functions

        /*
         * 6 / \ 10 2 / \ / \ 1 3 7 12
         *
         * 10 and 2 are swapped
         */

var root = new Node(6);
        root.left = new Node(10);
        root.right = new Node(2);
        root.left.left = new Node(1);
        root.left.right = new Node(3);
        root.right.right = new Node(12);
        root.right.left = new Node(7);

        document.write("Inorder Traversal" +
        " of the original tree<br/>");
        printInorder(root);

        correctBST(root);

        document.write("<br/>Inorder Traversal" +
        " of the fixed tree<br/>");
        printInorder(root);

// This code contributed by aashish1995

</script>

Output

Inorder Traversal of the original tree 
  1  10  3  6  7  2  12
Inorder Traversal of the fixed tree 
  1  2  3  6  7  10  12

Time Complexity: O(N) 
Auxiliary Space: O(N) for recursive call stack