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 8Input: 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 5Observe 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 25Here 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> |
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
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