Data structures

Question : Write a function to find inorder successor of a given node in a binary  search tree. Our inclination would be to write tree minimum of right subtree. Because we already use this mechanism while deleting a node with both subtrees. But what we fail to notice is that tree minimum of right subtree would be present if there IS a right subtree. What if the node has no right child? What if it is a leaf node? Which nodes are successors of these nodes? And how do we find them? The inorder successor of 3 can be found out as tree minimum of right subtree, which is 4. But what about successors of 4? Or 7? Or successor 13? One method would be to store parent link in each node. And travel up finding parent nodes until the parent node has a value greater than given node. But that needs modification of the structure. Another method is to start from root node and search for a given value and store node with larger value as successor and terminate when we come across a node w...

Question: Write a function to delete every k th node from circular linked list until only one node is left. This has a story associated with it. Flavius Josephus was Jewish Historian from 1st century. He and 40 other soldiers were trapped in a cave by Romans. They decided to kill themselves rather than surrendering to Romans. Their method was like this. All the soldiers will stand in a circle and every k th soldier will be shot dead. Josephus said to have calculated the starting point so that he would remain alive. So we have similar problem at hand. We delete every kth node in a circular list. Eventually only one node will be left. e.g. Let us say this is our list And we are deleting every third node.  We will delete 30. Then we delete 60. Next we delete 10. Next it will be 50. Next to be deleted is 20. Next 80. This continues. Implementation   We can count k-1 nodes and delete next node. This can be repeated in  a loop. What must be the termina...

Question : Write a function for BFS traversal of a binary tree. Bread first traversal (also called level order traversal) is a traversal method where you visit the siblings of a node before you visit its descendants. The other method of traversal is called depth first traversal(DFS) where you visit the descendants of a node before you visit its siblings. In-order, pre-order and post-order are all DFS traversal methods. In BFS, first you visit all the nodes at level 0, then you visit all the nodes at level 1, then you visit nodes at level 2 etc. For the diagram shown above, the BFS output should be 8 3 10 1 6 14  4 7 13  ( there is no newline between levels) To write a code for BFS, we need to take the help of another data structure - a queue. To start with we insert this root to the queue. Then as long as queue is not empty, we remove a node from the queue, visit this node (display its value) and enqueue its both child nodes.  Here is C function f...

Question : Write a function to print the lowest common ancestor of two nodes in a binary search tree.  Lowest common ancestor of two nodes x and y in a binary tree is the lowest node that has both x and y as descendants. Here lowest common ancestor of 1 and 7 is 3. LCA of 13 and 7 is root - 8. And LCA of 6 and 7 is 6 itself. The program to find gets complicated for an ordinary binary tree. But for a binary search tree, it is quite simple. As we see from the diagram above, the paths to 1 and 4 are common till the node 3. And at 3 they branch in different directions. So 3 is our LCA. That is lowest common ancestor is the node where the paths to x and y from root deviate. As long as they branch in same direction, we continue to traverse. When they branch in different directions, that is the lowest common ancestor. So let us write a simple algorithm, set temp=root if temp->val >x and temp->val>y temp = temp->left else if temp->val<x and ...

Question : Write a function for in-order traversal of nodes in the range x to y from a binary search tree. This is quite a simple function. As a first solution we can just traverse our binary search tree in inorder and display only the nodes which are in the range x to y. But if the current node has a value less than x, do we have to traverse its left subtree? No. Because all the nodes in left subtree will be smaller than x. Similarly if the current node has a key value more than y, we need not visit its right subtree. Now we are ready to write our algorithm.     if nd is NOT NULL  if nd->val >=x then visit all the nodes of left subtree of nd recursively display nd->val if nd->val <y then visit all the nodes of right subtree of nd recursively  That's all. We have our function ready. void in_order_middle (NODEPTR nd, int x, int y) { if (nd) { if (nd -> val >= x) in_order_middle(nd...

Question : Write a function to mirror a binary tree. The mirror tree will have a left subtree and right subtree swapped. But this has to be done for each and every node. So to convert a tree to its mirror, we can write an algorithm like this               1) mirror left subtree recursively               2) mirror right subtree recursively               3) swap left and right children of the current node. Here is the function for it. void mirror_tree (NODEPTR root) { if (root != NULL ) { NODEPTR temp = root -> left; root -> left = root -> right; root -> right = temp; mirror_tree(root -> left); mirror_tree(root -> right); } }

A binary tree is a non-linear data structure where every node has maximum two branches - left subtree and right subtree. An empty node is also a binary tree. In earlier posts we have seen how to insert a node to binary tree , how to traverse a tree and how to delete nodes from tree. The functions look almost similar in C++. Except that all these functions and root pointer are all parts of the class binary tree. That is a good thing and a bad thing. If root is a data member (so private), how do we use root as a parameter in all the recursive functions - insert, delete, inorder etc? Easy answer would be don't use recursion. Anyway no one like them. So we can write insert and delete functions without using recursion and even search function. But traversal functions have to be recursive. Ok, let us write a function to return root of the tree and use it as first parameter in all traversal functions. Here is the complete class. You can download this code along with t...

Queue is a FIFO data structure. It is used in all situations where the values returned must be in the same order as values entered. We have discussed the terminologies, function needed and also implemented a queue in C language earlier. We can implement a queue by using an array or a linked list for storing values. Let us look at array implementation of a queue in C++ Data members We will need the array, front, rear and size of the array. We can use a static array or a dynamic array.  class Queue { static int size; int arr[ 40 ]; int front,rear; public: Queue(); void enqueue ( int num); int dequeue (); bool is_empty (); bool is_full (); void display (); static int ERR_EMPTY; }; int Queue :: ERR_EMPTY =- 9999 ; int Queue :: size = 40 ; Why are we using two static members in this class. size is the array size. And ERR_EMPTY is a constant which can be returned from dequeue function when the queue is empty. Const...