Data structures

Reference 
http://cs-fundamentals.com/data-structures/data-structures-tutorials.php
http://www.geeksforgeeks.org/data-structures/
 


In computer science, a data structure is a particular way of organizing data in a computer so that it can be used efficiently. Data structures can implement one or more particular abstract data types, which are the means of specifying the contract of operations and their complexity.

Linked List | Set 1 (Introduction)

Like arrays, Linked List is a linear data structure. Unlike arrays, linked list elements are not stored at contiguous location; the elements are linked using pointers.
Why Linked List?
Arrays can be used to store linear data of similar types, but arrays have following limitations.
1) The size of the arrays is fixed: So we must know the upper limit on the number of elements in advance. Also, generally, the allocated memory is equal to the upper limit irrespective of the usage.
2) Inserting a new element in an array of elements is expensive, because room has to be created for the new elements and to create room existing elements have to shifted.
For example, in a system if we maintain a sorted list of IDs in an array id[].
id[] = [1000, 1010, 1050, 2000, 2040].
And if we want to insert a new ID 1005, then to maintain the sorted order, we have to move all the elements after 1000 (excluding 1000).
Deletion is also expensive with arrays until unless some special techniques are used. For example, to delete 1010 in id[], everything after 1010 has to be moved.
Advantages over arrays
1) Dynamic size
2) Ease of insertion/deletion
Drawbacks:
1) Random access is not allowed. We have to access elements sequentially starting from the first node. So we cannot do binary search with linked lists.
2) Extra memory space for a pointer is required with each element of the list.
Representation in C:
A linked list is represented by a pointer to the first node of the linked list. The first node is called head. If the linked list is empty, then value of head is NULL.
Each node in a list consists of at least two parts:
1) data
2) pointer to the next node
In C, we can represent a node using structures. Below is an example of a linked list node with an integer data.

struct node {   int data;   struct node *next; };

First Simple Linked List in C Let us create a simple linked list with 3 nodes.

#include<stdio.h> #include<stdlib.h> struct node {   int data;   struct node *next; }; // Program to create a simple linked list with 3 nodes int main() {   struct node* head = NULL;   struct node* second = NULL;   struct node* third = NULL;       // allocate 3 nodes in the heap    head = (struct node*)malloc(sizeof(struct node));   second = (struct node*)malloc(sizeof(struct node));   third = (struct node*)malloc(sizeof(struct node));   /* Three blocks have been allocated  dynamically.      We have pointers to these three blocks as first, second and third            head           second           third         |                |               |         |                |               |     +---+-----+     +----+----+     +----+----+     | #  | #  |     | #  | #  |     |  # |  # |     +---+-----+     +----+----+     +----+----+         # represents any random value.    Data is random because we haven’t assigned anything yet  */       head->data = 1; //assign data in first node   head->next = second; // Link first node with the second node       /* data has been assigned to data part of first block (block     pointed by head).  And next pointer of first block points to     second.  So they both are linked.        head          second         third         |              |              |         |              |              |     +---+---+     +----+----+     +-----+----+     | 1  | o----->| #  | #  |     |  #  | #  |     +---+---+     +----+----+     +-----+----+      */        second->data = 2; //assign data to second node   second->next = third;       /* data has been assigned to data part of second block (block pointed by      second). And next pointer of the second block points to third block.      So all three blocks are linked.            head         second         third         |             |             |         |             |             |     +---+---+     +---+---+     +----+----+     | 1  | o----->| 2 | o-----> |  # |  # |     +---+---+     +---+---+     +----+----+      */          third->data = 3; //assign data to third node   third->next = NULL;       /* data has been assigned to data part of third block (block pointed     by third). And next pointer of the third block is made NULL to indicate     that the linked list is terminated here.      We have the linked list ready.             head                 |              |         +---+---+     +---+---+       +----+------+         | 1  | o----->|  2  | o-----> |  3 | NULL |         +---+---+     +---+---+       +----+------+                      Note that only head is sufficient to represent the whole list.  We can     traverse the complete list by following next pointers.    */           getchar();   return 0; }

Linked List Traversal
In the previous program, we have created a simple linked list with three nodes. Let us traverse the created list and print the data of each node. For traversal, let us write a general purpose function printList() that prints any given list.

#include<stdio.h> #include<stdlib.h> struct node {   int data;   struct node *next; }; // This function prints contents of linked list starting from the given node void printList(struct node *n) {   while (n != NULL)   {      printf(" %d ", n->data);      n = n->next;   } } int main() {   struct node* head = NULL;   struct node* second = NULL;   struct node* third = NULL;       // allocate 3 nodes in the heap    head  = (struct node*)malloc(sizeof(struct node));   second = (struct node*)malloc(sizeof(struct node));   third  = (struct node*)malloc(sizeof(struct node));      head->data = 1; //assign data in first node   head->next = second; // Link first node with the second node       second->data = 2; //assign data to second node   second->next = third;       third->data = 3; //assign data to third node   third->next = NULL;       printList(head);      getchar();   return 0; }

Output:

 1  2  3

Linked List vs Array

Difficulty Level: Rookie
Both Arrays and Linked List can be used to store linear data of similar types, but they both have some advantages and disadvantages over each other.
Following are the points in favour of Linked Lists.
(1) The size of the arrays is fixed: So we must know the upper limit on the number of elements in advance. Also, generally, the allocated memory is equal to the upper limit irrespective of the usage, and in practical uses, upper limit is rarely reached.
(2) Inserting a new element in an array of elements is expensive, because room has to be created for the new elements and to create room existing elements have to shifted.
For example, suppose we maintain a sorted list of IDs in an array id[].
id[] = [1000, 1010, 1050, 2000, 2040, …..].
And if we want to insert a new ID 1005, then to maintain the sorted order, we have to move all the elements after 1000 (excluding 1000).
Deletion is also expensive with arrays until unless some special techniques are used. For example, to delete 1010 in id[], everything after 1010 has to be moved.
So Linked list provides following two advantages over arrays
1) Dynamic size
2) Ease of insertion/deletion
Linked lists have following drawbacks:
1) Random access is not allowed. We have to access elements sequentially starting from the first node. So we cannot do binary search with linked lists.
2) Extra memory space for a pointer is required with each element of the list.
3) Arrays have better cache locality that can make a pretty big difference in performance.
Please also see this thread.
References:
http://cslibrary.stanford.edu/103/LinkedListBasics.pdf
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

Circular Linked List | Set 1 (Introduction and Applications)

We have discussed singly and doubly linked lists in the following posts.
Introduction to Linked List & Insertion
Doubly Linked List Introduction and Insertion
Circular linked list is a linked list where all nodes are connected to form a circle. There is no NULL at the end. A circular linked list can be a singly circular linked list or doubly circular linked list.

Advantages of Circular Linked Lists:
1) Any node can be a starting point. We can traverse the whole list by starting from any point. We just need to stop when the first visited node is visited again.
2) Useful for implementation of queue. Unlike this implementation, we don’t need to maintain two pointers for front and rear if we use circular linked list. We can maintain a pointer to the last inserted node and front can always be obtained as next of last.
3) Circular lists are useful in applications to repeatedly go around the list. For example, when multiple applications are running on a PC, it is common for the operating system to put the running applications on a list and then to cycle through them, giving each of them a slice of time to execute, and then making them wait while the CPU is given to another application. It is convenient for the operating system to use a circular list so that when it reaches the end of the list it can cycle around to the front of the list. (Source http://web.eecs.utk.edu/~bvz/cs140/notes/Dllists/)
4) Circular Doubly Linked Lists are used for implementation of advanced data structures like Fibonacci Heap.

Doubly Linked List | Set 1 (Introduction and Insertion)

We strongly recommend to refer following post as a prerequisite of this post.
Linked List Introduction
Inserting a node in Singly Linked List
A Doubly Linked List (DLL) contains an extra pointer, typically called previous pointer, together with next pointer and data which are there in singly linked list.

Following is representation of a DLL node in C language.

/* Node of a doubly linked list */ struct node {   int data;   struct node *next; // Pointer to next node in DLL   struct node *prev; // Pointer to previous node in DLL  };

Following are advantages/disadvantages of doubly linked list over singly linked list.
Advantages over singly linked list
1) A DLL can be traversed in both forward and backward direction.
2) The delete operation in DLL is more efficient if pointer to the node to be deleted is given.
In singly linked list, to delete a node, pointer to the previous node is needed. To get this previous node, sometimes the list is traversed. In DLL, we can get the previous node using previous pointer.
Disadvantages over singly linked list
1) Every node of DLL Require extra space for an previous pointer. It is possible to implement DLL with single pointer though (See this and this).
2) All operations require an extra pointer previous to be maintained. For example, in insertion, we need to modify previous pointers together with next pointers. For example in following functions for insertions at different positions, we need 1 or 2 extra steps to set previous pointer.
Insertion
A node can be added in four ways
1) At the front of the DLL
2) After a given node.
3) At the end of the DLL
4) Before a given node.
1) Add a node at the front: (A 5 steps process)
The new node is always added before the head of the given Linked List. And newly added node becomes the new head of DLL. For example if the given Linked List is 10<->15<->20<->25 and we add an item 5 at the front, then the Linked List becomes 5<->10<->15<->20<->25. Let us call the function that adds at the front of the list is push(). The push() must receive a pointer to the head pointer, because push must change the head pointer to point to the new node (See this)
Following are the 5 steps to add node at the front.

/* Given a reference (pointer to pointer) to the head of a list    and an int, inserts a new node on the front of the list. */ void push(struct node** head_ref, int new_data) {     /* 1. allocate node */     struct node* new_node = (struct node*) malloc(sizeof(struct node));         /* 2. put in the data  */     new_node->data  = new_data;         /* 3. Make next of new node as head and previous as NULL */     new_node->next = (*head_ref);     new_node->prev = NULL;     /* 4. change prev of head node to new node */     if((*head_ref) !=  NULL)       (*head_ref)->prev = new_node ;         /* 5. move the head to point to the new node */     (*head_ref)    = new_node; }

Four steps of the above five steps are same as the 4 steps used for inserting at the front in singly linked list. The only extra step is to change previous of head.
2) Add a node after a given node.: (A 7 steps process)
We are given pointer to a node as prev_node, and the new node is inserted after the given node.

/* Given a node as prev_node, insert a new node after the given node */ void insertAfter(struct node* prev_node, int new_data) {     /*1. check if the given prev_node is NULL */     if (prev_node == NULL)     {         printf("the given previous node cannot be NULL");         return;     }     /* 2. allocate new node */     struct node* new_node =(struct node*) malloc(sizeof(struct node));     /* 3. put in the data  */     new_node->data  = new_data;     /* 4. Make next of new node as next of prev_node */     new_node->next = prev_node->next;     /* 5. Make the next of prev_node as new_node */     prev_node->next = new_node;     /* 6. Make prev_node as previous of new_node */     new_node->prev = prev_node;     /* 7. Change previous of new_node's next node */     if (new_node->next != NULL)       new_node->next->prev = new_node; }

Five of the above steps step process are same as the 5 steps used for inserting after a given node in singly linked list. The two extra steps are needed to change previous pointer of new node and previous pointer of new node’s next node.
3) Add a node at the end: (7 steps process)
The new node is always added after the last node of the given Linked List. For example if the given DLL is 5<->10<->15<->20<->25 and we add an item 30 at the end, then the DLL becomes 5<->10<->15<->20<->25<->30.
Since a Linked List is typically represented by the head of it, we have to traverse the list till end and then change the next of last node to new node.
Following are the 7 steps to add node at the end.

/* Given a reference (pointer to pointer) to the head    of a DLL and an int, appends a new node at the end  */ void append(struct node** head_ref, int new_data) {     /* 1. allocate node */     struct node* new_node = (struct node*) malloc(sizeof(struct node));     struct node *last = *head_ref;  /* used in step 5*/     /* 2. put in the data  */     new_node->data  = new_data;     /* 3. This new node is going to be the last node, so           make next of it as NULL*/     new_node->next = NULL;     /* 4. If the Linked List is empty, then make the new           node as head */     if (*head_ref == NULL)     {         new_node->prev = NULL;         *head_ref = new_node;         return;     }     /* 5. Else traverse till the last node */     while (last->next != NULL)         last = last->next;     /* 6. Change the next of last node */     last->next = new_node;     /* 7. Make last node as previous of new node */     new_node->prev = last;     return; }

Six of the above 7 steps are same as the 6 steps used for inserting after a given node in singly linked list. The one extra step is needed to change previous pointer of new node.
4) Add a node before a given node
This is left as an exercise for the readers.
A complete working program to test above functions.
Following is complete C program to test above functions.

// A complete working C program to demonstrate all insertion methods #include <stdio.h> #include <stdlib.h> // A linked list node struct node {     int data;     struct node *next;     struct node *prev; }; /* Given a reference (pointer to pointer) to the head of a list    and an int, inserts a new node on the front of the list. */ void push(struct node** head_ref, int new_data) {     /* 1. allocate node */     struct node* new_node = (struct node*) malloc(sizeof(struct node));     /* 2. put in the data  */     new_node->data  = new_data;     /* 3. Make next of new node as head and previous as NULL */     new_node->next = (*head_ref);     new_node->prev = NULL;     /* 4. change prev of head node to new node */     if((*head_ref) !=  NULL)       (*head_ref)->prev = new_node ;     /* 5. move the head to point to the new node */     (*head_ref)    = new_node; } /* Given a node as prev_node, insert a new node after the given node */ void insertAfter(struct node* prev_node, int new_data) {     /*1. check if the given prev_node is NULL */     if (prev_node == NULL)     {         printf("the given previous node cannot be NULL");         return;     }     /* 2. allocate new node */     struct node* new_node =(struct node*) malloc(sizeof(struct node));     /* 3. put in the data  */     new_node->data  = new_data;     /* 4. Make next of new node as next of prev_node */     new_node->next = prev_node->next;     /* 5. Make the next of prev_node as new_node */     prev_node->next = new_node;     /* 6. Make prev_node as previous of new_node */     new_node->prev = prev_node;     /* 7. Change previous of new_node's next node */     if (new_node->next != NULL)       new_node->next->prev = new_node; } /* Given a reference (pointer to pointer) to the head    of a DLL and an int, appends a new node at the end  */ void append(struct node** head_ref, int new_data) {     /* 1. allocate node */     struct node* new_node = (struct node*) malloc(sizeof(struct node));     struct node *last = *head_ref;  /* used in step 5*/     /* 2. put in the data  */     new_node->data  = new_data;     /* 3. This new node is going to be the last node, so           make next of it as NULL*/     new_node->next = NULL;     /* 4. If the Linked List is empty, then make the new           node as head */     if (*head_ref == NULL)     {         new_node->prev = NULL;          *head_ref = new_node;         return;     }     /* 5. Else traverse till the last node */     while (last->next != NULL)         last = last->next;     /* 6. Change the next of last node */     last->next = new_node;     /* 7. Make last node as previous of new node */     new_node->prev = last;     return; } // This function prints contents of linked list starting from the given node void printList(struct node *node) {     struct node *last;     printf("\nTraversal in forward direction \n");     while (node != NULL)     {         printf(" %d ", node->data);         last = node;         node = node->next;     }     printf("\nTraversal in reverse direction \n");     while (last != NULL)     {         printf(" %d ", last->data);         last = last->prev;     } } /* Drier program to test above functions*/ int main() {     /* Start with the empty list */     struct node* head = NULL;     // Insert 6.  So linked list becomes 6->NULL     append(&head, 6);     // Insert 7 at the beginning. So linked list becomes 7->6->NULL     push(&head, 7);     // Insert 1 at the beginning. So linked list becomes 1->7->6->NULL     push(&head, 1);     // Insert 4 at the end. So linked list becomes 1->7->6->4->NULL     append(&head, 4);     // Insert 8, after 7. So linked list becomes 1->7->8->6->4->NULL     insertAfter(head->next, 8);     printf("\n Created DLL is: ");     printList(head);     getchar();     return 0; }

Output:

 Created DLL is:
Traversal in forward direction
 1  7  8  6  4
Traversal in reverse direction
 4  6  8  7  1