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### Data Structures: Stacks ( with C Program source code)

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Some Important Linear Data Structures- at a glance

## Stack

Stack is a specialized data storage structure (Abstract data type). Unlike, arrays access of elements in a stack is restricted. It has two main functions push and pop. Insertion in a stack is done using push function and removal from a stack is done using pop function. Stack allows access to only the last element inserted hence, an item can be inserted or removed from the stack from one end called the top of the stack. It is therefore, also called Last-In-First-Out (LIFO) list. Stack has three properties: capacity stands for the maximum number of elements stack can hold, size stands for the current size of the stack and elements is the array of elements.

### Algorithm:

Stack structure is defined with fields capacity, size and *elements (pointer to the array of elements).

### Functions – (explained in greater detail in the document)

1. createStack function– This function takes the maximum number of elements (maxElements) the stack can hold as an argument, creates a stack according to it and returns a pointer to the stack. It initializes Stack S using malloc function and its properties.
2. push function - This function takes the pointer to the top of the stack S and the item (element) to be inserted as arguments. Check for the emptiness of stack
3. pop function - This function takes the pointer to the top of the stack S as an argument.
4. top function – This function takes the pointer to the top of the stack S as an argument and returns the topmost element of the stack S.

### Properties of stacks:

1. Each function runs in O(1) time.
2. It has two basic implementations
Array-based implementation – It is simple and efficient but the maximum size of the stack is fixed.
Singly Linked List-based implementation – It’s complicated but there is no limit on the stack size, it is subjected to the available memory.

## Stacks - C Program source code

`#include<stdio.h>#include<stdlib.h>/* Stack has three properties. capacity stands for the maximum number of elements stack can hold.   Size stands for the current size of the stack and elements is the array of elements */typedef struct Stack{        int capacity;        int size;        int *elements;}Stack;/* crateStack function takes argument the maximum number of elements the stack can hold, creates   a stack according to it and returns a pointer to the stack. */Stack * createStack(int maxElements){        /* Create a Stack */        Stack *S;        S = (Stack *)malloc(sizeof(Stack));        /* Initialise its properties */        S->elements = (int *)malloc(sizeof(int)*maxElements);        S->size = 0;        S->capacity = maxElements;        /* Return the pointer */        return S;}void pop(Stack *S){        /* If stack size is zero then it is empty. So we cannot pop */        if(S->size==0)        {                printf("Stack is Empty\n");                return;        }        /* Removing an element is equivalent to reducing its size by one */        else        {                S->size--;        }        return;}int top(Stack *S){        if(S->size==0)        {                printf("Stack is Empty\n");                exit(0);        }        /* Return the topmost element */        return S->elements[S->size-1];}void push(Stack *S,int element){        /* If the stack is full, we cannot push an element into it as there is no space for it.*/        if(S->size == S->capacity)        {                printf("Stack is Full\n");        }        else        {                /* Push an element on the top of it and increase its size by one*/                 S->elements[S->size++] = element;        }        return;}int main(){        Stack *S = createStack(5);        push(S,7);        push(S,5);        push(S,21);        push(S,-1);        printf("Top element is %d\n",top(S));        pop(S);        printf("Top element is %d\n",top(S));        pop(S);        printf("Top element is %d\n",top(S));        pop(S);        printf("Top element is %d\n",top(S));}`
Related Tutorials :

 Stacks Last In First Out data structures ( LIFO ). Like a stack of cards from which you pick up the one on the top ( which is the last one to be placed on top of the stack ). Documentation of the various operations and the stages a stack passes through when elements are inserted or deleted. C program to help you get an idea of how a stack is implemented in code. Queues First in First Out data structure (FIFO). Like people waiting to buy tickets in a queue - the first one to stand in the queue, gets the ticket first and gets to leave the queue first. Documentation of the various operations and the stages a queue passes through as elements are inserted or deleted. C Program source code to help you get an idea of how a queue is implemented in code.

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Tutorials on Sorting- at a glance

 Bubble Sort - One of the most elementary sorting algorithms to implement - and also very inefficient. Runs in quadratic time. A good starting point to understand sorting in general, before moving on to more advanced techniques and algorithms. A general idea of how the algorithm works and a the code for a C program.Insertion Sort - Another quadratic time sorting algorithm - an example of dynamic programming. An explanation and step through of how the algorithm works, as well as the source code for a C program which performs insertion sort.Selection Sort - Another quadratic time sorting algorithm - an example of a greedy algorithm. An explanation and step through of how the algorithm works, as well as the source code for a C program which performs selection sort.Shell Sort- An inefficient but interesting algorithm, the complexity of which is not exactly known.Merge Sort An example of a Divide and Conquer algorithm. Works in O(n log n) time. The memory complexity for this is a bit of a disadvantage.Quick Sort In the average case, this works in O(n log n) time. No additional memory overhead - so this is better than merge sort in this regard. A partition element is selected, the array is restructured such that all elements greater or less than the partition are on opposite sides of the partition. These two parts of the array are then sorted recursively.Heap Sort- Efficient sorting algorithm which runs in O(n log n) time. Uses the Heap data structure.Binary Search Algorithm- Commonly used algorithm used to find the position of an element in a sorted array. Runs in O(log n) time.

Basic Data Structures and Algorithms

Stacks Last In First Out data structures ( LIFO ). Like a stack of cards from which you pick up the one on the top ( which is the last one to be placed on top of the stack ). Documentation of the various operations and the stages a stack passes through when elements are inserted or deleted. C program to help you get an idea of how a stack is implemented in code.

Queues First in First Out data structure (FIFO). Like people waiting to buy tickets in a queue - the first one to stand in the queue, gets the ticket first and gets to leave the queue first. Documentation of the various operations and the stages a queue passes through as elements are inserted or deleted. C Program source code to help you get an idea of how a queue is implemented in code.

Single Linked List A self referential data structure. A list of elements, with a head and a tail; each element points to another of its own kind.

Double Linked List- A self referential data structure. A list of elements, with a head and a tail; each element points to another of its own kind in front of it, as well as another of its own kind, which happens to be behind it in the sequence.

Circular Linked List Linked list with no head and tail - elements point to each other in a circular fashion.

Binary Search Trees A basic form of tree data structures. Inserting and deleting elements in them. Different kind of binary tree traversal algorithms.

Heaps A tree like data structure where every element is lesser (or greater) than the one above it. Heap formation, sorting using heaps in O(n log n) time.

Height Balanced Trees - Ensuring that trees remain balanced to optimize complexity of operations which are performed on them.

Graphs

Depth First Search - Traversing through a graph using Depth First Search in which unvisited neighbors of the current vertex are pushed into a stack and visited in that order.

Breadth First Search - Traversing through a graph using Breadth First Search in which unvisited neighbors of the current vertex are pushed into a queue and then visited in that order.

Minimum Spanning Trees: Kruskal Algorithm- Finding the Minimum Spanning Tree using the Kruskal Algorithm which is a greedy technique. Introducing the concept of Union Find.

Minumum Spanning Trees: Prim's Algorithm- Finding the Minimum Spanning Tree using the Prim's Algorithm.

Dijkstra Algorithm for Shortest Paths- Popular algorithm for finding shortest paths : Dijkstra Algorithm.

Floyd Warshall Algorithm for Shortest Paths- All the all shortest path algorithm: Floyd Warshall Algorithm

Bellman Ford Algorithm - Another common shortest path algorithm : Bellman Ford Algorithm.

Dynamic Programming A technique used to solve optimization problems, based on identifying and solving sub-parts of a problem first.

Integer Knapsack problemAn elementary problem, often used to introduce the concept of dynamic programming.

Matrix Chain Multiplication Given a long chain of matrices of various sizes, how do you parenthesize them for the purpose of multiplication - how do you chose which ones to start multiplying first?

Longest Common Subsequence Given two strings, find the longest common sub sequence between them.

Elementary cases : Fractional Knapsack Problem, Task Scheduling - Elementary problems in Greedy algorithms - Fractional Knapsack, Task Scheduling. Along with C Program source code.

Data Compression using Huffman TreesCompression using Huffman Trees. A greedy technique for encoding information.