Algorithm In C Language

One frequently employed algorithm in C programming is the sorting algorithm. This type of algorithm organizes a set of elements in a specific sequence, like numerically or alphabetically.

There exist numerous sorting algorithms, each presenting its own set of pros and cons. Among the frequently used sorting algorithms in C are quicksort, merge sort, and sort algorithms.

Pointer support is a fundamental aspect of the C programming language, enabling effective handling of data structures like arrays, queues, and more. This functionality is particularly beneficial for executing algorithms that involve intricate data manipulation tasks, including sorting and algorithmic searching.

A well-known instance of a software library developed in C is the Standard Template Library (STL). This particular library offers a diverse range of algorithms for functions like arranging, locating, and handling data structures.

Features of the algorithm

It defines several important features of the algorithm, including:

• ✅ Inputs : Algorithms must receive inputs that can be represented as values or data.
• ✅ Output : The algorithm should produce some output. It can be a consequence of a problem or a solution designed to solve it.
• ✅ Clarity : Algorithms must be precisely defined, using unambiguous instructions that a computer or other system can follow unambiguously.
• ✅ Finiteness : The algorithm requires a limited steps. It means that it should be exited after executing a certain number of commands.
• ✅ Validity : The algorithm must be valid. In other words, it should be able to produce a solution to the problem that the algorithm is designed to solve in a reasonable amount of time.
• ✅ Effectiveness: An algorithm must be effective, meaning that it must be able to produce a solution to the problem it is designed to solve in a reasonable amount of time.
• ✅ Generality: An algorithm must be general, meaning that it can be applied to a wide range of problems rather than being specific to a single problem.

Algorithm Analysis

Algorithmic analysis involves assessing the efficiency, complexity, and other factors related to algorithm performance. It is commonly carried out to compare multiple algorithms and determine the most suitable solution for a specific problem or software application.

Evaluating algorithms typically includes assessing their temporal and spatial complexity.

Similar to space complexity, which indicates the quantity of memory or disk space required, time complexity represents the duration that an algorithm takes to execute a specific operation.

There exist various methods for evaluating the time complexity of algorithms, including Big O and Omega notation. The Omega symbol establishes a ceiling for the time complexity of an algorithm, whereas the Omega symbol sets a floor.

In addition to measuring time and space complexity, algorithm analysis also includes other criteria such as stability, parallelism, and scalability.

• ✅ Stability :- This refers to the ability of the algorithm to maintain the relative order of the elements in the data set.
• ✅ Parallelization :- This is referring to the capacity to execute operations in parallel across several processors.
• ✅ Scalability :- On the other hand, it refers to the ability of an algorithm to handle large volumes of data and other inputs.

They include two types of analysis.

• ✅ Preceding examination.
• ✅ Subsequent analysis.

Prior Analysis

Prior is a technique in algorithm analysis that centers on predicting the efficiency of an algorithm by considering its mathematical characteristics rather than running the algorithm itself.

This method enables you to evaluate the time and space efficiency of algorithms and additional metrics without the necessity of executing the algorithms.

Posterior analysis

Conversely, posterior analysis involves running the algorithm and evaluating its efficiency as a technique for algorithm analysis.

This method offers a higher level of precision and in-depth insights into the algorithm's performance, necessitating the actual implementation and running of the algorithm.

Algorithm Complexity

Algorithmic complexity serves as a metric for assessing the efficiency and effectiveness of an algorithm. Typically, algorithms are assessed based on the time and memory resources needed to solve a problem or accomplish a particular objective.

Two elements contribute to the complexity of the algorithm.

• ✅ Temporal element.
• ✅ Spatial element.

Time factor

• ✅ The amount of time an algorithm needs to do a task is referred to as time complexity.It is usually measured by the number of operations or steps an algorithm must perform to solve a problem.
• ✅ The time complexity of an algorithm is important because it determines how long it takes to execute and can have a significant impact on program and system performance.
• ✅ The time complexity of an algorithm can be expressed using Big O notation, a way of expressing an upper bound on the time complexity of an algorithm.
• ✅ An algorithm with time complexity O(n) means that the time required to run the algorithm is directly proportional to the size of the input data (n).
• ✅ Other common time complexities are O(n^2) quadratic complexity and O(log n) logarithmic complexity.

Space analysis

• ✅ On the other hand, space complexity refers to the amount of memory or storage space required to execute the algorithm.
• ✅ This is important because it determines the number of resources required to run algorithms that can affect the overall performance of your application or system.
• ✅ If the space complexity of the algorithm is O(n), it uses an amount of memory that grows linearly with the size of the input.
• ✅ If the algorithm has O(1) space complexity, it uses a fixed amount of memory regardless of the size of the input.

Begin by clearly outlining the issue that you aim for the algorithm to address.

For example, suppose we want to write an algorithm to find the maximum value from a list of numbers.

1. Break the problem down into smaller, manageable steps.

• ✅ Initialize the 'max' variable to the first value in the list.
• ✅ For each subsequent value in the list, compare with "max".
• ✅ If the value is greater than "max", set "max" to that value.
• ✅ Continue doing this until every value in the list has been compared.
• ✅ Returns the final "max" value.

1. Write your algorithm in pseudocode or a programming language.

Algorithm written in pseudo code:

Evaluate your algorithm to ensure its accuracy and effectiveness.

You have the option to evaluate the algorithm by inputting various number sequences and confirming its accurate identification of the maximum value. Additionally, you can assess the algorithm's time complexity to gauge its efficiency when handling larger input sizes.

Example:-

Input: [1, 5, 2, 7, 3]

Output: 7.

In this case, 7 represents the highest value within the given list.

1. Enhance the efficiency of the algorithm.

Seek opportunities to enhance algorithms to boost their speed and efficiency. This process may entail adjusting pseudocode or integrating superior data structures or algorithms for improved performance.

Basic writing of algorithms

Example: - The sum of two integers.

Step 1 - Get started

Step 2 - Declare three integers a, b, c

Step 3 - Define the values of a and b

Step 4 - Add the values of a and b

Step 5 - Save the output of step 4 in c

Step 6 - Print c

Step 7 - Stop

Type of algorithms used in C language.

1. Sorting algorithms

C offers a diverse range of data types and operators that are valuable for executing different sorting techniques like bubble sort, insertion sort, and quick sort.

These algorithms prove to be valuable across various applications as they are capable of organizing data with varying sizes and types.

There are different sorting algorithms.

they are:-

(i) Bubble sort is a straightforward sorting technique that iteratively compares adjacent elements and swaps them if they are in the wrong order.

The Algorithm for Bubble sort is:-

• ✅ Start with an unsorted list of elements.
• ✅ Compare the first two elements in the list. If the first element is larger than the second element, swap them.
• ✅ Move on to the next pair of elements and repeat step 2 until the end of the list is reached.
• ✅ For each item on the list, repeat steps 2 and 3 once more. that is referred to as passes.
• ✅ Repeat steps 2-4 for the entire list. As you repeat the passes, elements will "bubble up" to their correct position in the sorted list.
• ✅ Once a pass is completed and no swaps are made, the list is sorted, and the algorithm can stop.
• ✅ The final sorted list is returned.

(ii) Insertion sort: a sorting technique that gradually builds a sorted list by inserting elements one at a time into their correct positions.

The Algorithm for Insertion sort is:-

• ✅ Initialize an empty sorted list and an unsorted list of the elements to be sorted.
• ✅ The first member from the unsorted list should be taken and placed in the appropriate position in the sorted list.
• ✅ Repeat step 2 for each subsequent element in the unsorted list.
• ✅ Compare the current element with the elements in the sorted list, starting with the element immediately to the left.
• ✅ Swap the two elements if the current element is smaller than the element to its left.
• ✅ If the current element is larger than the element to its left, insert it at its correct position in the sorted list.
• ✅ Repeat steps 4-6 for each subsequent element in the unsorted list.
• ✅ Once all elements have been processed, the sorted list will contain all elements in the correct order.
• ✅ The sorting process is complete.

(iii) Selection sort is an algorithm for sorting data that begins by selecting the smallest element from the unsorted portion and moving it to the sorted portion.

The Algorithm for Selection sort is:-

• ✅ Begin by setting the primary element of list as the min element.
• ✅ Repeat through the remaining items in the list, comparing each one to the current minimum.
• ✅ Set a new minimum if an element is found to be smaller than the existing one.
• ✅ Change the current minimum to the first element of the list whenever it reaches its conclusion.
• ✅ For the remaining unsorted portion of the listing, repeat steps 2-4, but begin with the second item on the list (as the first element is already sorted).
• ✅ Continue sorting the list in this manner until it is all sorted.

(iv) Quick sort: An efficient sorting technique that follows the divide-and-conquer approach by selecting a pivot element to partition the list into sublists based on their relationship to the pivot. These sublists are then recursively sorted until the entire list is sorted in ascending or descending order.

The Algorithm for Quick sort is:-

• ✅ Choose a pivot element from the list. This is typically the first element, but it can also be a random element or the median of the list.
• ✅ Divide the list into two sublists: one containing elements less than the pivot and one containing elements greater than the pivot.
• ✅ Recursively sort the sublist containing elements less than the pivot using the same process.
• ✅ Use the same procedure to recursively sort the sublist of entries larger than the pivot.
• ✅ Concatenate the sorted sublists with the pivot element in between to form a fully sorted list.
• ✅ Return the fully sorted list.

(v) Merge sort is a sorting algorithm that follows the divide-and-conquer approach by splitting the list into two equal halves, sorting them individually, and then merging the sorted halves to produce the final sorted list.

Merge-sort Algorithm:

• ✅ Make two sublists out of the list: one with elements below the pivot and one with elements above the pivot.
• ✅ Produces a new sorted sublist by iteratively merging sublists until only one sublist exists. This will be your sorted list.
• ✅ Steps to merge two sub-directories:-
• ✅ Create an empty list to hold the sorted elements.
• ✅ Compares the first element of each sublist.
• ✅ Adds the smaller element to the new list and removes it from the parent sublist.
• ✅ Repeat the steps 2 and 3 until a list is completly empty.
• ✅ Adds the remaining elements from other sublists to a new list.
• ✅ Replaces the merged sublist with the new sorted list.
• ✅ Repeat this process until all sublists are merged into one sorted list.

(vi) Heapsort : An algorithm for sorting elements by leveraging a data structure known as heap.

This is the classification algorithm:

• ✅ Build max heap : Starting with the first non-leaf node, compare each node with its child nodes and replace the nodes with the largest of its children to satisfy the max heap property.
• ✅ Swap root with last element : Swap the root (largest element) with the last element in the stack.
• ✅ Stack the rest of the elements. Starting from the root, each node is compared with its children, swapping nodes with their older children until the max heap property is satisfied.
• ✅ Repeat steps 2 and 3 with the newly stacked elements, except for the last element in the correct position.
• ✅ Repeat this process until only one element remains in the stack. This is now sorted.
• ✅ Heapify Down : Starting from the root node, it compares elements with its children and swaps with the larger of the two until the max heap property is satisfied.
• ✅ Heapify Up : Start with the last element in the heap, compare it to its parent, and swap it with the parent to satisfy the max heap property.

(vii) Radix sort is an algorithm for arranging elements according to the digits or bit sequences in their binary form.

The Algorithm for Radix sort is:-

• ✅ determine how many digits are contained in the input listing's largest element.
• ✅ Initialize a variable, say digit place, to 1, which represents the current digit place.
• ✅ Create an empty list for each possible digit value from 0 to 9.
• ✅ Iterate through the input list and add each element to the appropriate list based on the value of the current digit place.
• ✅ Concatenate all the lists together to form the new list in the order of the digit lists.
• ✅ Multiply digitPlace by 10 to move to the next digit place.
• ✅ Repeat steps 4-6 for each digit place until all digits in the largest element have been considered.
• ✅ The final list will be sorted in ascending order by the digits of the elements.
• ✅ Return the final sorted list.

2. Searching algorithms

C also offers the resources needed to execute a range of search algorithms, including linear search and binary search. These algorithms are efficient in locating particular elements within a dataset, proving beneficial across various scenarios.

There are many types of search algorithms.

They are:-

(i) Sequential search: An elementary search technique that inspects each element in the array individually until locating the target element.

Algorithm for Linear search:-

• ✅ Define the input for the algorithm: The input for a linear search algorithm is a list of elements (or an array) and a target element we are searching for.
• ✅ Initialize a variable called "index" to -1: This variable will be used to store the index of the target element if it is found.
• ✅ Loop through the list of elements: Starting from the first element, check each element in the list one by one.
• ✅ Compare the present element to the desired element for evaluation: Keep the index of the current element in the index variable and exit the loop if the modern element and the goal element are identical.
• ✅ Return the index of the target element: After the loop completes, return the value stored in the index variable. If the target element is not found, the value of the index will be -1.

(ii) Binary search: A search technique that works by dividing the array into two parts and then searching within one of those parts, increasing the chances of finding the desired element.

Algorithm for Binary search:-

• ✅ Input: A sorted list of n elements and a target element x.
• ✅ Initialize variables: Set the low index to 0, the high index to n-1, and mid to (low+high)/2.
• ✅ Start a loop: While the low index is less than or equal to the high index, repeat the following steps.
• ✅ Compare the mid element with x: If the mid element is equal to x, return the mid index.
• ✅ Update the low or high index: If x is greater than the mid element, set the low index to mid + 1. Else, set the high index to mid - 1.
• ✅ Update the mid index: Mid = (low+high)/2.
• ✅ End of the loop: If the low index is greater than the high index, then x is not in the list, and the algorithm returns a failure.
• ✅ Output: The index of x in the list or failure message.

(iii) Depth-first search: An exploration technique that investigates each branch extensively before backtracking.

The following guidelines apply to depth-first search:

• ✅ select the graph's starting vertex or node to start with.
• ✅ Add a visiting mark to the first vertex.
• ✅ Directly place the beginning vertex into a stack.
• ✅ Until the stack is empty, repeat the following actions: - Remove the stack's top vertex. Mark as visited and insert into the stack each unvisited neighbour of the popped vertex.
• ✅ Continue this process until all vertices in the graph have been visited.
• ✅ Once all vertices have been visited, the algorithm is complete, and a depth-first search is performed on the graph.
• ✅ Remove the stack's top vertex.
• ✅ Mark as visited and insert into the stack each unvisited neighbour of the popped vertex.

Breadth-first search is an exploration algorithm that investigates all the adjacent nodes of a particular node before progressing to the subsequent level.

The algorithm for the breadth-first search is:-

• ✅ Start with the root node or the initial state.
• ✅ Add the root node to a queue.
• ✅ Check if the queue is empty; if yes, then terminate the algorithm.
• ✅ Take the first element from the queue and mark it as visited.
• ✅ Amplify the contemporary node by adding all its unvisited neighbors to the queue.
• ✅ Until the desired node is located or the queue is empty, repeat steps 3 to 5.
• ✅ Return the path from the preliminary state to the target state if the goal node is found.
• ✅ Terminate the set of rules and report that the goal state was not identified if the queue is empty.

(v) Interpolation Search: An algorithm for searching that estimates the position of the desired element based on its values within the index.

It is crucial that the array is uniformly spread out. Otherwise, it constitutes an algorithm.

It works as expected.

The algorithm can be summarized as follows.

• ✅ Get the input list and key value to search.
• ✅ Initialize the lower and upper variables at the first and last indices of the list.
• ✅ If the Lower value is less than or equal to higher value, then :- Calculate the estimated location using the following formula: pos = low + ((high - low) / (arr[high] - arr[low])) * (x - arr[low]). Return the position if the estimated position value is a key value. c) If the estimated position value is less than the key value, set it lower. Position + 1. d) If the value of the estimated position is greater than the key Set value, position - 1 up.
• ✅ If the key value is not found, return -1 to indicate that the value is not in the list.
• ✅ Calculate the estimated location using the following formula: pos = low + ((high - low) / (arr[high] - arr[low])) * (x - arr[low]).
• ✅ Return the position if the estimated position value is a key value.
• ✅ c) If the estimated position value is less than the key value, set it lower. Position + 1.
• ✅ d) If the value of the estimated position is greater than the key Set value, position - 1 up.

(vi) Jump search: A searching technique that scans through the list in fixed-size increments until it locates the desired item or confirms its absence.

The jump search algorithm is as follows:

• ✅ First, set the jump size to the square root of the number of array elements.
• ✅ Sets a variable named "current" to the first element of the array.
• ✅ Iterates over the array by jumping by jump size while incrementing a variable called "jump".
• ✅ Move on to the following leap if the existing element is smaller than the desired element.
• ✅ If the current element is larger than the target element, perform a linear search between the current element and the previous jump element to find the target element.
• ✅ If the target element is not found in the array, it returns -1 to indicate that it is not in the array.
• ✅ If the element is found, it returns the element's index in the array.

3. Graph algorithms

C's backing for pointers and data structures like arrays and linked lists renders it appropriate for executing algorithms that modify graphs, like determining the most efficient route between two nodes within a graph.

There are different types of graph algorithms.

they are:-

• ✅ Dijkstra's Algorithm : An algorithm that finds the shortest path between two nodes in a graph by continuously updating the shortest distance from each node.
• ✅ Algorithm A* : A method that continually updates the shortest course to each node in a graph to determine the shortest route between them.
• ✅ Prim's Algorithm : An approach for figuring out the weighted connected graph's smallest spanning tree.
• ✅ Kruskal's algorithm : An approach to identify the linked weighted graph's lowest spanning tree.
• ✅ Bellman-Ford Algorithm : An algorithm that, even when the graph has negative edge weights, displays the shortest path between a particular supply node and every other node in the network.

4. Cryptographic Algorithms

C is well-suited for carrying out low-level tasks and optimizing data handling, making it a prime choice for developing cryptographic algorithms like encryption and decryption techniques.

There exist various categories of encryption algorithms.

They are:-

• ✅ Hash Algorithms : These algorithms produce fixed-size outputs (hash) from arbitrary-sized inputs. Examples include MD5, SHA-1 and SHA-2.
• ✅ Symmetric key algorithms : The encryption and decryption steps in such algorithms employ the same private key. AES, DES, and Blowfish are a few examples.
• ✅ Asymmetric key algorithms : A public key and a non-public key are used by those methods as separate keys for encryption and decryption. Some examples include RSA, ECC, and DSA.
• ✅ Key exchange algorithms : These algorithms allow two parties to exchange keys over an insecure channel securely. For example, we can mention Diffie-Hellman and Elliptic Curve Diffie-Hellman.

Advantages of the algorithm

Algorithms have many advantages.

they are:-

• ✅ Speed and efficiency : Algorithms can process large amounts of data quickly and accurately, making them useful for tasks that are too time-consuming or error-prone for people to perform.
• ✅ Consistency : Algorithms follow a set of predetermined guidelines. It can produce consistent results without being influenced by personal biases and emotions.
• ✅ Automation : Algorithms can perform tasks automatically, leaving people free to focus on more complex or creative tasks.
• ✅ Increased accuracy : Algorithms can often achieve higher levels of accuracy than humans, especially when dealing with large amounts of data.
• ✅ Better Decision Making : Algorithms help us make more informed and objective decisions by analyzing data and identifying patterns and trends that are not easily visible to people.
• ✅ Scalability : Algorithms can be easily scaled up or down to meet changing demands and workloads.

Disadvantages of the algorithm

Algorithms are highly beneficial in the realm of programming, yet they also come with limitations.

they are:-

• ✅ Limited scope : Algorithms can only solve problems within their scope and may not be able to solve complex or abstract problems.
• ✅ Bias : Algorithms can perpetuate and reinforce biases in the data used for training, leading to unfair results.
• ✅ Insufficient transparency : Many algorithms conceal the process through which they arrive at their conclusions. This could make it tough to think about or check the results.
• ✅ Reliance on the fineness of the data: The correctness of the set of rules is heavily dependent on the fineness and applicability of the data utilised in instruction. Inaccurate or inaccurate effects may be the result of faulty data.
• ✅ restrained adaptability: Algorithms are designed to follow guidelines and won't adapt to changing circumstances and conditions.