Know about Algorithm Complexity
Complexity in algorithms refers to the amount of resources (such as time or memory) required to solve a problem or perform a task. The most common measure of complexity is time complexity, which refers to the amount of time an algorithm takes to produce a result as a function of the size of the input. Memory complexity refers to the amount of memory used by an algorithm. Algorithm designers strive to develop algorithms with the lowest possible time and memory complexities, since this makes them more efficient and scalable.
The complexity of an algorithm is a function describing the efficiency of the algorithm in terms of the amount of data the algorithm must process.
Usually there are natural units for the domain and range of this function.
An algorithm is analyzed using Time Complexity and Space Complexity. Writing an efficient algorithm help to consume the minimum amount of time for processing the logic. For algorithm A, it is judged on the basis of two parameters for an input of size n :
- Time Complexity: Time taken by the algorithm to solve the problem. It is measured by calculating the iteration of loops, number of comparisons etc.
- Time complexity is a function describing the amount of time an algorithm takes in terms of the amount of input to the algorithm.
- “Time” can mean the number of memory accesses performed, the number of comparisons between integers, the number of times some inner loop is executed, or some other natural unit related to the amount of real time the algorithm will take.
- Space Complexity: Space taken by the algorithm to solve the problem. It includes space used by necessary input variables and any extra space (excluding the space taken by inputs) that is used by the algorithm. For example, if we use a hash table (a kind of data structure), we need an array to store values so
- this is an extra space occupied, hence will count towards the space complexity of the algorithm. This extra space is known as Auxiliary Space.
- Space complexity is a function describing the amount of memory(space)an algorithm takes in terms of the amount of input to the algorithm.
- Space complexity is sometimes ignored because the space used is minimal and/ or obvious, but sometimes it becomes an issue as time.
.The time complexity of the operations:
- The choice of data structure should be based on the time complexity of the operations that will be performed.
- Time complexity is defined in terms of how many times it takes to run a given algorithm, based on the length of the input.
- The time complexity of an algorithm is the amount of time it takes for each statement to complete. It is highly dependent on the size of the processed data.
- For example, if you need to perform searches frequently, you should use a binary search tree.
.The space complexity of the operations:
- The choice of data structure should be based on the space complexity of the operations that will be performed.
- The amount of memory used by a program to execute it is represented by its space complexity.
- Because a program requires memory to store input data and temporal values while running , the space complexity is auxiliary and input space.
- For example, if you need to store a lot of data, you should use an array.
Definition, Types, Complexity and Examples of Algorithm
An algorithm is a well-defined sequential computational technique that accepts a value or a collection of values as input and produces the output(s) needed to solve a problem.
Or we can say that an algorithm is said to be accurate if and only if it stops with the proper output for each input instance.
NEED OF THE ALGORITHMS :
Algorithms are used to solve problems or automate tasks in a systematic and efficient manner. They are a set of instructions or rules that guide the computer or software in performing a particular task or solving a problem.
There are several reasons why we use algorithms:
- Efficiency: Algorithms can perform tasks quickly and accurately, making them an essential tool for tasks that require a lot of calculations or data processing.
- Consistency: Algorithms are repeatable and produce consistent results every time they are executed. This is important when dealing with large amounts of data or complex processes.
- Scalability: Algorithms can be scaled up to handle large datasets or complex problems, which makes them useful for applications that require processing large volumes of data.
- Automation: Algorithms can automate repetitive tasks, reducing the need for human intervention and freeing up time for other tasks.
- Standardization: Algorithms can be standardized and shared among different teams or organizations, making it easier for people to collaborate and share knowledge.
Overall, algorithms are an essential tool for solving problems in a variety of fields, including computer science, engineering, data analysis, finance, and many others.
Example:
Consider a box where no one can see what’s happening inside, we say a black box.
We give input to the box and it gives us the output we need but the procedure that we might need to know behind the conversion of input to desired output is an ALGORITHM.
An algorithm is independent of the language used. It tells the programmer the logic used to solve the problem. So, it is a logical step-by-step procedure that acts as a blueprint to programmers.