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# What is Data Structures and Algorithms?

## Definition of Algorithm

*Algorithm* is a set of instructions or operations to solve a problem (or a set of problems) in a finite amount of time. Algorithms have the following characteristics:

- The problem is clear, and the input and output definitions are clear.
- Deterministic, that is, the same input will always produce the same output.
- Feasible, that is, it can be completed in a finite number of steps, a finite amount of time, and a finite amount of memory space.
- Independent of programming languages, in other words, it can be implemented in multiple languages.

## Definition of Data Structure

*Data Structure* is a way of organizing and storing data in a computer. In order to improve the performance of data storage and operation, the design principles of data structures are:

- Occupying as little space as possible, saving computer memory.
- Data operations should be as fast as possible, including data access, addition, deletion, update, etc.
- Provide concise data representation and logical information to facilitate efficient operation by algorithms.

Data structure design is a process full of compromises, this means that if you get an advantage in one aspect, you will have to make a compromise in another aspect. For example, linked lists are more convenient for data addition and deletion than arrays, but they sacrifice the speed of data access; graphs provide more logical information than linked lists, but occupy more memory space. 

## Relationship between Data Structures and Algorithms

*Data Structures* and *Algorithms* are highly related and tightly integrated, which are shown in the following:

- Data structures are the foundation of algorithms. Data structures provide structured data storage and corresponding methods for manipulating data.
- Algorithms are the stage for data structures to show their advantages. Data structures only store information, and only with algorithms can they solve specific problems.
- Algorithms have corresponding optimal data structures. Given an algorithm, it can be implemented based on different data structures, and the final execution efficiency may vary greatly.

![relationship_between_data_structure_and_algorithm](what_is_dsa.assets/relationship_between_data_structure_and_algorithm.png)

<p align="center"> Fig. Relationship between data structures and algorithms </p>

If we compare *Data Structures and Algorithms* to *LEGO*, we can get the corresponding relationship shown in the following table.

<div class="center-table" markdown>

| Data Structures & Algorithms | LEGO                                |
| ------------------------- | -------------------------------------- |
| Input data            | LEGO blocks                             |
| Data structure       | The way blocks piece together (including size, shape, connection interface, etc.) |
| Algorithm           | The steps to piece all the blocks together to get the desired model       |
| Output data       | A LEGO model                                 |

</div>

!!! tip "A conventional abbreviation"

    In discussions, we usually abbreviate *Data Structures and Algorithms* as *Algorithms*. For example, the algorithm problems on LeetCode, actually involve both data structures and algorithms.