Data structure definition
A data structure is a way of organizing and storing data, which defines how it is organized and manipulated. Common data structures include arrays, linked lists, stacks, queues, trees, graphs, etc.
Data Structure Classification
1. Classified according to logical structure: (abstract concept)
- Linear structure: There is a one-to-one relationship between data elements, such as arrays, linked lists, stacks, and queues.
- Tree structure: There is a one-to-many relationship between data elements, such as binary tree, heap, AVL tree, and red-black tree.
- Graph structure: There is a many-to-many relationship between data elements, such as directed graphs and undirected graphs.
2. Classified according to the storage structure: the storage in the specific hard disk
- Sequential storage structure: Data elements are sequentially stored in a continuous memory space according to their logical order, such as an array.
- Linked storage structure: store data elements in discontinuous memory space through pointers, and link them through pointers, such as a linked list.
Algorithm definition
An algorithm is a series of problem-solving steps and instructions for performing a specific task or accomplishing a specific goal. It is a precise and orderly calculation process, through input data, through a series of operations and calculations, and finally produce output results.
Basic properties of the algorithm:
-
Inputs : The algorithm accepts zero or more inputs.
-
Output : An algorithm produces one or more outputs.
-
Clarity : Each step of the algorithm must be clearly defined, without ambiguity, to ensure that everyone can understand and execute it.
-
Finiteness : An algorithm must complete in a finite number of steps, without infinite loops or never terminating.
-
Determinism : Each step of the algorithm must be deterministic, that is, given the same input, the execution result of the algorithm must be consistent.
-
Feasibility : Algorithms must be able to be executed in a feasible manner, using reasonable computing resources.
-
Input-output relationship : The output of an algorithm should be related to the input, i.e., for the same input, the same output should be produced.
-
Understandability : Algorithms should be sufficiently readable and understandable to be understood and used by others.
These basic properties ensure the correctness, feasibility, readability and reliability of the algorithm. Algorithms are designed and analyzed to optimize these properties to provide efficient and reliable solutions.
Basic concepts of algorithm analysis
The basic concepts of algorithm analysis involve evaluating and understanding the efficiency and performance of algorithms. It aims to analyze the behavior of algorithms in terms of time complexity and space complexity.
Time Complexity : It measures the amount of time an algorithm takes to run as a function of the input size. It helps to understand how the runtime of an algorithm increases as the input size increases.
Common ways to calculate the time complexity of an algorithm are as follows:
-
Big O notation: Big O notation is a notation used to describe the time complexity of an algorithm. It represents the relationship between the running time of the algorithm and the growth rate of the input size. Common time complexities include O(1), O(log n), O(n), O(n log n), O(n^2), etc.
-
Worst-case complexity: Worst-case complexity is the longest time an algorithm takes to execute given the most unfavorable input conditions. This is a conservative estimate of the performance of the algorithm.
-
Average-case complexity: Average-case complexity is the average time required for an algorithm to execute for all possible input cases. It usually requires assumptions and analysis of the probability distribution of the input.
-
Best-case complexity: Best-case complexity refers to the minimum time required for an algorithm to execute under the most ideal input conditions. This tends to be an optimistic estimate of algorithm performance.
Space Complexity : It measures the amount of memory space required for an algorithm to run as a function of input size. It helps to see how the memory usage of the algorithm increases with the input size.
When calculating the space complexity of an algorithm, the following aspects can be considered:
-
Input Space: The space occupied by the input data required by the algorithm.
-
Auxiliary Space: Additional space used during algorithm execution, excluding the input data itself. For example, space occupied by additional variables, arrays, stacks, queues, and other data structures.
-
Recursive stack space: If the algorithm uses recursive calls, then the space occupied by the recursive stack also needs to be considered.
For the calculation of space complexity, the big O notation is usually used to express the relationship between the additional space required by the algorithm and the growth rate of the input size. For example, O(1) means that the space complexity of the algorithm is constant, and O(n) means that the space complexity is linear with the input size.
By analyzing the time and space complexity of an algorithm, we can determine its efficiency and scalability. This analysis allows us to compare different algorithms, choose the most appropriate algorithm for a particular problem, and optimize an algorithm to improve its performance.