Today I would like to share with you a piece of useful information, suitable for those who have just entered the industry or those who are preparing to change careers. Next, let’s take a look at the algorithms that programmers need, as well as the common applications and importance of algorithms!
1: The importance and application scenarios of algorithms, and the reasons why programmers need to master algorithms
As we all know, algorithm is an important branch of computer science, which studies the steps and methods of solving problems. The importance of algorithms is that they can help us better solve practical problems and improve the efficiency and performance of programs.
In software development, application scenarios include but are not limited to:
- Search engines: Search engines need to quickly return the results required by users, so they need to use efficient algorithms to process massive amounts of data.
- Database query: Database query needs to return qualified data quickly, so efficient algorithms need to be used to process large amounts of data.
- Image processing: Image processing requires various operations on images (such as scaling, rotation, cropping, etc.), so efficient algorithms need to be used to implement these operations.
- Artificial Intelligence: Artificial Intelligence requires the analysis and processing of large amounts of data, and therefore requires the use of efficient algorithms to process this data.
Reasons why programmers need to master algorithms:
- Algorithms can improve the efficiency and performance of programs. By using appropriate algorithms, the time complexity and space complexity of the program can be reduced, thereby improving the running efficiency and response speed of the program.
- Algorithms can help us understand problems better. By using algorithms, we can decompose complex problems into smaller sub-problems and solve these sub-problems step by step to better understand the nature of the problem.
- Algorithms can help us design programs better. By understanding different algorithms and their advantages and disadvantages, we can choose the most appropriate algorithm to solve the problem and design a more efficient, reliable, and maintainable program.
2: Introduction to common algorithms
Here are some common sorting algorithms:
1. Bubble Sort
2. Selection Sort
3. Insertion Sort
4. Shell Sort
5. Merge Sort
6. Quick Sort
7. Heap Sort
8. Counting Sort
9. Bucket Sort
10. Radix Sort
Search algorithms include:
1. Sequential Search
2. Binary Search
3. Interpolation Search
4. Fibonacci Search
5. Hashing
6. Indexed Search )
7. B-Tree Search
8. Hash Table Lookup
9. Red-Black Tree Search
10. Trie Tree Search
Graph theory algorithms include:
1. Shortest path algorithm (Dijkstra algorithm and Floyd algorithm)
2. Minimum spanning tree algorithm (Prim algorithm and Kruskal algorithm)
3. Topological sorting algorithm (Topological Sorting)
4. Strongly Connected Components algorithm (Strongly Connected Components)
5. Graph isomorphism Algorithm (Graph Isomorphism)
6. Graph Coloring Algorithm (Graph Coloring)
7. Maximal Flow Algorithm (Maximal Flow)
8. Minimum Cut Algorithm (Min Cut)
9. Network Flow Algorithm (Network flow)
10. Graph Approximation
Three: Summary of key algorithms
Here is a summary of some common algorithms and their highlights:
Sorting algorithm:
1. Bubble sort: Compare adjacent elements and swap larger elements to the right. The time complexity is O(n^2).
2. Selection sort: Select the smallest element from the unsorted elements and put it at the end of the sorted sequence. The time complexity is O(n^2).
3. Insertion sort: Insert unsorted elements into the correct position of the sorted sequence. The time complexity is O(n^2).
4. Hill sorting: Sorting the array by inserting subsequences with an interval of h, the time complexity is O(n^2/h).
5. Merge sort: Recursively divide the array into two halves, sort them separately and then merge them. The time complexity is O(nlogn).
6. Quick sort: Select a benchmark element and divide the array into two sub-arrays, one less than or equal to the benchmark element, and the other greater than or equal to the benchmark element. The two subarrays are then quickly sorted recursively. The time complexity is O(nlogn).
7. Heap sort: Treat the array as a big top heap or a small top heap, and take out the maximum or minimum value in sequence until there is only one element left in the heap. The time complexity is O(nlogn).
8. Counting sorting: Count the number of occurrences of each element and then output it in order. The time complexity is O(n+k), where k is the range of elements.
9. Bucket sorting: Put elements into different buckets, sort the elements in each bucket, and then take them out one after another. The time complexity is O(n+k), where k is the number of buckets.
10. Radix sort: Cut the number into different numbers by digits, and then sort by each digit. The time complexity is O(d(n+b)), where d is the number of digits in the number and b is the range of digits in the number.
Search algorithm:
1. Sequential search: Compare elements one by one until the target element is found. The time complexity is O(n).
2. Binary search: Find the target element in the ordered sequence, and each search reduces the sequence by half. The time complexity is O(logn).
3. Interpolation search: Search by calculating the approximate position of the target element in the list. The time complexity is O(logn).
4. Fibonacci search: For ordered sequences, determine the position of the target element by finding the positions of the Fibonacci sequence of the first two elements. The time complexity is O(logn).
5. Hash lookup: Use a hash function to map an element to a location in the table, and then access that location directly. The time complexity is O(1).
6. Index search: Use the index table to store data and corresponding location information, and then directly access the index table to find the target element. The time complexity is O(1).
7. B-tree search: Use the B-tree data structure to store data and corresponding location information, and then directly access the B-tree to find the target element. The time complexity is O(logn).
8. Hash table lookup: Similar to hash table lookup, but the hash table can also dynamically increase and decrease in size to adapt to the distribution of data. The time complexity is O(1).
9. Red-black tree search: A self-balancing binary search tree that can efficiently find, insert, and delete elements. The time complexity is O(logn).
10. Tries tree search: a special multi-tree, used to efficiently find whether a string contains a certain substring. The time complexity is O(m+k), where m is the length of the string and k is the length of the substring.
Graph theory algorithm:
1. Shortest path algorithm: Both Dijkstra's algorithm and Floyd's algorithm can be used to solve the single-source shortest path problem. The former is suitable for directed graphs, and the latter is suitable for undirected graphs. The time complexity is O(|V||E|) or O((|V|+|E|)log|V|) (Dijkstra's algorithm).
2. Minimum spanning tree algorithm: Both Prim's algorithm and Kruskal's algorithm can be used to solve the minimum spanning tree problem. The former is suitable for dense graphs, and the latter is suitable for sparse graphs or disconnected directed graphs. The time complexity is O(|V||E|log|V|) (Prim's algorithm), or O(|V||E|log|V|+|E|log|V|) (Kruskal's algorithm).
3. Topological sorting algorithm: used to solve the problem of vertex arrangement order in directed acyclic graphs. The time complexity is O(|V|+|E|) (depth-first search).
4. Strongly connected component algorithm: used to solve the problem of strongly connected components in directed graphs. The time complexity is O(|V||C|) (Tarjan algorithm).
5. Graph isomorphism algorithm: used to determine whether two graphs are isomorphic. The time complexity is O(|V||E|) (brute force algorithm).
6. Graph coloring algorithm: used to solve the problem of node coloring in graphs. Two commonly used methods are greedy algorithm and backtracking method. The time complexity of the greedy algorithm is O(|V||C|+|E|) (greedy strategy), and the time complexity of the backtracking method is O(|V||C||E|!) (backtracking strategy).
7. Maximum flow algorithm: used to solve the maximum flow problem in network flow problems. Two commonly used methods are the Ford-Fulkerson algorithm and the Edmonds-Karp algorithm. Ford-Fulkerson algorithm time complex
at last:
In general, algorithm is a very important concept in computer science, which involves the design, development and optimization of computer programs. Therefore, mastering algorithms is very important for those working in these fields.
OK, because of time constraints, I’ll stop here first. If you pass by, please like and support!