Classic algorithms that must be mastered as a programmer
During the career of a programmer, you will encounter a variety of algorithm problems. Some algorithms are essential skills for programmers because they are widely used in practical work and have high practicality. In this blog, we will introduce some of the most important algorithms that programmers must be familiar with and master. These algorithms include: sorting (quick sort, merge sort, heap sort), search (binary search, hash table), graph algorithms (shortest path, minimum spanning tree), dynamic programming, and divide-and-conquer strategies.
Sorting Algorithm
Sorting algorithms are one of the most basic algorithms in computer science, and their goal is to sort a set of data according to certain rules. The following are three classic sorting algorithms:
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Quicksort : Quicksort is an efficient sorting algorithm that uses a divide-and-conquer strategy to decompose a large problem into two smaller ones. The basic idea of quick sort is to select a reference value from the array, and then divide the array into two parts: one part contains elements smaller than the reference value, and the other part contains elements larger than the reference value. Then quickly sort the two parts separately. The average time complexity of quicksort is O(nlogn).
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Merge Sort : Merge sort is another sorting algorithm based on divide and conquer strategy. It first splits the array in half and then does a merge sort on each half. Finally, the two sorted subarrays are merged into one sorted array. The time complexity of merge sort is O(nlogn), and the space complexity is O(n).
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Heap sort : Heap sort is a sorting algorithm based on comparison. It uses the data structure of the heap for sorting. The process of heap sorting consists of two steps: building the heap and extracting the maximum (or minimum) value. The time complexity of heap sort is O(nlogn), and the space complexity is O(1).
search algorithm
Finding algorithms are used to find specific elements in a dataset. The following are two commonly used lookup algorithms:
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Binary Search : Binary Search is an efficient search algorithm that works on sorted datasets. During the search process, the binary search will continue to halve the search range until the target element is found or the search range is empty. The time complexity of binary search is O(logn).
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Hash table : A hash table is a data structure that enables fast lookup, insertion, and deletion operations by mapping the keys of elements into a fixed-size table. The average time complexity of a hash table is O(1).
graph algorithm
Graph algorithms are used to solve problems related to graphs, such as finding the shortest path, minimum spanning tree, etc. The following are two classic graph algorithms:
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Shortest Path : The shortest path problem is to find the shortest path from one vertex to another in a graph. Commonly used shortest path algorithms include Dijkstra algorithm and Bellman-Ford algorithm. Dijkstra's algorithm works on graphs with non-negative weights and has a time complexity of O(|V|^2) or O(|E|+|V|log|V|), depending on the implementation. The Bellman-Ford algorithm works on graphs with negative weights and has a time complexity of O(|V||E|).
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Minimum spanning tree : The minimum spanning tree problem is to find the minimum weight connected subgraph of a connected undirected graph. Commonly used minimum spanning tree algorithms are Kruskal's algorithm and Prim's algorithm. The time complexity of Kruskal's algorithm is O(|E|log|E|), and the time complexity of Prim's algorithm is O(|V|^2) or O(|E|+|V|log|V|), depending on in the way of implementation.
dynamic programming
Dynamic programming is a method for solving optimization problems. Its core idea is to decompose the problem into several sub-problems and store the solutions of the sub-problems to avoid repeated calculations. Dynamic programming is suitable for problems with overlapping subproblems and optimal substructure. Classical dynamic programming problems include knapsack problem, longest common subsequence, longest ascending subsequence, etc.
divide and conquer strategy
The divide-and-conquer strategy is a method of solving problems. It decomposes a large problem into several small problems, then recursively solves the small problems, and combines the solutions of these small problems into the solution of the original problem. Divide and conquer strategy is suitable for problems with recursive structure. In addition to the aforementioned quick sort and merge sort, other classic divide-and-conquer algorithms include Strassen matrix multiplication, Karatsuba large number multiplication, etc.
Summarize
As a programmer, it is very important to master these classic algorithms. These algorithms not only often appear in interviews, but also have a wide range of applications in actual work. By learning these algorithms, you will improve your programming ability and better solve practical problems. Of course, the algorithms introduced here are just the tip of the iceberg. As programmers, we should keep learning and exploring to deal with increasingly complex computing problems.