基础
算法复杂度分析 (Algorithmic Complexity Analysis)
中文介绍：算法复杂度分析是评估算法性能的过程，包括时间复杂度和空间复杂度。时间复杂度表示算法执行所需的时间，空间复杂度表示算法所需的额外空间。
英文介绍：Algorithmic complexity analysis is the process of evaluating the performance of an algorithm, including time complexity and space complexity. Time complexity represents the time required for an algorithm to execute, while space complexity represents the additional space required by the algorithm.
以下是递归、回溯和迭代的知识点的中文介绍和英文介绍：
递归 (Recursion)
中文介绍：递归是一种解决问题的方法，通过将问题分解为更小的、相同类型的子问题，并通过调用自身来解决这些子问题。递归通常使用基本情况作为终止条件来结束递归过程。
英文介绍：Recursion is a problem-solving approach that breaks down a problem into smaller, identical subproblems and solves them by calling itself. Recursion typically uses a base case as a termination condition to end the recursive process.
回溯 (Backtracking)
中文介绍：回溯是一种通过穷举所有可能的解，并逐步构建可行解的算法。在搜索过程中，当发现当前解不可行时，回溯算法会返回上一步并尝试其他选择，直到找到所有可能的解或找到符合条件的解。
英文介绍：Backtracking is an algorithmic technique that exhaustively explores all possible solutions and incrementally builds feasible solutions. During the search process, when a current solution is found to be infeasible, the backtracking algorithm backtracks to the previous step and tries other choices until all possible solutions are found or a solution that meets certain criteria is found.
迭代 (Iteration)
中文介绍：迭代是一种重复执行一系列操作的过程，通常使用循环结构来实现。在迭代过程中，每次重复执行的操作都是基于上一次迭代的结果。迭代是一种与递归相对的问题解决方法。
英文介绍：Iteration is a process of repeatedly executing a series of operations, often implemented using loops. In the iteration process, each repetition of the operation is based on the result of the previous iteration. Iteration is a problem-solving approach that is opposite to recursion.
各种算法
查找算法 (Search Algorithms)
中文介绍：查找算法用于在数据集中查找特定元素的算法。常见的查找算法包括线性查找、二分查找、哈希查找等。
英文介绍：Search algorithms are used to find specific elements in a dataset. Common search algorithms include linear search, binary search, hash-based search, and more.
排序算法 (Sorting Algorithms)
中文介绍：排序算法用于将一组元素按照特定的顺序进行排列的算法。常见的排序算法包括冒泡排序、插入排序、选择排序、快速排序、归并排序等。
英文介绍：Sorting algorithms are used to arrange a collection of elements in a specific order. Common sorting algorithms include bubble sort, insertion sort, selection sort, quicksort, mergesort, and more.
贪婪算法 (Greedy Algorithms)
中文介绍：贪婪算法是一种基于贪婪策略的算法，每一步都选择当前最优的解决方案，最终达到全局最优解。贪婪算法通常用于优化问题，但不保证一定能得到最优解。
英文介绍：Greedy algorithms are algorithms based on the greedy strategy, where at each step, the algorithm chooses the locally optimal solution, aiming to reach a globally optimal solution. Greedy algorithms are commonly used in optimization problems, but they do not guarantee the optimal solution.
分治算法 (Divide and Conquer Algorithms)
中文介绍：分治算法是一种将问题分解成更小的子问题，递归地解决子问题，然后合并子问题的解以得到原始问题解决方案的算法。分治算法常用于解决复杂问题，例如归并排序和快速排序。
英文介绍：Divide and conquer algorithms are algorithms that break down a problem into smaller subproblems, recursively solve the subproblems, and then combine the solutions of the subproblems to obtain the solution to the original problem. Divide and conquer algorithms are commonly used to solve complex problems, such as mergesort and quicksort.
动态规划算法 (Dynamic Programming Algorithms)
中文介绍：动态规划算法是一种将复杂问题分解成重叠子问题，并利用子问题的解构建原问题解的算法。动态规划算法通常用于优化问题，通过存储中间结果来避免重复计算。
英文介绍：Dynamic programming algorithms are algorithms that break down complex problems into overlapping subproblems and build the solution to the original problem using the solutions to the subproblems. Dynamic programming algorithms are commonly used in optimization problems, avoiding redundant computations by storing intermediate results.
字符串相关算法 (String-related Algorithms)
中文介绍：字符串相关算法是用于处理字符串的算法。它们包括字符串匹配算法（如暴力匹配、KMP算法）、字符串编辑距离算法（如莱文斯坦距离）、字符串压缩算法（如Huffman编码）等。
英文介绍：String-related algorithms are algorithms used for processing strings. They include string matching algorithms (such as brute force matching, Knuth-Morris-Pratt algorithm), string edit distance algorithms (such as Levenshtein distance), string compression algorithms (such as Huffman coding), and more.
树与图相关算法 (Tree and Graph Algorithms)
中文介绍：树与图相关算法是用于处理树和图数据结构的算法。它们包括图遍历算法（如深度优先搜索、广度优先搜索）、最短路径算法（如Dijkstra算法、Floyd-Warshall算法）、最小生成树算法（如Prim算法、Kruskal算法）等。
英文介绍：Tree and graph algorithms are algorithms used for processing tree and graph data structures. They include graph traversal algorithms (such as depth-first search, breadth-first search), shortest path algorithms (such as Dijkstra's algorithm, Floyd-Warshall algorithm), minimum spanning tree algorithms (such as Prim's algorithm, Kruskal's algorithm), and more.