算法 - 全栈紫升

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algorithm [ˈælɡərɪðəm]

An algorithm is a set of instructions or steps to solve a particular problem.（算法是解决特定问题的一组指令或步骤。）

例句：

算法的设计：The design of an algorithm is the process of defining the input, output, and steps required to solve a problem.（算法的设计是定义输入、输出和解决问题所需的步骤的过程。）
算法的实现：The implementation of an algorithm is the actual code that performs the steps defined in the algorithm.（算法的实现是实际执行算法中定义的步骤的代码。）
算法的效率：The efficiency of an algorithm is measured by its time complexity and space complexity.（算法的效率通常通过时间复杂度和空间复杂度来衡量。）
算法的复杂性：The complexity of an algorithm is a measure of how difficult it is to solve a problem using that algorithm.（算法的复杂性是衡量使用该算法解决问题的难度的指标。）
算法的应用：Algorithms are used in a wide range of applications, including computer science, mathematics, and engineering.（算法在计算机科学、数学和工程等领域中得到广泛应用。）
算法的研究：Research in algorithms focuses on finding efficient solutions to problems and improving the performance of existing algorithms.（算法研究的重点是寻找高效的解决方案来解决问题，并改进现有算法的性能。）
算法的发展：Algorithms have evolved over time, with new techniques and improvements being developed to solve more complex problems.（随着时间的推移，算法不断发展，新的技术和改进被用来解决更复杂的问题。）

DFS 深度优先搜索

Depth-First-Search. It is a algorithm used to traverse or search graphs (including trees which are a special kind of graph). The basic idea is to start from the initial vertex and explore as deeply as possible along a path until it's no longer possible, and then backtrack to the previous step and continue to explore other paths. It's like in a maze, you keep walking along a path, and when you reach a dead - end, you go back and choose another path to continue. This algorithm is applied in many scenarios, such as topological sorting and finding the connected components of a graph.

DFS（Dept-First-Search）深度优先搜索是一种用于遍历或搜索图（包括树这种特殊的图）的算法。它的基恩思想是从起始顶点开始，沿着一条路径尽可能深地探索下去，直到无法继续，然后回溯到前一步，继续探索其他路径。就好比在一个迷宫中，你一直沿着一条路走，走到死胡同就会退回来换一条路继续走。这种算法在很多场景下都有应用，比如拓扑排序、寻找图的连通分量等。

BFS 广度优先搜索

BFS stands for Breadth-First-Search. It's a commonly - used traversal algorithm for graph - based data structures. The fundamental concept is similar to exploring a maze. Starting from the initial point, it first discovers all the directly accessible nodes around the starting point. It's like the spread of water waves, expanding the search layer by layer.

For example, in a tree-structured data, when you aim to find a specific leaf node. BFS will begin from the root node, visit all the nodes at the same level as the root node first, and then visit the nodes of the next level one by one until the target node is found or the whole tree is traversed. This algorithm is usually implemented with the help of a queue data structure. The starting node is first enqueued, and then the head node of the queue is continuously removed, its adjacent nodes are visited and enqueued, thus completing the breadth-first search process. It has a wide range of applications in many fields such as problem-solving related to graph theory, web-crawling, and path-planning.

DFS 是广度优先搜索（Breadth-First-Search）的英文缩写。它是一种图形数据结构中常用的遍历算法。其基本思想就像是在一个迷宫中，从起点开始，先把起点周围所有能直接到达的节点找出来，就像水波一样，一层一层向外扩展搜索。

例如，有一个树形结构，要找到某个叶子节点。BFS 就会从根节点开始，先访问根节点同一层的所有节点，再依次访问下一层的节点，直到找到目标节点或者遍历完整个树。这种算法通常借助队列这种数据结构来实现，先将起始节点入队，然后不断地取出队首节点，访问它的相邻节点并将其入队，从而完成广度优先的搜索过程，在很多图论相关的问题求解、网络爬虫、路径规划等领域都有广泛的应用。

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algorithm [ˈælɡərɪðəm]

An algorithm is a set of instructions or steps to solve a particular problem.（算法是解决特定问题的一组指令或步骤。）

例句：

算法的设计：The design of an algorithm is the process of defining the input, output, and steps required to solve a problem.（算法的设计是定义输入、输出和解决问题所需的步骤的过程。）
算法的实现：The implementation of an algorithm is the actual code that performs the steps defined in the algorithm.（算法的实现是实际执行算法中定义的步骤的代码。）
算法的效率：The efficiency of an algorithm is measured by its time complexity and space complexity.（算法的效率通常通过时间复杂度和空间复杂度来衡量。）
算法的复杂性：The complexity of an algorithm is a measure of how difficult it is to solve a problem using that algorithm.（算法的复杂性是衡量使用该算法解决问题的难度的指标。）
算法的应用：Algorithms are used in a wide range of applications, including computer science, mathematics, and engineering.（算法在计算机科学、数学和工程等领域中得到广泛应用。）
算法的研究：Research in algorithms focuses on finding efficient solutions to problems and improving the performance of existing algorithms.（算法研究的重点是寻找高效的解决方案来解决问题，并改进现有算法的性能。）
算法的发展：Algorithms have evolved over time, with new techniques and improvements being developed to solve more complex problems.（随着时间的推移，算法不断发展，新的技术和改进被用来解决更复杂的问题。）

DFS 深度优先搜索

Depth-First-Search. It is a algorithm used to traverse or search graphs (including trees which are a special kind of graph). The basic idea is to start from the initial vertex and explore as deeply as possible along a path until it's no longer possible, and then backtrack to the previous step and continue to explore other paths. It's like in a maze, you keep walking along a path, and when you reach a dead - end, you go back and choose another path to continue. This algorithm is applied in many scenarios, such as topological sorting and finding the connected components of a graph.

DFS（Dept-First-Search）深度优先搜索是一种用于遍历或搜索图（包括树这种特殊的图）的算法。它的基恩思想是从起始顶点开始，沿着一条路径尽可能深地探索下去，直到无法继续，然后回溯到前一步，继续探索其他路径。就好比在一个迷宫中，你一直沿着一条路走，走到死胡同就会退回来换一条路继续走。这种算法在很多场景下都有应用，比如拓扑排序、寻找图的连通分量等。

BFS 广度优先搜索

BFS stands for Breadth-First-Search. It's a commonly - used traversal algorithm for graph - based data structures. The fundamental concept is similar to exploring a maze. Starting from the initial point, it first discovers all the directly accessible nodes around the starting point. It's like the spread of water waves, expanding the search layer by layer.

For example, in a tree-structured data, when you aim to find a specific leaf node. BFS will begin from the root node, visit all the nodes at the same level as the root node first, and then visit the nodes of the next level one by one until the target node is found or the whole tree is traversed. This algorithm is usually implemented with the help of a queue data structure. The starting node is first enqueued, and then the head node of the queue is continuously removed, its adjacent nodes are visited and enqueued, thus completing the breadth-first search process. It has a wide range of applications in many fields such as problem-solving related to graph theory, web-crawling, and path-planning.

DFS 是广度优先搜索（Breadth-First-Search）的英文缩写。它是一种图形数据结构中常用的遍历算法。其基本思想就像是在一个迷宫中，从起点开始，先把起点周围所有能直接到达的节点找出来，就像水波一样，一层一层向外扩展搜索。

例如，有一个树形结构，要找到某个叶子节点。BFS 就会从根节点开始，先访问根节点同一层的所有节点，再依次访问下一层的节点，直到找到目标节点或者遍历完整个树。这种算法通常借助队列这种数据结构来实现，先将起始节点入队，然后不断地取出队首节点，访问它的相邻节点并将其入队，从而完成广度优先的搜索过程，在很多图论相关的问题求解、网络爬虫、路径规划等领域都有广泛的应用。

TABLE OF CONTENTS

TABLE OF CONTENTS

algorithm [ˈælɡərɪðəm]

DFS 深度优先搜索

BFS 广度优先搜索

algorithm [ˈælɡərɪðəm]

DFS 深度优先搜索

BFS 广度优先搜索