Moved A* algorithm close to Dijkstra's algorithm.

gazeldx · gazeldx · commit a10d65b0f66a · 2025-02-16T11:52:46.000+08:00
diff --git a/README.md b/README.md
@@ -115,10 +115,10 @@ You can skip the more difficult problems and do them later.
 - [1584. Min Cost to Connect All Points](en/1001-2000/1584-min-cost-to-connect-all-points.md) was solved in _Python, Java, C++, JavaScript, C#, Go, Ruby_ and 2 ways.
 - [207. Course Schedule](en/1-1000/207-course-schedule.md) was solved in _Python, Java, C++, C#_ and 2 ways.
 - [1514. Path with Maximum Probability](en/1001-2000/1514-path-with-maximum-probability.md) was solved in _Python_ and 2 ways.
+- [752. Open the Lock](en/1-1000/752-open-the-lock.md) was solved in _Python_ and 2 ways.
 - [743. Network Delay Time](en/1-1000/743-network-delay-time.md) was solved in _Python_ and 2 ways.
 - [787. Cheapest Flights Within K Stops](en/1-1000/787-cheapest-flights-within-k-stops.md) was solved in _Python_.
 - [1334. Find the City With the Smallest Number of Neighbors at a Threshold Distance](en/1001-2000/1334-find-the-city-with-the-smallest-number-of-neighbors-at-a-threshold-distance.md) was solved in _Python_.
-- [752. Open the Lock](en/1-1000/752-open-the-lock.md) was solved in _Python_ and 2 ways.
 
 # Others
 - [433. Minimum Genetic Mutation](en/1-1000/433-minimum-genetic-mutation.md) was solved in _Python_ and 2 ways.
diff --git a/en/1-1000/743-network-delay-time.md b/en/1-1000/743-network-delay-time.md
@@ -56,11 +56,12 @@ For a detailed description of **Dijkstra's algorithm**, please refer to [1514. P
 ### Common graph theory algorithm comparison table
 |Algorithm name|Main application scenarios|Optimization methods|Importance|Difficulty|min_<br>distances|Negative weights|Additional application scenarios|
 |--------------|--------------------------|--------------------|----------|----------|-------------|----------------|--------------------------------|
-|[Prim's algorithm](../1001-2000/1584-min-cost-to-connect-all-points.md)                                                     |Minimum Spanning Tree       |Heap Sort Simplify|Important     |Medium         |Used    |Can handle||
-|[Kruskal's algorithm](../1001-2000/1584-min-cost-to-connect-all-points-2.md)                                                |Minimum Spanning Tree       |No need           |important     |Relatively hard|Not used|Can handle|Relative: [Undirected Graph Cycle Detection](./684-redundant-connection.md), [Directed Graph Cycle Detection](./685-redundant-connection-ii.md)|
-|[Dijkstra's algorithm](../1001-2000/1514-path-with-maximum-probability.md)                                                  |Single-Source Shortest Path |Heap Sort         |Very important|Relatively hard|Used    |Cannot handle||
-|[Bellman-Ford algorithm](./743-network-delay-time.md)                                                                       |Single-Source Shortest Path |Queue-Improved    |Very Important|Easy           |Used    |Can handle|[Detect Negative Cycles](https://www.geeksforgeeks.org/detect-negative-cycle-graph-bellman-ford/), <br>[Shortest Hop-Bounded Paths](./787-cheapest-flights-within-k-stops.md)|
-|[Floyd–Warshall](../1001-2000/1334-find-the-city-with-the-smallest-number-of-neighbors-at-a-threshold-distance.md)|Multi-Source Shortest Path  |No need           |Less important|Relatively hard|Used    |Can handle||
+|[Prim's algorithm](../1001-2000/1584-min-cost-to-connect-all-points.md)                                           |Minimum Spanning Tree      |Heap Sort Simplify|Important     |Medium         |Used    |Can handle||
+|[Kruskal's algorithm](../1001-2000/1584-min-cost-to-connect-all-points-2.md)                                      |Minimum Spanning Tree      |No need           |important     |Relatively hard|Not used|Can handle|Relative: [Undirected Graph Cycle Detection](./684-redundant-connection.md), [Directed Graph Cycle Detection](./685-redundant-connection-ii.md)|
+|[Dijkstra's algorithm](../1001-2000/1514-path-with-maximum-probability.md)                                        |Single-Source Shortest Path|Heap Sort         |Very important|Relatively hard|Used    |Cannot handle||
+|[A* search algorithm](./752-open-the-lock.md)                                                                     |Single-Source Shortest Path|Built-in Heap Sort|Very important|Medium         |Not used|It depends||
+|[Bellman-Ford algorithm](./743-network-delay-time.md)                                                             |Single-Source Shortest Path|Queue-Improved    |Very Important|Easy           |Used    |Can handle|[Detect Negative Cycles](https://www.geeksforgeeks.org/detect-negative-cycle-graph-bellman-ford/), <br>[Shortest Hop-Bounded Paths](./787-cheapest-flights-within-k-stops.md)|
+|[Floyd–Warshall](../1001-2000/1334-find-the-city-with-the-smallest-number-of-neighbors-at-a-threshold-distance.md)|Multi-Source Shortest Path |No need           |Less important|Relatively hard|Used    |Can handle||
 
 ## Complexity
 **V**: vertex count, **E**: Edge count.
diff --git a/en/1-1000/752-open-the-lock.md b/en/1-1000/752-open-the-lock.md
@@ -69,7 +69,7 @@ We can think of this problem as a shortest path problem on a graph: there are `1
 
 **Breadth-First Search** treats each vertex equally, which inevitably leads to poor performance.
 
-The `A* (A-star) search algorithm` calculates the **distance** between each `vertex` and the `target vertex`, and **prioritizes vertices with closer distances**, which is equivalent to indicating which vertex to process next, so the performance is greatly improved!
+The _A* (A-star) search algorithm_ calculates the **distance** between each `vertex` and the `target vertex`, and **prioritizes vertices with closer distances**, which is equivalent to indicating which vertex to process next, so the performance is greatly improved!
 
 _A* (A-star) search algorithm_ is similar to _Dijkstra's algorithm_, but the `target vertex` of _A* (A-star) search algorithm_ is clear, while that of _Dijkstra's algorithm_ is not. _Dijkstra's algorithm_ calculates the `distance` from the `starting vertex` to the `vertex` it reaches.
 
diff --git a/zh/1-1000/743-network-delay-time.md b/zh/1-1000/743-network-delay-time.md
@@ -58,10 +58,11 @@
 
 |算法名称|主要的适用场景|优化方式|重要度|难度|min_<br>distances|负边权值|额外的适用场景|
 |-------|-----------|-------|-------|---|-------------|--------|------------|
-|[Prim算法](../1001-2000/1584-min-cost-to-connect-all-points.md)                                                       |最小生成树  |堆排序简化|重要   |中等|用到|能处理||
-|[Kruskal算法](../1001-2000/1584-min-cost-to-connect-all-points-2.md)                                                  |最小生成树  |无需优化  |重要   |较难|不用|能处理|相关：[无向图环检测](./684-redundant-connection.md), [有向图环检测](./685-redundant-connection-ii.md)|
-|[Dijkstra算法](../1001-2000/1514-path-with-maximum-probability.md)                                                    |单源最短路径|堆排序优化 |很重要 |较难|用到|无能力||
-|[Bellman-Ford](./743-network-delay-time.md)                                                                       |单源最短路径|集合优化  |很重要  |简单|用到|能处理|[负环检测](https://www.geeksforgeeks.org/detect-negative-cycle-graph-bellman-ford/), [限定步数最短路径](./787-cheapest-flights-within-k-stops.md)|
+|[Prim算法](../1001-2000/1584-min-cost-to-connect-all-points.md)                                                    |最小生成树 |堆排序简化|重要   |中等|用到|能处理||
+|[Kruskal算法](../1001-2000/1584-min-cost-to-connect-all-points-2.md)                                               |最小生成树 |无需优化  |重要   |较难|不用|能处理|相关：[无向图环检测](./684-redundant-connection.md), [有向图环检测](./685-redundant-connection-ii.md)|
+|[Dijkstra算法](../1001-2000/1514-path-with-maximum-probability.md)                                                 |单源最短路径|堆排序优化|很重要 |较难|用到|无能力||
+|[A* 算法](./752-open-the-lock.md)                                                                                  |单源最短路径|固有堆排序|很重要 |中等|不用|看情况||
+|[Bellman-Ford](./743-network-delay-time.md)                                                                       |单源最短路径|集合优化  |很重要 |简单|用到|能处理|[负环检测](https://www.geeksforgeeks.org/detect-negative-cycle-graph-bellman-ford/), [限定步数最短路径](./787-cheapest-flights-within-k-stops.md)|
 |[Floyd–Warshall](../1001-2000/1334-find-the-city-with-the-smallest-number-of-neighbors-at-a-threshold-distance.md)|多源最短路径|无需优化  |较不重要|较难|用到|能处理||
 
 ## 复杂度
diff --git a/zh/1-1000/752-open-the-lock.md b/zh/1-1000/752-open-the-lock.md
@@ -72,6 +72,8 @@
 
 `A* (A-Star) 算法` 会对每一个`顶点`与`目标顶点`的**距离**进行计算，**距离近的顶点优先处理**，相当于为下一步处理哪个顶点指明了方向，因此性能有很大的提升！
 
+`A* (A-Star) 算法` 和 `Dijkstra's 算法` 比较像，但`A* 算法`的`目标顶点`是明确的，但`Dijkstra's 算法`不明确。`Dijkstra's 算法`是走到哪个顶点就计算从`起点`到`那个顶点`的距离。
+
 #### A* (A-Star) 算法的两（三）个关键动作
 1. 要用 `priority_queue`。
 2. 计算距离的`启发式函数`要**精心设计**。设计不好，将导致不易察觉的结果错误!
