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临近期末，算法老师留下一个斯坦福公开课的课堂思考题，说本题做出来的同学在期末成绩上+5分，有这等好机会能争取一下还是得争取一下的。本题的思路并不难，主要是基于小顶堆对Dijkstra进行稍做改进。

该思考题如下：

In lecture we define the length of a path to be the sum of the lengths of its edges. Define the bottleneck of a path to be the maximum length of one of its edges. A mininum-bottleneck path between two vertices s and t is a path with bottleneck no larger than that of any other s−t path. Show how to modify Dijkstra’s algorithm to compute a minimum-bottleneck path between two given vertices. The running time should be 𝑂(𝑚log𝑛), as in lecture.

1 Dijkstra

在进行改进Dijkstra之前，我先进行回顾+总结一下Dijkstra。详细请看：

回顾+总结：单源最短路Dijkstra

2. 用Dijkstra处理bottleneck与mininum bottleneck问题

下面结合小顶堆及Dijkstra的思想进行处理mininum bottleneck问题，详细请看：

基于单源最短路Dijkstra解决mininum bottleneck问题