——The content of this section is the video content notes of P65 of Bilibili Wangdao Postgraduate Entrance Examination "Data Structure".
Table of contents
1. Definition
Directed Acyclic Graph: If there is no cycle in a directed graph, it is called a directed acyclic graph, referred to as DAG graph (Directed Acyclic Graph), as shown below shown;
2. Problem description
1. I have previously learned to use the form of a tree to represent an expression, such as the following tree:
2. It is not difficult to find that many parts of the tree above can be merged. After the merge, it becomes:
3. Generally, an arithmetic expression will be given. Let us find the minimum number of vertices required. The solution steps are given below;
3. Problem-solving steps
1. For example, the question is given:
2. Step one: Arrange each operand in a row without repetition, as shown below:
3. Step 2: Mark the order in which each operator takes effect (it doesn’t matter if the order is slightly different), as shown below:
4. Step 3: Add operators in order, paying attention to "layering", as shown below:
5. Step 4: Check whether operators at the same level can be combined layer by layer from bottom to top, as shown below:
4. Special examples
