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en/docs/chapter_backtracking/backtracking_algorithm.md
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<u>Backtracking algorithm</u> is a method to solve problems by exhaustive search, where the core idea is to start from an initial state and brute force all possible solutions, recording the correct ones until a solution is found or all possible choices are exhausted without finding a solution.
Backtracking typically employs "depth-first search" to traverse the solution space. In the "Binary Tree" chapter, we mentioned that preorder, inorder, and postorder traversals are all depth-first searches. Next, we use preorder traversal to construct a backtracking problem to gradually understand the workings of the backtracking algorithm.
Backtracking typically employs "depth-first search" to traverse the solution space. In the "Binary Tree" chapter, we mentioned that pre-order, in-order, and post-order traversals are all depth-first searches. Next, we use pre-order traversal to construct a backtracking problem to gradually understand the workings of the backtracking algorithm.
!!! question "Example One"
Given a binary tree, search and record all nodes with a value of $7$, please return a list of nodes.
For this problem, we traverse this tree in preorder and check if the current node's value is $7$. If it is, we add the node's value to the result list `res`. The relevant process is shown in Figure 13-1:
For this problem, we traverse this tree in pre-order and check if the current node's value is $7$. If it is, we add the node's value to the result list `res`. The relevant process is shown in Figure 13-1:
=== "Python"
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[class]{}-[func]{preOrder}
```
![Searching nodes in preorder traversal](backtracking_algorithm.assets/preorder_find_nodes.png){ class="animation-figure" }
![Searching nodes in pre-order traversal](backtracking_algorithm.assets/preorder_find_nodes.png){ class="animation-figure" }
<p align="center"> Figure 13-1 &nbsp; Searching nodes in preorder traversal </p>
<p align="center"> Figure 13-1 &nbsp; Searching nodes in pre-order traversal </p>
## 13.1.1 &nbsp; Trying and retreating
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<p align="center"> Figure 13-4 &nbsp; Comparison of retaining and removing the return in the search process </p>
Compared to the implementation based on preorder traversal, the code implementation based on the backtracking algorithm framework seems verbose, but it has better universality. In fact, **many backtracking problems can be solved within this framework**. We just need to define `state` and `choices` according to the specific problem and implement the methods in the framework.
Compared to the implementation based on pre-order traversal, the code implementation based on the backtracking algorithm framework seems verbose, but it has better universality. In fact, **many backtracking problems can be solved within this framework**. We just need to define `state` and `choices` according to the specific problem and implement the methods in the framework.
## 13.1.4 &nbsp; Common terminology