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Bug fixes and improvements (#1348)

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* Add "reference" for EN version. Bug fixes.

* Unify the figure reference as "the figure below" and "the figure above".
Bug fixes.

* Format the EN markdown files.

* Replace "" with <u></u> for EN version and bug fixes

* Fix biary_tree_dfs.png

* Fix biary_tree_dfs.png

* Fix zh-hant/biary_tree_dfs.png

* Fix heap_sort_step1.png

* Sync zh and zh-hant versions.

* Bug fixes

* Fix EN figures

* Bug fixes

* Fix the figure labels for EN version
This commit is contained in:
Yudong Jin
2024-05-06 14:44:48 +08:00
committed by GitHub
parent 8e60d12151
commit c4a7966882
99 changed files with 615 additions and 259 deletions
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6
en/docs/chapter_dynamic_programming/unbounded_knapsack_problem.md
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@@ -40,7 +40,7 @@ Comparing the code for the two problems, the state transition changes from $i-1$
Since the current state comes from the state to the left and above, **the space-optimized solution should perform a forward traversal for each row in the $dp$ table**.
This traversal order is the opposite of that for the 0-1 knapsack. Please refer to the following figures to understand the difference.
This traversal order is the opposite of that for the 0-1 knapsack. Please refer to the figure below to understand the difference.
=== "<1>"
![Dynamic programming process for the unbounded knapsack problem after space optimization](unbounded_knapsack_problem.assets/unbounded_knapsack_dp_comp_step1.png)
@@ -117,7 +117,7 @@ For this reason, we use the number $amt + 1$ to represent an invalid solution, b
[file]{coin_change}-[class]{}-[func]{coin_change_dp}
```
The following images show the dynamic programming process for the coin change problem, which is very similar to the unbounded knapsack problem.
The figure below show the dynamic programming process for the coin change problem, which is very similar to the unbounded knapsack problem.
=== "<1>"
![Dynamic programming process for the coin change problem](unbounded_knapsack_problem.assets/coin_change_dp_step1.png)
@@ -176,7 +176,7 @@ The space optimization for the coin change problem is handled in the same way as
!!! question
Given $n$ types of coins, where the denomination of the $i^{th}$ type of coin is $coins[i - 1]$, and the target amount is $amt$. **Each type of coin can be selected multiple times**, **ask how many combinations of coins can make up the target amount**. See the example below.
Given $n$ types of coins, where the denomination of the $i^{th}$ type of coin is $coins[i - 1]$, and the target amount is $amt$. Each type of coin can be selected multiple times, **ask how many combinations of coins can make up the target amount**. See the example below.
![Example data for Coin Change Problem II](unbounded_knapsack_problem.assets/coin_change_ii_example.png)