matrix: Add btree sparse matrix chart

XuShaohua · Aug 19, 2024 · 72d4c2f · 72d4c2f
1 parent 306ee2f
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diff --git a/src/SUMMARY.md b/src/SUMMARY.md
@@ -16,7 +16,7 @@
         - [数组](matrix/sparse-matrix/array.md)
         - [链表](matrix/sparse-matrix/linked-list.md)
         - [List of Lists](matrix/sparse-matrix/list-of-lists.md)
-        - [字典 Dictionary](matrix/sparse-matrix/dictionary.md)
+        - [BTree](matrix/sparse-matrix/btree.md)
 - [动态数组 Vector](vector/index.md)
     - [动态数组的常用操作](vector/adt.md)
     - [标准库中 Vec 的实现](vector/impl-of-vec.md)

diff --git a/src/matrix/sparse-matrix/assets/array-sparse-matrix.drawio b/src/matrix/sparse-matrix/assets/array-sparse-matrix.drawio
@@ -1,4 +1,4 @@
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diff --git a/src/matrix/sparse-matrix/assets/btree-sparse-matrix.drawio b/src/matrix/sparse-matrix/assets/btree-sparse-matrix.drawio
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diff --git a/src/matrix/sparse-matrix/assets/btree-sparse-matrix.svg b/src/matrix/sparse-matrix/assets/btree-sparse-matrix.svg
diff --git a/src/matrix/sparse-matrix/assets/btree_sparse_matrix.rs b/src/matrix/sparse-matrix/assets/btree_sparse_matrix.rs
@@ -0,0 +1 @@
+../../../../matrix/src/btree_sparse_matrix.rs
diff --git a/src/matrix/sparse-matrix/btree.md b/src/matrix/sparse-matrix/btree.md
@@ -0,0 +1,33 @@
+# BTree
+
+以下面的矩阵为例:
+
+\begin{bmatrix} \\
+0 & 0 & 3 & 0 & 4 \\\\
+0 & 0 & 5 & 7 & 0 \\\\
+0 & 0 & 0 & 0 & 0 \\\\
+0 & 2 & 6 & 0 & 0 \\
+\end{bmatrix}
+
+这个矩阵用数组存放, 效果如下图:
+
+![btree sparse matrix](assets/btree-sparse-matrix.svg)
+
+这种存储方式的特点是:
+
+- BTree 中节点是按照 key 的顺序进行存储的, 而我们选用 (row, column) 作为 key, 这样
+    - 首先以行号递增排序
+    - 如果行号相同, 以列号递增排序
+- 查找/插入/删除矩阵中某个节点的值时的性能是 `O(log(m * n))`, 其中 `m` 和 `n` 是矩阵中非 0 元素的最大行列数
+- 比较适合存放随时增减节点的矩阵, 插入或者删除元素的成本比较低, 很灵活
+- 支持范围查找, 比如查找某一行中所有的列
+- 实现简单
+
+## 算法的实现
+
+使用 BTree 进行存储, 实现起来最简单, 因为我们要求的接口与 BTreeMap 本身的接口非常匹配, 需要额外
+花费的精力很少.
+
+```rust
+{{#include assets/btree_sparse_matrix.rs:5:73}}
+```
diff --git a/src/matrix/sparse-matrix/dictionary.md b/src/matrix/sparse-matrix/dictionary.md