237th Commit

README.md

@@ -43,8 +43,8 @@ $ pnpm test twoSum.test.ts
 9. [字典樹 (Trie)](./algorithms/9.trie/README.md)
 10. [排序 (Sorting)](./algorithms/10.sorting/README.md)
 11. [搜尋 (Searching)](./algorithms/11.searching/README.md)
-12. 分治 (Divide and Conquer)
-13. 回溯 (Backtracking)
+12. [分治 (Divide and Conquer)](./algorithms/12.divide-and-conquer/README.md)
+13. [回溯 (Backtracking)](./algorithms/13.backtracking/README.md)
 14. [動態規劃 (Dynamic Programming)](./algorithms/14.dynamic-programming/README.md)
 15. 貪婪 (Greedy)
 16. 位元操作 (Bit Manipulation)

algorithms/12.divide-and-conquer/README.md

@@ -1 +1,48 @@
 # 分治 (Divide and Conquer)
+
+- 分 (劃分)
+- 治 (合併)
+
+```ts
+[8, 4, 2, 6];
+```
+
+分：
+
+```mermaid
+flowchart TB
+    0(8, 4, 2, 6)
+    1(8, 4)
+    2(2, 6)
+    3(8)
+    4(4)
+    5(2)
+    6(6)
+
+    0 --> 1
+    0 --> 2
+    1 --> 3
+    1 --> 4
+    2 --> 5
+    2 --> 6
+```
+
+治：
+
+```mermaid
+flowchart TB
+    0(8)
+    1(4)
+    2(2)
+    3(6)
+    4(4, 8)
+    5(2, 6)
+    6(2, 4, 6, 8)
+
+    0 --> 4
+    1 --> 4
+    2 --> 5
+    3 --> 5
+    4 --> 6
+    5 --> 6
+```

algorithms/13.backtracking/README.md

@@ -1 +1,123 @@
 # 回溯 (Backtracking)
+
+### 全排列 (Permutations)
+
+```ts
+[1, 2];
+```
+
+```ts
+[
+  [1, 2],
+  [2, 1],
+];
+```
+
+```mermaid
+flowchart TB
+    0(_, _)
+    1(1, _)
+    2(2, _)
+    3(1, 1)
+    4(1, 2)
+    5(2, 1)
+    6(2, 2)
+
+    0 --> 1
+    0 --> 2
+    1 -. 剪枝 .-> 3
+    1 --> 4
+    2 --> 5
+    2 -. 剪枝 .-> 6
+```
+
+```ts
+[1, 2, 3];
+```
+
+```ts
+[
+  [1, 2, 3],
+  [1, 3, 2],
+  [2, 1, 3],
+  [2, 3, 1],
+  [3, 1, 2],
+  [3, 2, 1],
+];
+```
+
+```mermaid
+flowchart TB
+    0(_, _, _)
+    1(1, _, _)
+    2(2, _, _)
+    3(3, _, _)
+
+    4(1, 2, _)
+    5(1, 3, _)
+    6(2, 1, _)
+    7(2, 3, _)
+    8(3, 1, _)
+    9(3, 2, _)
+
+    10(1, 2, 3)
+    11(1, 3, 2)
+    12(2, 1, 3)
+    13(2, 3, 1)
+    14(3, 1, 2)
+    15(3, 2, 1)
+
+    0 --> 1
+    0 --> 2
+    0 --> 3
+
+    1 --> 4
+    1 --> 5
+    2 --> 6
+    2 --> 7
+    3 --> 8
+    3 --> 9
+
+    4 --> 10
+    5 --> 11
+    6 --> 12
+    7 --> 13
+    8 --> 14
+    9 --> 15
+```
+
+```ts
+function permute(nums: number[]): number[][] {
+  const result: number[][] = [];
+  const used: boolean[] = Array(nums.length).fill(false);
+
+  function backtrack(currentPermutation: number[]) {
+    // 如果當前排列的長度等於原數組長度，說明我們已經生成了一個完整排列
+    if (currentPermutation.length === nums.length) {
+      result.push([...currentPermutation]);
+      return;
+    }
+
+    // 走訪可用數字
+    for (let i = 0; i < nums.length; i++) {
+      // 如果該數字已經被選過，則跳過 (剪枝)
+      if (used[i]) continue;
+
+      // 做選擇
+      currentPermutation.push(nums[i]);
+      used[i] = true;
+
+      // 遞迴進行下一步選擇
+      backtrack(currentPermutation);
+
+      // 撤銷選擇 (回溯)
+      currentPermutation.pop();
+      used[i] = false;
+    }
+  }
+
+  backtrack([]); // 開始回溯
+
+  return result;
+}
+```

algorithms/7.heap/README.md

@@ -15,13 +15,13 @@ import { BinaryHeap, ascend, descend } from '@std/data-structures';
 ```
 
 ```mermaid
-graph TD
-    0[1] --> 1[3]
-    0 --> 2[6]
-    1 --> 3[5]
-    1 --> 4[9]
-    2 --> 5[8]
-    2 --> 6[15]
+flowchart TB
+    0(1) --> 1(3)
+    0 --> 2(6)
+    1 --> 3(5)
+    1 --> 4(9)
+    2 --> 5(8)
+    2 --> 6(15)
 ```
 
 ```ts
@@ -56,13 +56,13 @@ console.log(minHeap.isEmpty()); // false
 ```
 
 ```mermaid
-graph TD
-    0[15] --> 1[9]
-    0 --> 2[8]
-    1 --> 3[1]
-    1 --> 4[3]
-    2 --> 5[6]
-    2 --> 6[5]
+flowchart TB
+    0(15) --> 1(9)
+    0 --> 2(8)
+    1 --> 3(1)
+    1 --> 4(3)
+    2 --> 5(6)
+    2 --> 6(5)
 ```
 
 ```ts