add: fertility simulation solution

docs/assets/git-committers/page-authors.json

@@ -1 +1 @@
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+{"cache_date": "2024-06-18", "page_authors": {"docs/index.md": {"last_commit_date": "2023-09-28", "authors": [{"login": "shenxiangzhuang", "name": "shenxiangzhuang", "url": "https://github.com/shenxiangzhuang", "avatar": "https://avatars.githubusercontent.com/u/17157965?v=4"}]}, "docs/CHANGELOG.md": {"last_commit_date": "2023-09-27", "authors": [{"login": "shenxiangzhuang", "name": "shenxiangzhuang", "url": "https://github.com/shenxiangzhuang", "avatar": "https://avatars.githubusercontent.com/u/17157965?v=4"}]}, "docs/fifty/index.md": {"last_commit_date": "2023-09-28", "authors": [{"login": "shenxiangzhuang", "name": "shenxiangzhuang", "url": "https://github.com/shenxiangzhuang", "avatar": "https://avatars.githubusercontent.com/u/17157965?v=4"}]}, "docs/fifty/1_the_sock_drawer.md": {"last_commit_date": "2023-10-05", "authors": [{"login": "shenxiangzhuang", "name": "shenxiangzhuang", "url": "https://github.com/shenxiangzhuang", "avatar": "https://avatars.githubusercontent.com/u/17157965?v=4"}]}, "docs/fifty/2_successive_wins.md": {"last_commit_date": "2023-10-05", "authors": [{"login": "shenxiangzhuang", "name": "shenxiangzhuang", "url": "https://github.com/shenxiangzhuang", "avatar": "https://avatars.githubusercontent.com/u/17157965?v=4"}]}, "docs/fifty/3_flippant_jury.md": {"last_commit_date": "2023-10-05", "authors": [{"login": "shenxiangzhuang", "name": "shenxiangzhuang", "url": "https://github.com/shenxiangzhuang", "avatar": "https://avatars.githubusercontent.com/u/17157965?v=4"}]}, "docs/fifty/4_first_success.md": {"last_commit_date": "2023-10-06", "authors": [{"login": "shenxiangzhuang", "name": "shenxiangzhuang", "url": "https://github.com/shenxiangzhuang", "avatar": "https://avatars.githubusercontent.com/u/17157965?v=4"}]}, "docs/fifty/5_coin_in_square.md": {"last_commit_date": "2023-10-06", "authors": [{"login": "shenxiangzhuang", "name": "shenxiangzhuang", "url": "https://github.com/shenxiangzhuang", "avatar": "https://avatars.githubusercontent.com/u/17157965?v=4"}]}, "docs/fifty/6_chuck_a_luck.md": {"last_commit_date": "2023-10-25", "authors": [{"login": "pre-commit-ci[bot]", "name": "pre-commit-ci[bot]", "url": "https://github.com/apps/pre-commit-ci", "avatar": "https://avatars.githubusercontent.com/in/68672?v=4"}, {"login": "shenxiangzhuang", "name": "shenxiangzhuang", "url": "https://github.com/shenxiangzhuang", "avatar": "https://avatars.githubusercontent.com/u/17157965?v=4"}]}, "docs/util/problem_template.md": {"last_commit_date": "2023-09-28", "authors": [{"login": "shenxiangzhuang", "name": "shenxiangzhuang", "url": "https://github.com/shenxiangzhuang", "avatar": "https://avatars.githubusercontent.com/u/17157965?v=4"}]}, "docs/blog/index.md": {"last_commit_date": "2024-04-15", "authors": [{"login": "shenxiangzhuang", "name": "shenxiangzhuang", "url": "https://github.com/shenxiangzhuang", "avatar": "https://avatars.githubusercontent.com/u/17157965?v=4"}]}, "docs/blog/posts/about.md": {"last_commit_date": "2024-04-15", "authors": [{"login": "shenxiangzhuang", "name": "shenxiangzhuang", "url": "https://github.com/shenxiangzhuang", "avatar": "https://avatars.githubusercontent.com/u/17157965?v=4"}]}, "docs/fifty/8_perfect_bridge_hand.md": {"last_commit_date": "2024-05-27", "authors": [{"login": "shenxiangzhuang", "name": "shenxiangzhuang", "url": "https://github.com/shenxiangzhuang", "avatar": "https://avatars.githubusercontent.com/u/17157965?v=4"}]}, "docs/mystery/index.md": {"last_commit_date": "2024-06-18", "authors": [{"login": "shenxiangzhuang", "name": "shenxiangzhuang", "url": "https://github.com/shenxiangzhuang", "avatar": "https://avatars.githubusercontent.com/u/17157965?v=4"}]}, "docs/mystery/3_fertility_policy.md": {"last_commit_date": "2024-06-18", "authors": [{"login": "shenxiangzhuang", "name": "shenxiangzhuang", "url": "https://github.com/shenxiangzhuang", "avatar": "https://avatars.githubusercontent.com/u/17157965?v=4"}]}}}

docs/mystery/3_fertility_policy.md

@@ -29,7 +29,7 @@
 
 ## Solutions
 
-### Solution1
+### Solution1: Analysis
 
 ??? success "Solution1"
 
@@ -123,7 +123,7 @@
         \end{align}
         $$
 
-### Solution2
+### Solution2: Analysis
 
 ??? success "Solution2"
 
@@ -164,7 +164,7 @@
 
 ### Solution3
 
-??? success "Solution3"
+??? success "Solution3: Elegant Analysis"
 
     === "English"
 
@@ -181,4 +181,25 @@
         无论生育政策如何，最终都是一系列相互独立的生育事件，所以最终的男女比例是1:1。
 
 
-### TODO: Solution4: Simulation
+### Solution4: Simulation
+
+
+??? success "Solution4"
+
+    === "English"
+
+        We can simulate the birth process to obtain the numerical solution 
+        of the gender ratio under the current fertility policy:
+
+        ```python exec="true" source="material-block" session="fifty-3"
+        --8<-- "docs/mystery/snippet/3_fertility_policy.py:solution"
+        ```
+
+
+    === "中文"
+
+        我们可以通过模拟生育的过程来得到当前生育政策下性别比例的数值解:
+
+        ```python exec="true" source="material-block" session="fifty-3"
+        --8<-- "docs/mystery/snippet/3_fertility_policy.py:solution"
+        ```

docs/mystery/snippet/3_fertility_policy.py

@@ -0,0 +1,36 @@
+# --8<-- [start:solution]
+import random
+from enum import Enum
+
+
+class Gender(int, Enum):
+    MALE = 0
+    FEMALE = 1
+
+
+def birth_event() -> Gender:
+    if random.randint(0, 1) == 0:
+        return Gender.MALE
+    else:
+        return Gender.FEMALE
+
+
+def family_event() -> int:
+    female_count = 0
+    while birth_event() != Gender.MALE:
+        female_count += 1
+    return female_count
+
+
+def simulation(run_nums: int = 100000) -> None:
+    male_count, female_count = 0, 0
+    for _ in range(run_nums):
+        female_count += family_event()
+        male_count += 1
+    print(f'Males: {male_count}, Females: {female_count}\n')
+    print(f'Males/Female: {male_count / female_count}\n')
+
+
+simulation()
+
+# --8<-- [end:solution]