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docs/chapter_computational_complexity/iteration_and_recursion.md

@@ -185,7 +185,17 @@ comments: true
 === "Ruby"
 
     ```ruby title="iteration.rb"
-    [class]{}-[func]{for_loop}
+    ### for 循环 ###
+    def for_loop(n)
+      res = 0
+
+      # 循环求和 1, 2, ..., n-1, n
+      for i in 1..n
+        res += i
+      end
+
+      res
+    end
     ```
 
 === "Zig"
@@ -417,7 +427,19 @@ comments: true
 === "Ruby"
 
     ```ruby title="iteration.rb"
-    [class]{}-[func]{while_loop}
+    ### while 循环 ###
+    def while_loop(n)
+      res = 0
+      i = 1 # 初始化条件变量
+
+      # 循环求和 1, 2, ..., n-1, n
+      while i <= n
+        res += i
+        i += 1 # 更新条件变量
+      end
+
+      res
+    end
     ```
 
 === "Zig"
@@ -664,7 +686,21 @@ comments: true
 === "Ruby"
 
     ```ruby title="iteration.rb"
-    [class]{}-[func]{while_loop_ii}
+    ### while 循环（两次更新）###
+    def while_loop_ii(n)
+      res = 0
+      i = 1 # 初始化条件变量
+
+      # 循环求和 1, 4, 10, ...
+      while i <= n
+        res += i
+        # 更新条件变量
+        i += 1
+        i *= 2
+      end
+
+      res
+    end
     ```
 
 === "Zig"
@@ -904,7 +940,20 @@ comments: true
 === "Ruby"
 
     ```ruby title="iteration.rb"
-    [class]{}-[func]{nested_for_loop}
+    ### 双层 for 循环 ###
+    def nested_for_loop(n)
+      res = ""
+
+      # 循环 i = 1, 2, ..., n-1, n
+      for i in 1..n
+        # 循环 j = 1, 2, ..., n-1, n
+        for j in 1..n
+          res += "(#{i}, #{j}), "
+        end
+      end
+
+      res
+    end
     ```
 
 === "Zig"
@@ -1139,7 +1188,15 @@ comments: true
 === "Ruby"
 
     ```ruby title="recursion.rb"
-    [class]{}-[func]{recur}
+    ### 递归 ###
+    def recur(n)
+      # 终止条件
+      return 1 if n == 1
+      # 递：递归调用
+      res = recur(n - 1)
+      # 归：返回结果
+      n + res
+    end
     ```
 
 === "Zig"
@@ -1362,7 +1419,13 @@ comments: true
 === "Ruby"
 
     ```ruby title="recursion.rb"
-    [class]{}-[func]{tail_recur}
+    ### 尾递归 ###
+    def tail_recur(n, res)
+      # 终止条件
+      return res if n == 0
+      # 尾递归调用
+      tail_recur(n - 1, res + n)
+    end
     ```
 
 === "Zig"
@@ -1594,7 +1657,15 @@ comments: true
 === "Ruby"
 
     ```ruby title="recursion.rb"
-    [class]{}-[func]{fib}
+    ### 斐波那契数列：递归 ###
+    def fib(n)
+      # 终止条件 f(1) = 0, f(2) = 1
+      return n - 1 if n == 1 || n == 2
+      # 递归调用 f(n) = f(n-1) + f(n-2)
+      res = fib(n - 1) + fib(n - 2)
+      # 返回结果 f(n)
+      res
+    end
     ```
 
 === "Zig"
@@ -1936,7 +2007,25 @@ comments: true
 === "Ruby"
 
     ```ruby title="recursion.rb"
-    [class]{}-[func]{for_loop_recur}
+    ### 使用迭代模拟递归 ###
+    def for_loop_recur(n)
+      # 使用一个显式的栈来模拟系统调用栈
+      stack = []
+      res = 0
+
+      # 递：递归调用
+      for i in n.downto(0)
+        # 通过“入栈操作”模拟“递”
+        stack << i
+      end
+      # 归：返回结果
+      while !stack.empty?
+        res += stack.pop
+      end
+
+      # res = 1+2+3+...+n
+      res
+    end
     ```
 
 === "Zig"