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diff --git a/chapter_computational_complexity/index.html b/chapter_computational_complexity/index.html index a4f9958d6..90f1cbf12 100644 --- a/chapter_computational_complexity/index.html +++ b/chapter_computational_complexity/index.html @@ -3651,7 +3651,7 @@ aria-label="页脚"
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diff --git a/chapter_computational_complexity/iteration_and_recursion/index.html b/chapter_computational_complexity/iteration_and_recursion/index.html index 50efad075..78f214fda 100644 --- a/chapter_computational_complexity/iteration_and_recursion/index.html +++ b/chapter_computational_complexity/iteration_and_recursion/index.html @@ -3817,6 +3817,10 @@
+
+分步调试 +

+

图 2-1 是该求和函数的流程框图。

求和函数的流程框图

图 2-1   求和函数的流程框图

@@ -3997,6 +4001,10 @@
+
+分步调试 +

+

while 循环比 for 循环的自由度更高。在 while 循环中，我们可以自由地设计条件变量的初始化和更新步骤。

例如在以下代码中，条件变量 \(i\) 每轮进行两次更新，这种情况就不太方便用 for 循环实现：

@@ -4194,6 +4202,10 @@
+
+分步调试 +

+

总的来说，for 循环的代码更加紧凑，while 循环更加灵活，两者都可以实现迭代结构。选择使用哪一个应该根据特定问题的需求来决定。

3.   嵌套循环

我们可以在一个循环结构内嵌套另一个循环结构，下面以 for 循环为例：

@@ -4385,6 +4397,10 @@
+
+分步调试 +

+

图 2-2 是该嵌套循环的流程框图。

嵌套循环的流程框图

图 2-2   嵌套循环的流程框图

@@ -4564,6 +4580,10 @@
+
+分步调试 +

+

图 2-3 展示了该函数的递归过程。

求和函数的递归过程

图 2-3   求和函数的递归过程

@@ -4732,6 +4752,10 @@
+
+分步调试 +

+

尾递归的执行过程如图 2-5 所示。对比普通递归和尾递归，两者的求和操作的执行点是不同的。

+
+分步调试 +

+

观察以上代码，我们在函数内递归调用了两个函数，这意味着从一个调用产生了两个调用分支。如图 2-6 所示，这样不断递归调用下去，最终将产生一棵层数为 \(n\) 的「递归树 recursion tree」。

斐波那契数列的递归树

图 2-6   斐波那契数列的递归树

@@ -5230,6 +5258,10 @@ +
+分步调试 +

+

观察以上代码，当递归转化为迭代后，代码变得更加复杂了。尽管迭代和递归在很多情况下可以互相转化，但不一定值得这样做，有以下两点原因。