Add comparison between iteration and recursion.

Fix the figure of tail recursion.
Fix two links.

codes/cpp/chapter_computational_complexity/recursion.cpp

@@ -17,6 +17,26 @@ int recur(int n) {
     return n + res;
 }
 
+/* 使用迭代模拟递归 */
+int forLoopRecur(int n) {
+    // 使用一个显式的栈来模拟系统调用栈
+    stack<int> stack;
+    int res = 0;
+    // 递：递归调用
+    for (int i = n; i > 0; i--) {
+        // 通过“入栈操作”模拟“递”
+        stack.push(i);
+    }
+    // 归：返回结果
+    while (!stack.empty()) {
+        // 通过“出栈操作”模拟“归”
+        res += stack.top();
+        stack.pop();
+    }
+    // res = 1+2+3+...+n
+    return res;
+}
+
 /* 尾递归 */
 int tailRecur(int n, int res) {
     // 终止条件
@@ -45,6 +65,9 @@ int main() {
     res = recur(n);
     cout << "\n递归函数的求和结果 res = " << res << endl;
 
+    res = forLoopRecur(n);
+    cout << "\n使用迭代模拟递归求和结果 res = " << res << endl;
+
     res = tailRecur(n, 0);
     cout << "\n尾递归函数的求和结果 res = " << res << endl;
 

codes/java/chapter_computational_complexity/iteration.java

@@ -8,7 +8,7 @@ package chapter_computational_complexity;
 
 public class iteration {
     /* for 循环 */
-    public static int forLoop(int n) {
+    static int forLoop(int n) {
         int res = 0;
         // 循环求和 1, 2, ..., n-1, n
         for (int i = 1; i <= n; i++) {
@@ -18,7 +18,7 @@ public class iteration {
     }
 
     /* while 循环 */
-    public static int whileLoop(int n) {
+    static int whileLoop(int n) {
         int res = 0;
         int i = 1; // 初始化条件变量
         // 循环求和 1, 2, ..., n-1, n
@@ -30,7 +30,7 @@ public class iteration {
     }
 
     /* while 循环（两次更新） */
-    public static int whileLoopII(int n) {
+    static int whileLoopII(int n) {
         int res = 0;
         int i = 1; // 初始化条件变量
         // 循环求和 1, 4, ...
@@ -44,7 +44,7 @@ public class iteration {
     }
 
     /* 双层 for 循环 */
-    public static String nestedForLoop(int n) {
+    static String nestedForLoop(int n) {
         StringBuilder res = new StringBuilder();
         // 循环 i = 1, 2, ..., n-1, n
         for (int i = 1; i <= n; i++) {

codes/java/chapter_computational_complexity/recursion.java

@@ -6,9 +6,11 @@
 
 package chapter_computational_complexity;
 
+import java.util.Stack;
+
 public class recursion {
     /* 递归 */
-    public static int recur(int n) {
+    static int recur(int n) {
         // 终止条件
         if (n == 1)
             return 1;
@@ -18,8 +20,27 @@ public class recursion {
         return n + res;
     }
 
+    /* 使用迭代模拟递归 */
+    static int forLoopRecur(int n) {
+        // 使用一个显式的栈来模拟系统调用栈
+        Stack<Integer> stack = new Stack<>();
+        int res = 0;
+        // 递：递归调用
+        for (int i = n; i > 0; i--) {
+            // 通过“入栈操作”模拟“递”
+            stack.push(i);
+        }
+        // 归：返回结果
+        while (!stack.isEmpty()) {
+            // 通过“出栈操作”模拟“归”
+            res += stack.pop();
+        }
+        // res = 1+2+3+...+n
+        return res;
+    }
+
     /* 尾递归 */
-    public static int tailRecur(int n, int res) {
+    static int tailRecur(int n, int res) {
         // 终止条件
         if (n == 0)
             return res;
@@ -28,7 +49,7 @@ public class recursion {
     }
 
     /* 斐波那契数列：递归 */
-    public static int fib(int n) {
+    static int fib(int n) {
         // 终止条件 f(1) = 0, f(2) = 1
         if (n == 1 || n == 2)
             return n - 1;
@@ -46,6 +67,9 @@ public class recursion {
         res = recur(n);
         System.out.println("\n递归函数的求和结果 res = " + res);
 
+        res = forLoopRecur(n);
+        System.out.println("\n使用迭代模拟递归求和结果 res = " + res);
+
         res = tailRecur(n, 0);
         System.out.println("\n尾递归函数的求和结果 res = " + res);
 

codes/python/chapter_computational_complexity/recursion.py

@@ -16,6 +16,23 @@ def recur(n: int) -> int:
     return n + res
 
 
+def for_loop_recur(n: int) -> int:
+    """使用迭代模拟递归"""
+    # 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 range(n, 0, -1):
+        # 通过“入栈操作”模拟“递”
+        stack.append(i)
+    # 归：返回结果
+    while stack:
+        # 通过“出栈操作”模拟“归”
+        res += stack.pop()
+    # res = 1+2+3+...+n
+    return res
+
+
 def tail_recur(n, res):
     """尾递归"""
     # 终止条件
@@ -42,6 +59,9 @@ if __name__ == "__main__":
     res = recur(n)
     print(f"\n递归函数的求和结果 res = {res}")
 
+    res = for_loop_recur(n)
+    print(f"\n使用迭代模拟递归求和结果 res = {res}")
+
     res = tail_recur(n, 0)
     print(f"\n尾递归函数的求和结果 res = {res}")