Add the section of iteration and recursion. (#693)

codes/cpp/chapter_computational_complexity/CMakeLists.txt

@@ -1,3 +1,5 @@
+add_executable(iteration iteration.cpp)
+add_executable(recursion recursion.cpp)
 add_executable(space_complexity space_complexity.cpp)
 add_executable(time_complexity time_complexity.cpp)
 add_executable(worst_best_time_complexity worst_best_time_complexity.cpp)

codes/cpp/chapter_computational_complexity/iteration.cpp

@@ -0,0 +1,76 @@
+/**
+ * File: iteration.cpp
+ * Created Time: 2023-08-24
+ * Author: Krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* for 循环 */
+int forLoop(int n) {
+    int res = 0;
+    // 循环求和 1, 2, ..., n-1, n
+    for (int i = 1; i <= n; ++i) {
+        res += i;
+    }
+    return res;
+}
+
+/* while 循环 */
+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
+    while (i <= n) {
+        res += i;
+        i += 1; // 更新条件变量
+    }
+    return res;
+}
+
+/* while 循环（两次更新） */
+int whileLoopII(int n) {
+    int res = 0;
+    int i = 1; // 初始化条件变量
+    // 循环求和 1, 2, 4, 5...
+    while (i <= n) {
+        res += i;
+        i += 1; // 更新条件变量
+        res += i;
+        i *= 2; // 更新条件变量
+    }
+    return res;
+}
+
+/* 双层 for 循环 */
+string nestedForLoop(int n) {
+    ostringstream res;
+    // 循环 i = 1, 2, ..., n-1, n
+    for (int i = 1; i <= n; ++i) {
+        // 循环 j = 1, 2, ..., n-1, n
+        for (int j = 1; j <= n; ++j) {
+            res << "(" << i << ", " << j << "), ";
+        }
+    }
+    return res.str();
+}
+
+/* Driver Code */
+int main() {
+    int n = 5;
+    int res;
+
+    res = forLoop(n);
+    cout << "\nfor 循环的求和结果 res = " << res << endl;
+
+    res = whileLoop(n);
+    cout << "\nwhile 循环的求和结果 res = " << res << endl;
+
+    res = whileLoopII(n);
+    cout << "\nwhile 循环（两次更新）求和结果 res = " << res << endl;
+
+    string resStr = nestedForLoop(n);
+    cout << "\n双层 for 循环的遍历结果 " << resStr << endl;
+
+    return 0;
+}

codes/cpp/chapter_computational_complexity/recursion.cpp

@@ -0,0 +1,55 @@
+/**
+ * File: recursion.cpp
+ * Created Time: 2023-08-24
+ * Author: Krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* 递归 */
+int recur(int n) {
+    // 终止条件
+    if (n == 1)
+        return 1;
+    // 递：递归调用
+    int res = recur(n - 1);
+    // 归：返回结果
+    return n + res;
+}
+
+/* 尾递归 */
+int tailRecur(int n, int res) {
+    // 终止条件
+    if (n == 0)
+        return res;
+    // 尾递归调用
+    return tailRecur(n - 1, res + n);
+}
+
+/* 斐波那契数列：递归 */
+int fib(int n) {
+    // 终止条件 f(1) = 0, f(2) = 1
+    if (n == 1 || n == 2)
+        return n - 1;
+    // 递归调用 f(n) = f(n-1) + f(n-2)
+    int res = fib(n - 1) + fib(n - 2);
+    // 返回结果 f(n)
+    return res;
+}
+
+/* Driver Code */
+int main() {
+    int n = 5;
+    int res;
+
+    res = recur(n);
+    cout << "\n递归函数的求和结果 res = " << res << endl;
+
+    res = tailRecur(n, 0);
+    cout << "\n尾递归函数的求和结果 res = " << res << endl;
+
+    res = fib(n);
+    cout << "\n斐波那契数列的第 " << n << " 项为 " << res << endl;
+
+    return 0;
+}

codes/java/chapter_computational_complexity/iteration.java

@@ -0,0 +1,76 @@
+/**
+ * File: iteration.java
+ * Created Time: 2023-08-24
+ * Author: Krahets (krahets@163.com)
+ */
+
+package chapter_computational_complexity;
+
+public class iteration {
+    /* for 循环 */
+    public static int forLoop(int n) {
+        int res = 0;
+        // 循环求和 1, 2, ..., n-1, n
+        for (int i = 1; i <= n; i++) {
+            res += i;
+        }
+        return res;
+    }
+
+    /* while 循环 */
+    public 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
+        while (i <= n) {
+            res += i;
+            i += 1; // 更新条件变量
+        }
+        return res;
+    }
+
+    /* while 循环（两次更新） */
+    public static int whileLoopII(int n) {
+        int res = 0;
+        int i = 1; // 初始化条件变量
+        // 循环求和 1, 2, 4, 5...
+        while (i <= n) {
+            res += i;
+            i += 1; // 更新条件变量
+            res += i;
+            i *= 2; // 更新条件变量
+        }
+        return res;
+    }
+
+    /* 双层 for 循环 */
+    public static String nestedForLoop(int n) {
+        StringBuilder res = new StringBuilder();
+        // 循环 i = 1, 2, ..., n-1, n
+        for (int i = 1; i <= n; i++) {
+            // 循环 j = 1, 2, ..., n-1, n
+            for (int j = 1; j <= n; j++) {
+                res.append("(" + i + ", " + j + "), ");
+            }
+        }
+        return res.toString();
+    }
+
+    /* Driver Code */
+    public static void main(String[] args) {
+        int n = 5;
+        int res;
+
+        res = forLoop(n);
+        System.out.println("\nfor 循环的求和结果 res = " + res);
+
+        res = whileLoop(n);
+        System.out.println("\nwhile 循环的求和结果 res = " + res);
+
+        res = whileLoopII(n);
+        System.out.println("\nwhile 循环（两次更新）求和结果 res = " + res);
+
+        String resStr = nestedForLoop(n);
+        System.out.println("\n双层 for 循环的遍历结果 " + resStr);
+    }
+}

codes/java/chapter_computational_complexity/recursion.java

@@ -0,0 +1,55 @@
+/**
+ * File: recursion.java
+ * Created Time: 2023-08-24
+ * Author: Krahets (krahets@163.com)
+ */
+
+package chapter_computational_complexity;
+
+public class recursion {
+    /* 递归 */
+    public static int recur(int n) {
+        // 终止条件
+        if (n == 1)
+            return 1;
+        // 递：递归调用
+        int res = recur(n - 1);
+        // 归：返回结果
+        return n + res;
+    }
+
+    /* 尾递归 */
+    public static int tailRecur(int n, int res) {
+        // 终止条件
+        if (n == 0)
+            return res;
+        // 尾递归调用
+        return tailRecur(n - 1, res + n);
+    }
+
+    /* 斐波那契数列：递归 */
+    public static int fib(int n) {
+        // 终止条件 f(1) = 0, f(2) = 1
+        if (n == 1 || n == 2)
+            return n - 1;
+        // 递归调用 f(n) = f(n-1) + f(n-2)
+        int res = fib(n - 1) + fib(n - 2);
+        // 返回结果 f(n)
+        return res;
+    }
+
+    /* Driver Code */
+    public static void main(String[] args) {
+        int n = 5;
+        int res;
+
+        res = recur(n);
+        System.out.println("\n递归函数的求和结果 res = " + res);
+
+        res = tailRecur(n, 0);
+        System.out.println("\n尾递归函数的求和结果 res = " + res);
+
+        res = fib(n);
+        System.out.println("\n斐波那契数列的第 " + n + " 项为 " + res);
+    }
+}

codes/python/chapter_computational_complexity/iteration.py

@@ -0,0 +1,65 @@
+"""
+File: iteration.py
+Created Time: 2023-08-24
+Author: Krahets (krahets@163.com)
+"""
+
+
+def for_loop(n: int) -> int:
+    """for 循环"""
+    res = 0
+    # 循环求和 1, 2, ..., n-1, n
+    for i in range(1, n + 1):
+        res += i
+    return res
+
+
+def while_loop(n: int) -> int:
+    """while 循环"""
+    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
+    return res
+
+
+def while_loop_ii(n: int) -> int:
+    """while 循环（两次更新）"""
+    res = 0
+    i = 1  # 初始化条件变量
+    # 循环求和 1, 2, 4, 5...
+    while i <= n:
+        res += i
+        i += 1  # 更新条件变量
+        res += i
+        i *= 2  # 更新条件变量
+    return res
+
+
+def nested_for_loop(n: int) -> str:
+    """双层 for 循环"""
+    res = ""
+    # 循环 i = 1, 2, ..., n-1, n
+    for i in range(1, n + 1):
+        # 循环 j = 1, 2, ..., n-1, n
+        for j in range(1, n + 1):
+            res += f"({i}, {j}), "
+    return res
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    n = 5
+    res = for_loop(n)
+    print(f"\nfor 循环的求和结果 res = {res}")
+
+    res = while_loop(n)
+    print(f"\nwhile 循环的求和结果 res = {res}")
+
+    res = while_loop_ii(n)
+    print(f"\nwhile 循环（两次更新）求和结果 res = {res}")
+
+    res = nested_for_loop(n)
+    print(f"\n双层 for 循环的遍历结果 {res}")

codes/python/chapter_computational_complexity/recursion.py

@@ -0,0 +1,49 @@
+"""
+File: recursion.py
+Created Time: 2023-08-24
+Author: Krahets (krahets@163.com)
+"""
+
+
+def recur(n: int) -> int:
+    """递归"""
+    # 终止条件
+    if n == 1:
+        return 1
+    # 递：递归调用
+    res = recur(n - 1)
+    # 归：返回结果
+    return n + res
+
+
+def tail_recur(n, res):
+    """尾递归"""
+    # 终止条件
+    if n == 0:
+        return res
+    # 尾递归调用
+    return tail_recur(n - 1, res + n)
+
+
+def fib(n: int) -> int:
+    """斐波那契数列：递归"""
+    # 终止条件 f(1) = 0, f(2) = 1
+    if n == 1 or n == 2:
+        return n - 1
+    # 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)
+    return res
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    n = 5
+    res = recur(n)
+    print(f"\n递归函数的求和结果 res = {res}")
+
+    res = tail_recur(n, 0)
+    print(f"\n尾递归函数的求和结果 res = {res}")
+
+    res = fib(n)
+    print(f"\n斐波那契数列的第 {n} 项为 {res}")