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

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

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+"""
+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}")