From 3e64f68ae950113671ce6f4a4b8a2927b7bacb75 Mon Sep 17 00:00:00 2001 From: Yudong Jin Date: Thu, 24 Aug 2023 17:51:41 +0800 Subject: [PATCH] Add the section of iteration and recursion. (#693) --- .../CMakeLists.txt | 2 + .../iteration.cpp | 76 +++ .../recursion.cpp | 55 ++ .../iteration.java | 76 +++ .../recursion.java | 55 ++ .../iteration.py | 65 ++ .../recursion.py | 49 ++ .../iteration.png | Bin 0 -> 38849 bytes .../nested_iteration.png | Bin 0 -> 44742 bytes .../recursion_sum.png | Bin 0 -> 74341 bytes .../recursion_sum_depth.png | Bin 0 -> 75051 bytes .../recursion_tree.png | Bin 0 -> 54746 bytes .../tail_recursion_sum.png | Bin 0 -> 85361 bytes .../iteration_and_recursion.md | 631 ++++++++++++++++++ mkdocs.yml | 7 +- 15 files changed, 1013 insertions(+), 3 deletions(-) create mode 100644 codes/cpp/chapter_computational_complexity/iteration.cpp create mode 100644 codes/cpp/chapter_computational_complexity/recursion.cpp create mode 100644 codes/java/chapter_computational_complexity/iteration.java create mode 100644 codes/java/chapter_computational_complexity/recursion.java create mode 100644 codes/python/chapter_computational_complexity/iteration.py create mode 100644 codes/python/chapter_computational_complexity/recursion.py create mode 100644 docs/chapter_computational_complexity/iteration_and_recursion.assets/iteration.png create mode 100644 docs/chapter_computational_complexity/iteration_and_recursion.assets/nested_iteration.png create mode 100644 docs/chapter_computational_complexity/iteration_and_recursion.assets/recursion_sum.png create mode 100644 docs/chapter_computational_complexity/iteration_and_recursion.assets/recursion_sum_depth.png create mode 100644 docs/chapter_computational_complexity/iteration_and_recursion.assets/recursion_tree.png create mode 100644 docs/chapter_computational_complexity/iteration_and_recursion.assets/tail_recursion_sum.png create mode 100644 docs/chapter_computational_complexity/iteration_and_recursion.md diff --git a/codes/cpp/chapter_computational_complexity/CMakeLists.txt b/codes/cpp/chapter_computational_complexity/CMakeLists.txt index 4c1c11261..ea2845b75 100644 --- a/codes/cpp/chapter_computational_complexity/CMakeLists.txt +++ b/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) \ No newline at end of file diff --git a/codes/cpp/chapter_computational_complexity/iteration.cpp b/codes/cpp/chapter_computational_complexity/iteration.cpp new file mode 100644 index 000000000..16d9e1e0f --- /dev/null +++ b/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; +} diff --git a/codes/cpp/chapter_computational_complexity/recursion.cpp b/codes/cpp/chapter_computational_complexity/recursion.cpp new file mode 100644 index 000000000..36f9214fc --- /dev/null +++ b/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; +} diff --git a/codes/java/chapter_computational_complexity/iteration.java b/codes/java/chapter_computational_complexity/iteration.java new file mode 100644 index 000000000..4f1293fca --- /dev/null +++ b/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); + } +} diff --git a/codes/java/chapter_computational_complexity/recursion.java b/codes/java/chapter_computational_complexity/recursion.java new file mode 100644 index 000000000..3c5d0b29d --- /dev/null +++ b/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); + } +} diff --git a/codes/python/chapter_computational_complexity/iteration.py b/codes/python/chapter_computational_complexity/iteration.py new file mode 100644 index 000000000..596a9960d --- /dev/null +++ b/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}") diff --git a/codes/python/chapter_computational_complexity/recursion.py b/codes/python/chapter_computational_complexity/recursion.py new file mode 100644 index 000000000..435bcaa38 --- /dev/null +++ b/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}") diff --git a/docs/chapter_computational_complexity/iteration_and_recursion.assets/iteration.png b/docs/chapter_computational_complexity/iteration_and_recursion.assets/iteration.png new file mode 100644 index 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