From 1b356ba0a2b0c67b549cee72fe9ea5dd191d24cd Mon Sep 17 00:00:00 2001 From: sjinzh <99076655+sjinzh@users.noreply.github.com> Date: Tue, 3 Jan 2023 21:19:11 +0800 Subject: [PATCH] add c code for chapter_computational_complexity --- .../time_complexity.c | 192 ++++++++++++++++++ .../worst_best_time_complexity.c | 65 ++++++ 2 files changed, 257 insertions(+) create mode 100644 codes/c/chapter_computational_complexity/time_complexity.c create mode 100644 codes/c/chapter_computational_complexity/worst_best_time_complexity.c diff --git a/codes/c/chapter_computational_complexity/time_complexity.c b/codes/c/chapter_computational_complexity/time_complexity.c new file mode 100644 index 00000000..b7e6cef9 --- /dev/null +++ b/codes/c/chapter_computational_complexity/time_complexity.c @@ -0,0 +1,192 @@ +// File: time_complexity.c +// Created Time: 2023-01-03 +// Author: sjinzh (sjinzh@gmail.com) + +#include "stdio.h" +#include "stdlib.h" + +// 常数阶 +int constant(int n) +{ + int count = 0; + int size = 100000; + int i = 0; + for(int i = 0; i < size; i++){ + count ++; + } + return count; +} + +// 线性阶 +int linear(int n) +{ + int count = 0; + for(int i = 0; i < n; i++){ + count ++; + } + return count; +} + +// 线性阶（遍历数组） +int arrayTraversal(int *nums, int n) +{ + int count = 0; + // 循环次数与数组长度成正比 + for(int i = 0; i < n; i++){ + count ++; + } + return count; +} + +// 平方阶 +int quadratic(int n) +{ + int count = 0; + // 循环次数与数组长度成平方关系 + for(int i = 0; i < n; i++){ + for(int j = 0; j < n; j++){ + count ++; + } + } + return count; +} + +// 平方阶（冒泡排序） +int bubbleSort(int *nums, int n) +{ + int count = 0; // 计数器 + // 外循环：待排序元素数量为 n-1, n-2, ..., 1 + for(int i = n - 1; i > 0; i--){ + // 内循环：冒泡操作 + for (int j = 0; j < i; j++) + { + // 交换 nums[j] 与 nums[j + 1] + int tmp = nums[j]; + nums[j] = nums[j + 1]; + nums[j + 1] = tmp; + count += 3; // 元素交换包含 3 个单元操作 + } + + } + return count; +} + +// 指数阶（循环实现） +int exponential(int n) +{ + int count = 0; + int bas = 1; + // cell 每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1) + for (int i = 0; i < n; i++) + { + for (int j = 0; j < bas; j++) + { + count++; + } + bas *= 2; + } + // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1 + return count; +} + +// 指数阶（递归实现） +int expRecur(int n) +{ + if (n == 1) return 1; + return expRecur(n - 1) + expRecur(n - 1) + 1; +} + +// 对数阶（循环实现） +int logarithmic(float n) +{ + int count = 0; + while (n > 1) + { + n = n / 2; + count++; + } + return count; +} + +// 对数阶（递归实现） +int logRecur(float n) +{ + if (n <= 1) return 0; + return logRecur(n / 2) + 1; +} + +// 线性对数阶 +int linearLogRecur(float n) +{ + if (n <= 1) return 1; + int count = linearLogRecur(n / 2) + + linearLogRecur(n / 2); + for (int i = 0; i < n; i++) + { + count ++; + } + return count; +} + +// 阶乘阶（递归实现） +int factorialRecur(int n) +{ + if (n == 0) return 1; + int count = 0; + for (int i = 0; i < n; i++) + { + count += factorialRecur(n - 1); + } + return count; +} + +// Driver Code +int main(int argc, char *argv[]) + { + // 可以修改 n 运行，体会一下各种复杂度的操作数量变化趋势 + int n = 8; + printf("输入数据大小 n = %d\n", n); + + int count = constant(n); + printf("常数阶的计算操作数量 = %d\n", count); + + count = linear(n); + printf("线性阶的计算操作数量 = %d\n", count); + // 分配堆区内存（创建一维可变长数组：数组中元素数量为n，元素类型为int） + int *nums = (int *)malloc(n * sizeof(int)); + count = arrayTraversal(nums, n); + printf("线性阶（遍历数组）的计算操作数量 = %d\n", count); + + count = quadratic(n); + printf("平方阶的计算操作数量 = %d\n", count); + for(int i = 0; i < n; i++){ + nums[i] = n - i; // [n,n-1,...,2,1] + } + count = bubbleSort(nums, n); + printf("平方阶（冒泡排序）的计算操作数量 = %d\n", count); + + count = exponential(n); + printf("指数阶（循环实现）的计算操作数量 = %d\n", count); + count = expRecur(n); + printf("指数阶（递归实现）的计算操作数量 = %d\n", count); + + count = logarithmic(n); + printf("对数阶（循环实现）的计算操作数量 = %d\n", count); + count = logRecur(n); + printf("对数阶（递归实现）的计算操作数量 = %d\n", count); + + count = linearLogRecur(n); + printf("线性对数阶（递归实现）的计算操作数量 = %d\n", count); + + count = factorialRecur(n); + printf("阶乘阶（递归实现）的计算操作数量 = %d\n", count); + + // 释放堆区内存 + if(nums != NULL){ + free(nums); + nums = NULL; + } + getchar(); + return 0; +} + diff --git a/codes/c/chapter_computational_complexity/worst_best_time_complexity.c b/codes/c/chapter_computational_complexity/worst_best_time_complexity.c new file mode 100644 index 00000000..11139630 --- /dev/null +++ b/codes/c/chapter_computational_complexity/worst_best_time_complexity.c @@ -0,0 +1,65 @@ +// File: worst_best_time_complexity.c +// Created Time: 2023-01-03 +// Author: sjinzh (sjinzh@gmail.com) + +#include "stdio.h" +#include "stdlib.h" +#include "time.h" + +// 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱 +int *randomNumbers(int n) +{ + // 分配堆区内存（创建一维可变长数组：数组中元素数量为n，元素类型为int） + int *nums = (int *)malloc(n * sizeof(int)); + // 生成数组 nums = { 1, 2, 3, ..., n } + for (int i = 0; i < n; i++) + { + nums[i] = i + 1; + } + // 随机打乱数组元素 + for (int i = n - 1; i > 0; i--) + { + int j = rand() % (i + 1); + int temp = nums[i]; + nums[i] = nums[j]; + nums[j] = temp; + } + return nums; +} + +// 查找数组 nums 中数字 1 所在索引 +int findOne(int *nums, int n) +{ + for (int i = 0; i < n; i++) + { + if (nums[i] == 1) return i; + } + return -1; +} + +// Driver Code +int main(int argc, char *argv[]) +{ + // 初始化随机数种子 + srand((unsigned int)time(NULL)); + for (int i = 0; i < 10; i++) + { + int n = 100; + int *nums = randomNumbers(n); + int index = findOne(nums, n); + printf("\n数组 [ 1, 2, ..., n ] 被打乱后 = "); + for (int j = 0; j < n; j++) + { + printf("%d%s", nums[j], (j == n-1)? "" : "," ); + } + printf("\n数字 1 的索引为 %d\n", index); + // 释放堆区内存 + if(nums != NULL){ + free(nums); + nums = NULL; + } + } + getchar(); + return 0; +} +