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Merge pull request #208 from sjinzh/master
(PR #204) update c code and doc for time_complexity
This commit is contained in:
Yudong Jin
175
codes/c/chapter_computational_complexity/time_complexity.c
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175
codes/c/chapter_computational_complexity/time_complexity.c
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/*
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* File: time_complexity.c
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* Created Time: 2023-01-03
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* Author: sjinzh (sjinzh@gmail.com)
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*/
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#include "../include/include.h"
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/* 常数阶 */
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int constant(int n) {
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int count = 0;
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int size = 100000;
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int i = 0;
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for (int i = 0; i < size; i++) {
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count ++;
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}
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return count;
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}
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/* 线性阶 */
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int linear(int n) {
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int count = 0;
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for (int i = 0; i < n; i++) {
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count ++;
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}
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return count;
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}
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/* 线性阶（遍历数组） */
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int arrayTraversal(int *nums, int n) {
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int count = 0;
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// 循环次数与数组长度成正比
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for (int i = 0; i < n; i++) {
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count ++;
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}
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return count;
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}
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/* 平方阶 */
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int quadratic(int n)
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{
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int count = 0;
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// 循环次数与数组长度成平方关系
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for (int i = 0; i < n; i++) {
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for (int j = 0; j < n; j++) {
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count ++;
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}
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}
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return count;
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}
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/* 平方阶（冒泡排序） */
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int bubbleSort(int *nums, int n) {
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int count = 0; // 计数器
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// 外循环：待排序元素数量为 n-1, n-2, ..., 1
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for (int i = n - 1; i > 0; i--) {
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// 内循环：冒泡操作
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for (int j = 0; j < i; j++) {
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// 交换 nums[j] 与 nums[j + 1]
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int tmp = nums[j];
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nums[j] = nums[j + 1];
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nums[j + 1] = tmp;
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count += 3; // 元素交换包含 3 个单元操作
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}
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}
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return count;
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}
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/* 指数阶（循环实现） */
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int exponential(int n) {
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int count = 0;
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int bas = 1;
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// cell 每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)
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for (int i = 0; i < n; i++) {
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for (int j = 0; j < bas; j++) {
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count++;
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}
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bas *= 2;
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}
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// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1
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return count;
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}
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/* 指数阶（递归实现） */
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int expRecur(int n) {
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if (n == 1) return 1;
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return expRecur(n - 1) + expRecur(n - 1) + 1;
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}
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/* 对数阶（循环实现） */
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int logarithmic(float n) {
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int count = 0;
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while (n > 1) {
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n = n / 2;
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count++;
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}
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return count;
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}
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/* 对数阶（递归实现） */
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int logRecur(float n) {
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if (n <= 1) return 0;
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return logRecur(n / 2) + 1;
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}
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/* 线性对数阶 */
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int linearLogRecur(float n) {
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if (n <= 1) return 1;
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int count = linearLogRecur(n / 2) +
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linearLogRecur(n / 2);
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for (int i = 0; i < n; i++) {
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count ++;
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}
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return count;
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}
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/* 阶乘阶（递归实现） */
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int factorialRecur(int n) {
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if (n == 0) return 1;
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int count = 0;
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for (int i = 0; i < n; i++) {
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count += factorialRecur(n - 1);
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}
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return count;
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}
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/* Driver Code */
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int main(int argc, char *argv[]) {
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// 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
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int n = 8;
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printf("输入数据大小 n = %d\n", n);
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int count = constant(n);
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printf("常数阶的计算操作数量 = %d\n", count);
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count = linear(n);
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printf("线性阶的计算操作数量 = %d\n", count);
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// 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）
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int *nums = (int *)malloc(n * sizeof(int));
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count = arrayTraversal(nums, n);
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printf("线性阶（遍历数组）的计算操作数量 = %d\n", count);
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count = quadratic(n);
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printf("平方阶的计算操作数量 = %d\n", count);
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for (int i = 0; i < n; i++) {
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nums[i] = n - i; // [n,n-1,...,2,1]
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}
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count = bubbleSort(nums, n);
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printf("平方阶（冒泡排序）的计算操作数量 = %d\n", count);
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count = exponential(n);
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printf("指数阶（循环实现）的计算操作数量 = %d\n", count);
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count = expRecur(n);
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printf("指数阶（递归实现）的计算操作数量 = %d\n", count);
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count = logarithmic(n);
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printf("对数阶（循环实现）的计算操作数量 = %d\n", count);
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count = logRecur(n);
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printf("对数阶（递归实现）的计算操作数量 = %d\n", count);
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count = linearLogRecur(n);
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printf("线性对数阶（递归实现）的计算操作数量 = %d\n", count);
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count = factorialRecur(n);
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printf("阶乘阶（递归实现）的计算操作数量 = %d\n", count);
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// 释放堆区内存
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if (nums != NULL) {
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free(nums);
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nums = NULL;
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}
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getchar();
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return 0;
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}
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@ -0,0 +1,55 @@
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/*
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* File: worst_best_time_complexity.c
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* Created Time: 2023-01-03
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* Author: sjinzh (sjinzh@gmail.com)
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*/
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#include "../include/include.h"
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/* 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱 */
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int *randomNumbers(int n) {
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// 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）
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int *nums = (int *)malloc(n * sizeof(int));
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// 生成数组 nums = { 1, 2, 3, ..., n }
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for (int i = 0; i < n; i++) {
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nums[i] = i + 1;
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}
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// 随机打乱数组元素
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for (int i = n - 1; i > 0; i--) {
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int j = rand() % (i + 1);
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int temp = nums[i];
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nums[i] = nums[j];
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nums[j] = temp;
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}
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return nums;
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}
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/* 查找数组 nums 中数字 1 所在索引 */
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int findOne(int *nums, int n) {
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for (int i = 0; i < n; i++) {
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if (nums[i] == 1) return i;
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}
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return -1;
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}
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/* Driver Code */
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int main(int argc, char *argv[]) {
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// 初始化随机数种子
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srand((unsigned int)time(NULL));
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for (int i = 0; i < 10; i++) {
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int n = 100;
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int *nums = randomNumbers(n);
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int index = findOne(nums, n);
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printf("\n数组 [ 1, 2, ..., n ] 被打乱后 = ");
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printArray(nums, n);
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printf("数字 1 的索引为 %d\n", index);
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// 释放堆区内存
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if (nums != NULL) {
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free(nums);
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nums = NULL;
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}
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}
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getchar();
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return 0;
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}
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@ -1,12 +1,15 @@
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/*
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* File: include.h
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* Created Time: 2022-12-20
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* Author: MolDuM (moldum@163.com)
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*/
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdbool.h>
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#include "PrintUtil.h"
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/*
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* File: include.h
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* Created Time: 2022-12-20
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* Author: MolDuM (moldum@163.com)
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*/
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdbool.h>
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#include <time.h>
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#include "PrintUtil.h"
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