diff --git a/codes/c/chapter_computational_complexity/CMakeLists.txt b/codes/c/chapter_computational_complexity/CMakeLists.txt index b11e25877..6938858ce 100644 --- a/codes/c/chapter_computational_complexity/CMakeLists.txt +++ b/codes/c/chapter_computational_complexity/CMakeLists.txt @@ -1,3 +1,5 @@ add_executable(time_complexity time_complexity.c) add_executable(worst_best_time_complexity worst_best_time_complexity.c) -add_executable(space_complexity space_complexity.c) \ No newline at end of file +add_executable(space_complexity space_complexity.c) +add_executable(iteration iteration.c) +add_executable(recursion recursion.c) \ No newline at end of file diff --git a/codes/c/chapter_computational_complexity/iteration.c b/codes/c/chapter_computational_complexity/iteration.c new file mode 100644 index 000000000..6268f03ad --- /dev/null +++ b/codes/c/chapter_computational_complexity/iteration.c @@ -0,0 +1,82 @@ +/** + * File: iteration.c + * Created Time: 2023-09-09 + * Author: Gonglja (glj0@outlook.com) + */ + +#include "../utils/common.h" + +/* 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++; // 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, 4, ... + while (i <= n) { + res += i; + // 更新条件变量 + i++; + i *= 2; + } + return res; +} + +/* 双层 for 循环 */ +char *nestedForLoop(int n) { + // n * n 为对应点数量,"(i, j), " 对应字符串长最大为 6+10*2,加上最后一个空字符 \0 的额外空间 + int size = n * n * 26 + 1; + char *res = malloc(size * sizeof(char)); + + // 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) { + char tmp[26]; + snprintf(tmp, sizeof(tmp), "(%d, %d), ", i, j); + strncat(res, tmp, size - strlen(res) - 1); + } + } + return res; +} + +/* Driver Code */ +int main() { + int n = 5; + int res; + + res = forLoop(n); + printf("\nfor 循环的求和结果 res = %d\n", res); + + res = whileLoop(n); + printf("\nwhile 循环的求和结果 res = %d\n", res); + + res = whileLoopII(n); + printf("\nwhile 循环(两次更新)求和结果 res = %d\n", res); + + char *resStr = nestedForLoop(n); + printf("\n双层 for 循环的遍历结果 %s\r\n", resStr); + free(resStr); + + return 0; +} diff --git a/codes/c/chapter_computational_complexity/recursion.c b/codes/c/chapter_computational_complexity/recursion.c new file mode 100644 index 000000000..adf3db470 --- /dev/null +++ b/codes/c/chapter_computational_complexity/recursion.c @@ -0,0 +1,55 @@ +/** + * File: recursion.c + * Created Time: 2023-09-09 + * Author: Gonglja (glj0@outlook.com) + */ + +#include "../utils/common.h" + +/* 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); + printf("\n递归函数的求和结果 res = %d\n", res); + + res = tailRecur(n, 0); + printf("\n尾递归函数的求和结果 res = %d\n", res); + + res = fib(n); + printf("\n斐波那契数列的第 %d 项为 %d\n", n, res); + + return 0; +} diff --git a/codes/c/chapter_hashing/CMakeLists.txt b/codes/c/chapter_hashing/CMakeLists.txt index 7fa75fd5e..febf73f35 100644 --- a/codes/c/chapter_hashing/CMakeLists.txt +++ b/codes/c/chapter_hashing/CMakeLists.txt @@ -1,2 +1,3 @@ add_executable(array_hash_map array_hash_map.c) +add_executable(simple_hash simple_hash.c) diff --git a/codes/c/chapter_hashing/simple_hash.c b/codes/c/chapter_hashing/simple_hash.c new file mode 100644 index 000000000..f23ae49f7 --- /dev/null +++ b/codes/c/chapter_hashing/simple_hash.c @@ -0,0 +1,68 @@ +/** + * File: simple_hash.c + * Created Time: 2023-09-09 + * Author: Gonglja (glj0@outlook.com) + */ + +#include "../utils/common.h" + +/* 加法哈希 */ +int addHash(char *key) { + long long hash = 0; + const int MODULUS = 1000000007; + for (int i = 0; i < strlen(key); i++) { + hash = (hash + (unsigned char)key[i]) % MODULUS; + } + return (int)hash; +} + +/* 乘法哈希 */ +int mulHash(char *key) { + long long hash = 0; + const int MODULUS = 1000000007; + for (int i = 0; i < strlen(key); i++) { + hash = (31 * hash + (unsigned char)key[i]) % MODULUS; + } + return (int)hash; +} + +/* 异或哈希 */ +int xorHash(char *key) { + int hash = 0; + const int MODULUS = 1000000007; + + for (int i = 0; i < strlen(key); i++) { + hash ^= (unsigned char)key[i]; + } + return hash & MODULUS; +} + +/* 旋转哈希 */ +int rotHash(char *key) { + long long hash = 0; + const int MODULUS = 1000000007; + for (int i = 0; i < strlen(key); i++) { + hash = ((hash << 4) ^ (hash >> 28) ^ (unsigned char)key[i]) % MODULUS; + } + + return (int)hash; +} + +/* Driver Code */ +int main() { + char *key = "Hello dsad3241241dsa算123法"; + + int hash = addHash(key); + printf("加法哈希值为 %d\n", hash); + + hash = mulHash(key); + printf("乘法哈希值为 %d\n", hash); + + hash = xorHash(key); + printf("异或哈希值为 %d\n", hash); + + hash = rotHash(key); + printf("旋转哈希值为 %d\n", hash); + + return 0; +} diff --git a/codes/c/chapter_searching/CMakeLists.txt b/codes/c/chapter_searching/CMakeLists.txt index 8282333ab..5c0dddba0 100644 --- a/codes/c/chapter_searching/CMakeLists.txt +++ b/codes/c/chapter_searching/CMakeLists.txt @@ -1,5 +1,6 @@ add_executable(binary_search binary_search.c) add_executable(two_sum two_sum.c) -add_executable(binary_search_edge binary_search_edge.c) add_executable(hashing_search hashing_search.c) -add_executable(linear_search linear_search.c) \ No newline at end of file +add_executable(linear_search linear_search.c) +add_executable(binary_search_edge binary_search_edge.c) +add_executable(binary_search_insertion binary_search_insertion.c) \ No newline at end of file diff --git a/codes/c/chapter_searching/binary_search_edge.c b/codes/c/chapter_searching/binary_search_edge.c new file mode 100644 index 000000000..46237a348 --- /dev/null +++ b/codes/c/chapter_searching/binary_search_edge.c @@ -0,0 +1,66 @@ +/** + * File: binary_search_edge.c + * Created Time: 2023-09-09 + * Author: Gonglja (glj0@outlook.com) + */ + +#include "../utils/common.h" + +/* 二分查找插入点(存在重复元素) */ +int binarySearchInsertion(int *nums, int numSize, int target) { + int i = 0, j = numSize - 1; // 初始化双闭区间 [0, n-1] + while (i <= j) { + int m = i + (j - i) / 2; // 计算中点索引 m + if (nums[m] < target) { + i = m + 1; // target 在区间 [m+1, j] 中 + } else { + j = m - 1; // 首个小于 target 的元素在区间 [i, m-1] 中 + } + } + // 返回插入点 i + return i; +} + +/* 二分查找最左一个 target */ +int binarySearchLeftEdge(int *nums, int numSize, int target) { + // 等价于查找 target 的插入点 + int i = binarySearchInsertion(nums, numSize, target); + // 未找到 target ,返回 -1 + if (i == numSize || nums[i] != target) { + return -1; + } + // 找到 target ,返回索引 i + return i; +} + +/* 二分查找最右一个 target */ +int binarySearchRightEdge(int *nums, int numSize, int target) { + // 转化为查找最左一个 target + 1 + int i = binarySearchInsertion(nums, numSize, target + 1); + // j 指向最右一个 target ,i 指向首个大于 target 的元素 + int j = i - 1; + // 未找到 target ,返回 -1 + if (j == -1 || nums[j] != target) { + return -1; + } + // 找到 target ,返回索引 j + return j; +} + +/* Driver Code */ +int main() { + // 包含重复元素的数组 + int nums[] = {1, 3, 6, 6, 6, 6, 6, 10, 12, 15}; + printf("\n数组 nums = "); + printArray(nums, sizeof(nums) / sizeof(nums[0])); + + // 二分查找左边界和右边界 + int targets[] = {6, 7}; + for (int i = 0; i < sizeof(targets) / sizeof(targets[0]); i++) { + int index = binarySearchLeftEdge(nums, sizeof(nums) / sizeof(nums[0]), targets[i]); + printf("最左一个元素 %d 的索引为 %d\n", targets[i], index); + index = binarySearchRightEdge(nums, sizeof(nums) / sizeof(nums[0]), targets[i]); + printf("最右一个元素 %d 的索引为 %d\n", targets[i], index); + } + return 0; +} \ No newline at end of file diff --git a/codes/c/chapter_searching/binary_search_insertion.c b/codes/c/chapter_searching/binary_search_insertion.c new file mode 100644 index 000000000..48d2025d3 --- /dev/null +++ b/codes/c/chapter_searching/binary_search_insertion.c @@ -0,0 +1,68 @@ +/** + * File: binary_search_insertion.c + * Created Time: 2023-09-09 + * Author: Gonglja (glj0@outlook.com) + */ + +#include "../utils/common.h" + +/* 二分查找插入点(无重复元素) */ +int binarySearchInsertionSimple(int *nums, int numSize, int target) { + int i = 0, j = numSize - 1; // 初始化双闭区间 [0, n-1] + while (i <= j) { + int m = i + (j - i) / 2; // 计算中点索引 m + if (nums[m] < target) { + i = m + 1; // target 在区间 [m+1, j] 中 + } else if (nums[m] > target) { + j = m - 1; // target 在区间 [i, m-1] 中 + } else { + return m; // 找到 target ,返回插入点 m + } + } + // 未找到 target ,返回插入点 i + return i; +} + +/* 二分查找插入点(存在重复元素) */ +int binarySearchInsertion(int *nums, int numSize, int target) { + int i = 0, j = numSize - 1; // 初始化双闭区间 [0, n-1] + while (i <= j) { + int m = i + (j - i) / 2; // 计算中点索引 m + if (nums[m] < target) { + i = m + 1; // target 在区间 [m+1, j] 中 + } else if (nums[m] > target) { + j = m - 1; // target 在区间 [i, m-1] 中 + } else { + j = m - 1; // 首个小于 target 的元素在区间 [i, m-1] 中 + } + } + // 返回插入点 i + return i; +} + +/* Driver Code */ +int main() { + // 无重复元素的数组 + int nums1[] = {1, 3, 6, 8, 12, 15, 23, 26, 31, 35}; + printf("\n数组 nums = "); + printArray(nums1, sizeof(nums1) / sizeof(nums1[0])); + // 二分查找插入点 + int targets1[] = {6, 9}; + for (int i = 0; i < sizeof(targets1) / sizeof(targets1[0]); i++) { + int index = binarySearchInsertionSimple(nums1, sizeof(nums1) / sizeof(nums1[0]), targets1[i]); + printf("元素 %d 的插入点的索引为 %d\n", targets1[i], index); + } + + // 包含重复元素的数组 + int nums2[] = {1, 3, 6, 6, 6, 6, 6, 10, 12, 15}; + printf("\n数组 nums = "); + printArray(nums2, sizeof(nums2) / sizeof(nums2[0])); + // 二分查找插入点 + int targets2[] = {2, 6, 20}; + for (int i = 0; i < sizeof(targets2) / sizeof(int); i++) { + int index = binarySearchInsertion(nums2, sizeof(nums2) / sizeof(nums2[0]), targets2[i]); + printf("元素 %d 的插入点的索引为 %d\n", targets2[i], index); + } + + return 0; +}