diff --git a/codes/c/chapter_dynamic_programming/climbing_stairs_backtrack.c b/codes/c/chapter_dynamic_programming/climbing_stairs_backtrack.c new file mode 100644 index 000000000..1845ecd97 --- /dev/null +++ b/codes/c/chapter_dynamic_programming/climbing_stairs_backtrack.c @@ -0,0 +1,47 @@ +/** + * File: climbing_stairs_backtrack.c + * Created Time: 2023-09-22 + * Author: huawuque404 (huawuque404@163.com) + */ + +#include "../utils/common.h" + +/* 回溯 */ +void backtrack(int *choices, int state, int n, int *res, int len) { + // 当爬到第 n 阶时,方案数量加 1 + if (state == n) + res[0]++; + // 遍历所有选择 + for (int i = 0; i < len; i++) { + int choice = choices[i]; + // 剪枝:不允许越过第 n 阶 + if (state + choice > n) + break; + // 尝试:做出选择,更新状态 + backtrack(choices, state + choice, n, res, len); + // 回退 + } +} + +/* 爬楼梯:回溯 */ +int climbingStairsBacktrack(int n) { + int choices[2] = {1, 2}; // 可选择向上爬 1 或 2 阶 + int state = 0; // 从第 0 阶开始爬 + int *res = (int *)malloc(sizeof(int)); + *res = 0; // 使用 res[0] 记录方案数量 + int len = sizeof(choices) / sizeof(int); + backtrack(choices, state, n, res, len); + int result = *res; + free(res); + return result; +} + +/* Driver Code */ +int main() { + int n = 9; + + int res = climbingStairsBacktrack(n); + printf("爬 %d 阶楼梯共有 %d 种方案\n", n, res); + + return 0; +} \ No newline at end of file diff --git a/codes/c/chapter_dynamic_programming/climbing_stairs_dfs.c b/codes/c/chapter_dynamic_programming/climbing_stairs_dfs.c new file mode 100644 index 000000000..d62b7df20 --- /dev/null +++ b/codes/c/chapter_dynamic_programming/climbing_stairs_dfs.c @@ -0,0 +1,32 @@ +/** + * File: climbing_stairs_dfs.c + * Created Time: 2023-09-19 + * Author: huawuque404 (huawuque404@163.com) + */ + +#include "../utils/common.h" + +/* 搜索 */ +int dfs(int i) { + // 已知 dp[1] 和 dp[2] ,返回之 + if (i == 1 || i == 2) + return i; + // dp[i] = dp[i-1] + dp[i-2] + int count = dfs(i - 1) + dfs(i - 2); + return count; +} + +/* 爬楼梯:搜索 */ +int climbingStairsDFS(int n) { + return dfs(n); +} + +/* Driver Code */ +int main() { + int n = 9; + + int res = climbingStairsDFS(n); + printf("爬 %d 阶楼梯共有 %d 种方案\n", n, res); + + return 0; +} \ No newline at end of file diff --git a/codes/c/chapter_dynamic_programming/climbing_stairs_dfs_mem.c b/codes/c/chapter_dynamic_programming/climbing_stairs_dfs_mem.c new file mode 100644 index 000000000..a3443b644 --- /dev/null +++ b/codes/c/chapter_dynamic_programming/climbing_stairs_dfs_mem.c @@ -0,0 +1,44 @@ +/** + * File: climbing_stairs_dfs_mem.c + * Created Time: 2023-09-19 + * Author: huawuque404 (huawuque404@163.com) + */ + +#include "../utils/common.h" + +/* 记忆化搜索 */ +int dfs(int i, int *mem) { + // 已知 dp[1] 和 dp[2] ,返回之 + if (i == 1 || i == 2) + return i; + // 若存在记录 dp[i] ,则直接返回之 + if (mem[i] != -1) + return mem[i]; + // dp[i] = dp[i-1] + dp[i-2] + int count = dfs(i - 1, mem) + dfs(i - 2, mem); + // 记录 dp[i] + mem[i] = count; + return count; +} + +/* 爬楼梯:记忆化搜索 */ +int climbingStairsDFSMem(int n) { + // mem[i] 记录爬到第 i 阶的方案总数,-1 代表无记录 + int *mem = (int *)malloc((n + 1) * sizeof(int)); + for (int i = 0; i <= n; i++) { + mem[i] = -1; + } + int result = dfs(n, mem); + free(mem); + return result; +} + +/* Driver Code */ +int main() { + int n = 9; + + int res = climbingStairsDFSMem(n); + printf("爬 %d 阶楼梯共有 %d 种方案\n", n, res); + + return 0; +} \ No newline at end of file diff --git a/codes/c/chapter_dynamic_programming/climbing_stairs_dp.c b/codes/c/chapter_dynamic_programming/climbing_stairs_dp.c new file mode 100644 index 000000000..53be19a25 --- /dev/null +++ b/codes/c/chapter_dynamic_programming/climbing_stairs_dp.c @@ -0,0 +1,51 @@ +/** + * File: climbing_stairs_dp.c + * Created Time: 2023-09-19 + * Author: huawuque404 (huawuque404@163.com) + */ + +#include "../utils/common.h" + +/* 爬楼梯:动态规划 */ +int climbingStairsDP(int n) { + if (n == 1 || n == 2) + return n; + // 初始化 dp 表,用于存储子问题的解 + int *dp = (int *)malloc((n + 1) * sizeof(int)); + // 初始状态:预设最小子问题的解 + dp[1] = 1; + dp[2] = 2; + // 状态转移:从较小子问题逐步求解较大子问题 + for (int i = 3; i <= n; i++) { + dp[i] = dp[i - 1] + dp[i - 2]; + } + int result = dp[n]; + free(dp); + return result; +} + +/* 爬楼梯:空间优化后的动态规划 */ +int climbingStairsDPComp(int n) { + if (n == 1 || n == 2) + return n; + int a = 1, b = 2; + for (int i = 3; i <= n; i++) { + int tmp = b; + b = a + b; + a = tmp; + } + return b; +} + +/* Driver Code */ +int main() { + int n = 9; + + int res = climbingStairsDP(n); + printf("爬 %d 阶楼梯共有 %d 种方案\n", n, res); + + res = climbingStairsDPComp(n); + printf("爬 %d 阶楼梯共有 %d 种方案\n", n, res); + + return 0; +} \ No newline at end of file