diff --git a/codes/c/chapter_dynamic_programming/CMakeLists.txt b/codes/c/chapter_dynamic_programming/CMakeLists.txt index fa62173e..f5f5d023 100644 --- a/codes/c/chapter_dynamic_programming/CMakeLists.txt +++ b/codes/c/chapter_dynamic_programming/CMakeLists.txt @@ -1,3 +1,4 @@ +add_executable(climbing_stairs_constraint_dp climbing_stairs_constraint_dp.c) add_executable(min_cost_climbing_stairs_dp min_cost_climbing_stairs_dp.c) add_executable(min_path_sum min_path_sum.c) add_executable(knapsack knapsack.c) diff --git a/codes/c/chapter_dynamic_programming/climbing_stairs_constraint_dp.c b/codes/c/chapter_dynamic_programming/climbing_stairs_constraint_dp.c new file mode 100644 index 00000000..4752994d --- /dev/null +++ b/codes/c/chapter_dynamic_programming/climbing_stairs_constraint_dp.c @@ -0,0 +1,38 @@ +/** + * File: climbing_stairs_constraint_dp.c + * Created Time: 2023-10-02 + * Author: Zuoxun (845242523@qq.com) + */ + +#include "../utils/common.h" + +/* 带约束爬楼梯:动态规划 */ +int climbingStairsConstraintDP(int n) { + if (n == 1 || n == 2) { + return 1; + } + // 初始化 dp 表,用于存储子问题的解 + int dp[n + 1][3]; + memset(dp, 0, sizeof(dp)); + // 初始状态:预设最小子问题的解 + dp[1][1] = 1; + dp[1][2] = 0; + dp[2][1] = 0; + dp[2][2] = 1; + // 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][1] = dp[i - 1][2]; + dp[i][2] = dp[i - 2][1] + dp[i - 2][2]; + } + return dp[n][1] + dp[n][2]; +} + +/* Driver Code */ +int main() { + int n = 9; + + int res = climbingStairsConstraintDP(n); + printf("爬 %d 阶楼梯共有 %d 种方案\n", n, res); + + return 0; +}