/** * File: climbing_stairs_dp.cs * Created Time: 2023-06-30 * Author: hpstory (hpstory1024@163.com) */ namespace hello_algo.chapter_dynamic_programming; public class climbing_stairs_dp { /* Climbing stairs: Dynamic programming */ int ClimbingStairsDP(int n) { if (n == 1 || n == 2) return n; // Initialize dp table, used to store subproblem solutions int[] dp = new int[n + 1]; // Initial state: preset the smallest subproblem solution dp[1] = 1; dp[2] = 2; // State transition: gradually solve larger subproblems from smaller ones for (int i = 3; i <= n; i++) { dp[i] = dp[i - 1] + dp[i - 2]; } return dp[n]; } /* Climbing stairs: Space-optimized dynamic programming */ 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; } [Test] public void Test() { int n = 9; int res = ClimbingStairsDP(n); Console.WriteLine($"Climb {n} steps, there are {res} solutions in total"); res = ClimbingStairsDPComp(n); Console.WriteLine($"Climb {n} steps, there are {res} solutions in total"); } }