Step by Step – The DP Way Up!
Climbing Stairs – One Step at a Time Today’s challenge seems simple but teaches powerful fundamentals of dynamic programming . Problem: You are climbing a staircase. It takes n steps to reach the top. Each time you can climb either 1 or 2 steps. How many unique ways can you reach the top? Let’s explore from brute force to highly optimized solutions! Best Data Structure for Solving It No complex data structures required! In memoization , we use a HashMap to cache computed results and avoid recalculating. In tabulation , only two variables are needed — super efficient in terms of space. Different Approaches – Brute Force to Optimized Solutions 1. Brute Force (Recursive without Memoization) Try all possible combinations recursively. Simple but inefficient. public int climbStairsBrute ( int n) { if (n == 0 || n == 1 ) return 1 ; return climbStairsBrute(n - 1 ) + climbStairsBrute(n - 2 ); } 2. Memoization (Top-Down Dynamic Programming) Store the results ...