Climbing Stairs
You are climbing a stair case. It takes n steps to reach to the top. Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top? Note: Given n will be a positive integer. Example 1: Input: 2 Output: 2 Explanation: There are two ways to climb to the top. 1. 1 step + 1 step 2. 2 steps Example 2: Input: 3 Output: 3 Explanation: There are three ways to climb to the top. 1. 1 step + 1 step + 1 step 2. 1 step + 2 steps 3. 2 steps + 1 step Recursive Solution: class Solution { public int climbStairs(int n) { return climbStairs(0, n); } int climbStairs(int i, int n) { if (i > n) return 0; if (i == n) return 1; return climbStairs(i + 1, n) + climbStairs(i + 2, n); } } Recursive Solution with Memo class Solution { public int climbStairs(int n) { int[] memo = new int[n + 1]; return climbStairs(0, n, memo); } int climbStairs(int i, int n, int[] memo) { if (i > n) return 0; if (i == n) return 1; if (memo[i] > 0) { return memo[i]; } return memo[i] = climbStairs(i + 1, n, memo) + climbStairs(i + 2, n, memo); } }