0070-climbing-stairs.cpp

/*
    Climbing stairs, either 1 or 2 steps, distinct ways to reach top
    Ex. n = 2 -> 2 (1 + 1, 2), n = 3 -> 3 (1 + 1 + 1, 1 + 2, 2 + 1)

    Recursion w/ memoization -> DP, why DP? Optimal substructure
    Recurrence relation: dp[i] = dp[i - 1] + dp[i - 2]
    Reach ith step in 2 ways: 1) 1 step from i-1, 2) 2 steps from i-2

    Time: O(n)
    Space: O(1)
*/

class Solution {
public:
    int climbStairs(int n) {
        if (n == 1) {
            return 1;
        }
        if (n == 2) {
            return 2;
        }
        
        int first = 1;
        int second = 2;
        
        int result = 0;
        
        for (int i = 2; i < n; i++) {
            result = first + second;
            first = second;
            second = result;
        }
        
        return result;
    }
};