Climbing Stairs - Implementation

Here is the full solution:

function climbStairs(n)
    if n <= 2 then
        return n
    prev2 := 1
    prev1 := 2
    for i from 3 to n
        current := prev1 + prev2
        prev2 := prev1
        prev1 := current
    return prev1

Time: $O(n)$. Space: $O(1)$. This is the space-optimized version since you only need the last two values.