Climbing Stairs

This problem is actaully asking you to generate the Fibonacci sequence. According to the problem statement. When you are getting to the $n$th stair. You can at first get to the $n - 1$th stair and climb 1 stair to met the top, or, you can at first get to the $n - 2$th stair and then climb 2 stairs to the top. So the total ways to get the $n$th stair equals to the sum of ways to get $n - 1$th and $n - 2$th stair. If we regard this problem as a Dynamic Programing problem, we have

$$DP[i] = DP[i - 1] + DP[i - 2]$$

We have $DP[0] = DP[1] = 1$, so it will be a Fibonacci sequence generated for $DP[i]$.

public class ClimbingStairs {
    public int climbStairs(int n) {
        if (n < 2) return 1;

        int a = 1;
        int b = 1;
        int c = 1;

        for (int i = 2; i <= n; i++) {
            c = b;
            b = a + b;
            a = c;
        }

        return b;
    }
}