LintCode 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?

Example

Given an example n=3 , 1+1+1=2+1=1+2=3

return 3

For the problem, try to think about it in this way.

Firstly, we define the problem of DP(n) as the ways of approaching to n stairs. 

The problem of DP(n) depends on DP(n-1) and DP(n-2). Then the DP(n) = DP(n-1) + DP(n-2). Because there is two possibilities for DP(n) happen due to the rule that either it is accomplished by step 1 or step 2 stairs before approaching to n.

Initialize the DP(0) =1 and DP(1) = 1.

Solve problem DP(n)

public class Solution {
    /**
     * @param n: An integer
     * @return: An integer
     */
    public int climbStairs(int n) {
        // write your code here
        if (n <= 1) {
            return 1;
        }
        int last = 1, lastlast = 1;
        int now = 0;
        for (int i = 1; i < n; i++) {
            now = last + lastlast;
            lastlast = last;
            last = now;
        }
        return now;
    }
}

Then this problem is a fibonacci sequence