Climbing Stairs.java

/*
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

time = O(n)
space = O(n) for the dp array
*/

class Solution {
    public int climbStairs(int n) {
        if (n <= 0) {
            return 0;
        }
        if (n == 1) {
            return 1;
        }
        int[] record = new int[n + 1];
        record[0] = 0;
        record[1] = 1;
        record[2] = 2;
        for (int i = 3; i <= n; i++) {
            record[i] = record[i - 1] + record[i - 2];
        }
        return record[n];
    }
}