leetcode[70]：Climbing Stairs

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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.
3. 1 step + 1 step + 1 step
4. 1 step + 2 steps
5. 2 steps + 1 step

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

这道题其实是求斐波那契数列，这种解法存在优化，因为f[i-1]和f[i-2]在计算过程中确实是被重复计算了。优化的方法又叫备忘录法，牺牲一定的空间来保存每个中间解。