leetcode -- 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?

large data TLE

递归解法的时间复杂度为：O(2^lgn), 故当n逐渐变大时，由于计算重复解，时间复杂度呈指数级增长

public int climbStairs(int n) {
        // Start typing your Java solution below
        // DO NOT write main() function
        if(n <= 0){
            return 0;
        }
        if(n == 1){
            return 1;
        }
        if(n == 2){
            return 2;
        }
        
        return climbStairs(n-1) + climbStairs(n-2);
    }

bottom up

时间复杂度：O(n)

public int climbStairs(int n) {
        // Start typing your Java solution below
        // DO NOT write main() function
        int[] data = new int[n + 1];
        data[0] = 0;
        data[1] = 1;
        if(n >= 2){
            data[2] = 2;
        }
        for(int i = 3; i <= n; i++){
            data[i] = data[i-1] + data[i-2];
        }
        return data[n];        
    }