[LeetCode] 70. 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?
Note: Given n will be a positive integer.

Thought process:
  1. Sub-problem: in how many distinct ways can you climb to any step?
  2. Formula: f[i] = f[i - 1] + f[i - 2].
  3. Initialization: f[0] = f[1] = 1.
  4. Answer: f[n].

Solution:

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public class Solution {
    public int climbStairs(int 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];
    }
}
Time complexity: O(n).
Location: San Jose, CA, USA

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