# Climbing Stairs

## [Climbing Stairs](https://leetcode.com/problems/climbing-stairs)

You are climbing a staircase. It takes `n` steps to reach the top.

Each time you can either climb `1` or `2` steps. In how many distinct ways can you climb to the top?

**Example 1:**

```

Input: n = 2
Output: 2
Explanation: There are two ways to climb to the top.
1. 1 step + 1 step
2. 2 steps
```

**Example 2:**

```

Input: n = 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
```

**Constraints:**

* `1 <= n <= 45`

## Solutions

### 🧠 Cpp

```cpp
class Solution
{
    //max stairs num is 45
    array<int, 46> _storage = {0,1,2};
public:
    //DP solution, O(n)
    constexpr int climbStairs(int n)
    {
        if(!_storage[n])
            _storage[n] = climbStairs(n-1) + climbStairs(n-2);

        return _storage[n];
    }
};
```


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