<p>You are climbing a staircase. It takes <code>n</code> steps to reach the top.</p>

<p>Each time you can either climb <code>1</code> or <code>2</code> steps. In how many distinct ways can you climb to the top?</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 2
<strong>Output:</strong> 2
<strong>Explanation:</strong> There are two ways to climb to the top.
1. 1 step + 1 step
2. 2 steps
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 3
<strong>Output:</strong> 3
<strong>Explanation:</strong> 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
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 45</code></li>
</ul>

class Solution {
 public:
  int climbStairs(int n) {
    // dp[i] := the number of ways to climb to the i-th stair
    vector<int> dp(n + 1);
    dp[0] = 1;
    dp[1] = 1;

    for (int i = 2; i <= n; ++i)
      dp[i] = dp[i - 1] + dp[i - 2];

    return dp[n];
  }
};
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