<p>You are given an integer array <code>cost</code> where <code>cost[i]</code> is the cost of <code>i<sup>th</sup></code> step on a staircase. Once you pay the cost, you can either climb one or two steps.</p>

<p>You can either start from the step with index <code>0</code>, or the step with index <code>1</code>.</p>

<p>Return <em>the minimum cost to reach the top of the floor</em>.</p>

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

<pre>
<strong>Input:</strong> cost = [10,<u>15</u>,20]
<strong>Output:</strong> 15
<strong>Explanation:</strong> You will start at index 1.
- Pay 15 and climb two steps to reach the top.
The total cost is 15.
</pre>

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

<pre>
<strong>Input:</strong> cost = [<u>1</u>,100,<u>1</u>,1,<u>1</u>,100,<u>1</u>,<u>1</u>,100,<u>1</u>]
<strong>Output:</strong> 6
<strong>Explanation:</strong> You will start at index 0.
- Pay 1 and climb two steps to reach index 2.
- Pay 1 and climb two steps to reach index 4.
- Pay 1 and climb two steps to reach index 6.
- Pay 1 and climb one step to reach index 7.
- Pay 1 and climb two steps to reach index 9.
- Pay 1 and climb one step to reach the top.
The total cost is 6.
</pre>

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

<ul>
	<li><code>2 &lt;= cost.length &lt;= 1000</code></li>
	<li><code>0 &lt;= cost[i] &lt;= 999</code></li>
</ul>

class Solution {
    int f(int i, vector<int>& dp, vector<int>& cost) {
        // Base case: When you're at the 0th or 1st stair, return the cost of those stairs
        if (i == 0) return cost[0];
        if (i == 1) return cost[1];

        // If already computed, return the stored result
        if (dp[i] != -1) return dp[i];

        // Recursive case: cost of current step + minimum cost from previous steps (i-1 or i-2)
        int oneStepDown = cost[i] + f(i - 1, dp, cost);
        int twoStepsDown = cost[i] + f(i - 2, dp, cost);

        // Store and return the minimum cost to reach this stair
        return dp[i] = min(oneStepDown, twoStepsDown);
    }

public:
    int minCostClimbingStairs(vector<int>& cost) {
        int n = cost.size();
        vector<int> dp(n, -1);

        // Start from the last stair (n-1) or second-to-last stair (n-2)
        return min(f(n - 1, dp, cost), f(n - 2, dp, cost));
    }
};

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