# 746. Min Cost Climbing Stairs

## Problem Statement

<br>

You are given an integer array `cost` where `cost[i]` is the cost of `ith` step on a staircase. Once you pay the cost, you can either climb one or two steps.

You can either start from the step with index `0`, or the step with index `1`.

Return *the minimum cost to reach the top of the floor*.

&#x20;

**Example 1:**

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

**Example 2:**

<pre><code><strong>Input: cost = [1,100,1,1,1,100,1,1,100,1]
</strong><strong>Output: 6
</strong><strong>Explanation: You will start at index 0.
</strong>- 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.
</code></pre>

&#x20;

**Constraints:**

* `2 <= cost.length <= 1000`
* `0 <= cost[i] <= 999`

## Intuition

```
Approach:

Recursively travel and find out the answer
```

### Links

<https://leetcode.com/problems/min-cost-climbing-stairs/description/?envType=daily-question&envId=2023-10-13>

### Video Links

### Approach 1:

```
```

{% code title="C++" lineNumbers="true" %}

```cpp
class Solution {
public:
    vector<int> dp;
    int find_ans(vector<int> &cost, int index){
        if(index <= 1)
            return 0;

        if(dp[index] != -1)
            return dp[index];

        int one_step = cost[index-1] + find_ans(cost, index-1);
        int two_step = cost[index-2] + find_ans(cost, index-2);

        return dp[index] = min(one_step, two_step);
    }

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

        return find_ans(cost, n);
    }
};
```

{% endcode %}

### Approach 2:

```
```

{% code title="C++" lineNumbers="true" %}

```cpp
class Solution {
public:
    vector<int> dp;
    int minCostClimbingStairs(vector<int>& cost) {
        int n = cost.size();
        dp = vector<int> (n+1,0);

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

            dp[i] = min(one_step, two_step);
        }

        return dp[n];
    }
};
```

{% endcode %}

### Approach 3:

```
```

{% code title="C++" lineNumbers="true" %}

```cpp
```

{% endcode %}

### Approach 4:

```
```

{% code title="C++" lineNumbers="true" %}

```cpp
```

{% endcode %}

### Similar Problems

###


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