Painting the Walls
<p>You are given two <strong>0-indexed</strong> integer arrays,&nbsp;<code>cost</code> and <code>time</code>, of size <code>n</code> representing the costs and the time taken to paint <code>n</code> different walls respectively. There are two painters available:</p>

<ul>
	<li>A<strong>&nbsp;paid painter</strong>&nbsp;that paints the <code>i<sup>th</sup></code> wall in <code>time[i]</code> units of time and takes <code>cost[i]</code> units of money.</li>
	<li>A<strong>&nbsp;free painter</strong> that paints&nbsp;<strong>any</strong> wall in <code>1</code> unit of time at a cost of <code>0</code>. But the&nbsp;free painter can only be used if the paid painter is already <strong>occupied</strong>.</li>
</ul>

<p>Return <em>the minimum amount of money required to paint the </em><code>n</code><em>&nbsp;walls.</em></p>

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

<pre>
<strong>Input:</strong> cost = [1,2,3,2], time = [1,2,3,2]
<strong>Output:</strong> 3
<strong>Explanation:</strong> The walls at index 0 and 1 will be painted by the paid painter, and it will take 3 units of time; meanwhile, the free painter will paint the walls at index 2 and 3, free of cost in 2 units of time. Thus, the total cost is 1 + 2 = 3.
</pre>

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

<pre>
<strong>Input:</strong> cost = [2,3,4,2], time = [1,1,1,1]
<strong>Output:</strong> 4
<strong>Explanation:</strong> The walls at index 0 and 3 will be painted by the paid painter, and it will take 2 units of time; meanwhile, the free painter will paint the walls at index 1 and 2, free of cost in 2 units of time. Thus, the total cost is 2 + 2 = 4.
</pre>

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

<ul>
	<li><code>1 &lt;= cost.length &lt;= 500</code></li>
	<li><code>cost.length == time.length</code></li>
	<li><code>1 &lt;= cost[i] &lt;= 10<sup>6</sup></code></li>
	<li><code>1 &lt;= time[i] &lt;= 500</code></li>
</ul>
Array; Dynamic Programming
impl Solution {
    #[allow(dead_code)]
    pub fn paint_walls(cost: Vec<i32>, time: Vec<i32>) -> i32 {
        let n = cost.len();
        let mut record_vec: Vec<Vec<i32>> = vec![vec![-1; n << 1 | 1]; n];
        Self::dfs(&mut record_vec, 0, n as i32, n as i32, &time, &cost)
    }

    #[allow(dead_code)]
    fn dfs(
        record_vec: &mut Vec<Vec<i32>>,
        i: i32,
        j: i32,
        n: i32,
        time: &Vec<i32>,
        cost: &Vec<i32>,
    ) -> i32 {
        if n - i <= j - n {
            // All the remaining walls can be printed at no cost
            // Just return 0
            return 0;
        }
        if i >= n {
            // No way this case can be achieved
            // Just return +INF
            return 1 << 30;
        }
        if record_vec[i as usize][j as usize] == -1 {
            // This record hasn't been written
            record_vec[i as usize][j as usize] = std::cmp::min(
                Self::dfs(record_vec, i + 1, j + time[i as usize], n, time, cost)
                    + cost[i as usize],
                Self::dfs(record_vec, i + 1, j - 1, n, time, cost),
            );
        }
        record_vec[i as usize][j as usize]
    }
}
