Remove Boxes
<p>You are given several <code>boxes</code> with different colors represented by different positive numbers.</p>

<p>You may experience several rounds to remove boxes until there is no box left. Each time you can choose some continuous boxes with the same color (i.e., composed of <code>k</code> boxes, <code>k &gt;= 1</code>), remove them and get <code>k * k</code> points.</p>

<p>Return <em>the maximum points you can get</em>.</p>

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

<pre>
<strong>Input:</strong> boxes = [1,3,2,2,2,3,4,3,1]
<strong>Output:</strong> 23
<strong>Explanation:</strong>
[1, 3, 2, 2, 2, 3, 4, 3, 1] 
----&gt; [1, 3, 3, 4, 3, 1] (3*3=9 points) 
----&gt; [1, 3, 3, 3, 1] (1*1=1 points) 
----&gt; [1, 1] (3*3=9 points) 
----&gt; [] (2*2=4 points)
</pre>

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

<pre>
<strong>Input:</strong> boxes = [1,1,1]
<strong>Output:</strong> 9
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> boxes = [1]
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>1 &lt;= boxes.length &lt;= 100</code></li>
	<li><code>1 &lt;= boxes[i]&nbsp;&lt;= 100</code></li>
</ul>
Memoization; Array; Dynamic Programming
func removeBoxes(boxes []int) int {
	n := len(boxes)
	f := make([][][]int, n)
	for i := range f {
		f[i] = make([][]int, n)
		for j := range f[i] {
			f[i][j] = make([]int, n)
		}
	}
	var dfs func(i, j, k int) int
	dfs = func(i, j, k int) int {
		if i > j {
			return 0
		}
		for i < j && boxes[j] == boxes[j-1] {
			j, k = j-1, k+1
		}
		if f[i][j][k] > 0 {
			return f[i][j][k]
		}
		ans := dfs(i, j-1, 0) + (k+1)*(k+1)
		for h := i; h < j; h++ {
			if boxes[h] == boxes[j] {
				ans = max(ans, dfs(h+1, j-1, 0)+dfs(i, h, k+1))
			}
		}
		f[i][j][k] = ans
		return ans
	}
	return dfs(0, n-1, 0)
}