Binary Trees With Factors
<p>Given an array of unique integers, <code>arr</code>, where each integer <code>arr[i]</code> is strictly greater than <code>1</code>.</p>

<p>We make a binary tree using these integers, and each number may be used for any number of times. Each non-leaf node&#39;s value should be equal to the product of the values of its children.</p>

<p>Return <em>the number of binary trees we can make</em>. The answer may be too large so return the answer <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

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

<pre>
<strong>Input:</strong> arr = [2,4]
<strong>Output:</strong> 3
<strong>Explanation:</strong> We can make these trees: <code>[2], [4], [4, 2, 2]</code></pre>

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

<pre>
<strong>Input:</strong> arr = [2,4,5,10]
<strong>Output:</strong> 7
<strong>Explanation:</strong> We can make these trees: <code>[2], [4], [5], [10], [4, 2, 2], [10, 2, 5], [10, 5, 2]</code>.</pre>

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

<ul>
	<li><code>1 &lt;= arr.length &lt;= 1000</code></li>
	<li><code>2 &lt;= arr[i] &lt;= 10<sup>9</sup></code></li>
	<li>All the values of <code>arr</code> are <strong>unique</strong>.</li>
</ul>
Array; Hash Table; Dynamic Programming; Sorting
func numFactoredBinaryTrees(arr []int) int {
	const mod int = 1e9 + 7
	sort.Ints(arr)
	f := make([]int, len(arr))
	idx := map[int]int{}
	for i, v := range arr {
		f[i] = 1
		idx[v] = i
	}
	for i, a := range arr {
		for j := 0; j < i; j++ {
			b := arr[j]
			if c := a / b; a%b == 0 {
				if k, ok := idx[c]; ok {
					f[i] = (f[i] + f[j]*f[k]) % mod
				}
			}
		}
	}
	ans := 0
	for _, v := range f {
		ans = (ans + v) % mod
	}
	return ans
}