Count Pairs With XOR in a Range
<p>Given a <strong>(0-indexed)</strong> integer array <code>nums</code> and two integers <code>low</code> and <code>high</code>, return <em>the number of <strong>nice pairs</strong></em>.</p>

<p>A <strong>nice pair</strong> is a pair <code>(i, j)</code> where <code>0 &lt;= i &lt; j &lt; nums.length</code> and <code>low &lt;= (nums[i] XOR nums[j]) &lt;= high</code>.</p>

<p>&nbsp;</p>

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

<pre>

<strong>Input:</strong> nums = [1,4,2,7], low = 2, high = 6

<strong>Output:</strong> 6

<strong>Explanation:</strong> All nice pairs (i, j) are as follows:

    - (0, 1): nums[0] XOR nums[1] = 5 

    - (0, 2): nums[0] XOR nums[2] = 3

    - (0, 3): nums[0] XOR nums[3] = 6

    - (1, 2): nums[1] XOR nums[2] = 6

    - (1, 3): nums[1] XOR nums[3] = 3

    - (2, 3): nums[2] XOR nums[3] = 5

</pre>

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

<pre>

<strong>Input:</strong> nums = [9,8,4,2,1], low = 5, high = 14

<strong>Output:</strong> 8

<strong>Explanation:</strong> All nice pairs (i, j) are as follows:

​​​​​    - (0, 2): nums[0] XOR nums[2] = 13

&nbsp;   - (0, 3): nums[0] XOR nums[3] = 11

&nbsp;   - (0, 4): nums[0] XOR nums[4] = 8

&nbsp;   - (1, 2): nums[1] XOR nums[2] = 12

&nbsp;   - (1, 3): nums[1] XOR nums[3] = 10

&nbsp;   - (1, 4): nums[1] XOR nums[4] = 9

&nbsp;   - (2, 3): nums[2] XOR nums[3] = 6

&nbsp;   - (2, 4): nums[2] XOR nums[4] = 5</pre>

<p>&nbsp;</p>

<p><strong>Constraints:</strong></p>

<ul>

    <li><code>1 &lt;= nums.length &lt;= 2 * 10<sup>4</sup></code></li>

    <li><code>1 &lt;= nums[i] &lt;= 2 * 10<sup>4</sup></code></li>

    <li><code>1 &lt;= low &lt;= high &lt;= 2 * 10<sup>4</sup></code></li>

</ul>
Bit Manipulation; Trie; Array
type Trie struct {
	children [2]*Trie
	cnt      int
}

func newTrie() *Trie {
	return &Trie{}
}

func (this *Trie) insert(x int) {
	node := this
	for i := 15; i >= 0; i-- {
		v := (x >> i) & 1
		if node.children[v] == nil {
			node.children[v] = newTrie()
		}
		node = node.children[v]
		node.cnt++
	}
}

func (this *Trie) search(x, limit int) (ans int) {
	node := this
	for i := 15; i >= 0 && node != nil; i-- {
		v := (x >> i) & 1
		if (limit >> i & 1) == 1 {
			if node.children[v] != nil {
				ans += node.children[v].cnt
			}
			node = node.children[v^1]
		} else {
			node = node.children[v]
		}
	}
	return
}

func countPairs(nums []int, low int, high int) (ans int) {
	tree := newTrie()
	for _, x := range nums {
		ans += tree.search(x, high+1) - tree.search(x, low)
		tree.insert(x)
	}
	return
}