Minimum Interval to Include Each Query
<p>You are given a 2D integer array <code>intervals</code>, where <code>intervals[i] = [left<sub>i</sub>, right<sub>i</sub>]</code> describes the <code>i<sup>th</sup></code> interval starting at <code>left<sub>i</sub></code> and ending at <code>right<sub>i</sub></code> <strong>(inclusive)</strong>. The <strong>size</strong> of an interval is defined as the number of integers it contains, or more formally <code>right<sub>i</sub> - left<sub>i</sub> + 1</code>.</p>

<p>You are also given an integer array <code>queries</code>. The answer to the <code>j<sup>th</sup></code> query is the <strong>size of the smallest interval</strong> <code>i</code> such that <code>left<sub>i</sub> &lt;= queries[j] &lt;= right<sub>i</sub></code>. If no such interval exists, the answer is <code>-1</code>.</p>

<p>Return <em>an array containing the answers to the queries</em>.</p>

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

<pre>
<strong>Input:</strong> intervals = [[1,4],[2,4],[3,6],[4,4]], queries = [2,3,4,5]
<strong>Output:</strong> [3,3,1,4]
<strong>Explanation:</strong> The queries are processed as follows:
- Query = 2: The interval [2,4] is the smallest interval containing 2. The answer is 4 - 2 + 1 = 3.
- Query = 3: The interval [2,4] is the smallest interval containing 3. The answer is 4 - 2 + 1 = 3.
- Query = 4: The interval [4,4] is the smallest interval containing 4. The answer is 4 - 4 + 1 = 1.
- Query = 5: The interval [3,6] is the smallest interval containing 5. The answer is 6 - 3 + 1 = 4.
</pre>

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

<pre>
<strong>Input:</strong> intervals = [[2,3],[2,5],[1,8],[20,25]], queries = [2,19,5,22]
<strong>Output:</strong> [2,-1,4,6]
<strong>Explanation:</strong> The queries are processed as follows:
- Query = 2: The interval [2,3] is the smallest interval containing 2. The answer is 3 - 2 + 1 = 2.
- Query = 19: None of the intervals contain 19. The answer is -1.
- Query = 5: The interval [2,5] is the smallest interval containing 5. The answer is 5 - 2 + 1 = 4.
- Query = 22: The interval [20,25] is the smallest interval containing 22. The answer is 25 - 20 + 1 = 6.
</pre>

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

<ul>
	<li><code>1 &lt;= intervals.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= queries.length &lt;= 10<sup>5</sup></code></li>
	<li><code>intervals[i].length == 2</code></li>
	<li><code>1 &lt;= left<sub>i</sub> &lt;= right<sub>i</sub> &lt;= 10<sup>7</sup></code></li>
	<li><code>1 &lt;= queries[j] &lt;= 10<sup>7</sup></code></li>
</ul>
Array; Binary Search; Sorting; Line Sweep; Heap (Priority Queue)
func minInterval(intervals [][]int, queries []int) []int {
	n, m := len(intervals), len(queries)
	sort.Slice(intervals, func(i, j int) bool { return intervals[i][0] < intervals[j][0] })
	qs := make([][2]int, m)
	ans := make([]int, m)
	for i := range qs {
		qs[i] = [2]int{queries[i], i}
		ans[i] = -1
	}
	sort.Slice(qs, func(i, j int) bool { return qs[i][0] < qs[j][0] })
	pq := hp{}
	i := 0
	for _, q := range qs {
		x, j := q[0], q[1]
		for i < n && intervals[i][0] <= x {
			a, b := intervals[i][0], intervals[i][1]
			heap.Push(&pq, pair{b - a + 1, b})
			i++
		}
		for len(pq) > 0 && pq[0].r < x {
			heap.Pop(&pq)
		}
		if len(pq) > 0 {
			ans[j] = pq[0].v
		}
	}
	return ans
}

type pair struct{ v, r int }
type hp []pair

func (h hp) Len() int           { return len(h) }
func (h hp) Less(i, j int) bool { return h[i].v < h[j].v }
func (h hp) Swap(i, j int)      { h[i], h[j] = h[j], h[i] }
func (h *hp) Push(v any)        { *h = append(*h, v.(pair)) }
func (h *hp) Pop() any          { a := *h; v := a[len(a)-1]; *h = a[:len(a)-1]; return v }