<p>You are given a <strong>0-indexed</strong> 2D integer array <code>flowers</code>, where <code>flowers[i] = [start<sub>i</sub>, end<sub>i</sub>]</code> means the <code>i<sup>th</sup></code> flower will be in <strong>full bloom</strong> from <code>start<sub>i</sub></code> to <code>end<sub>i</sub></code> (<strong>inclusive</strong>). You are also given a <strong>0-indexed</strong> integer array <code>people</code> of size <code>n</code>, where <code>people[i]</code> is the time that the <code>i<sup>th</sup></code> person will arrive to see the flowers.</p>

<p>Return <em>an integer array </em><code>answer</code><em> of size </em><code>n</code><em>, where </em><code>answer[i]</code><em> is the <strong>number</strong> of flowers that are in full bloom when the </em><code>i<sup>th</sup></code><em> person arrives.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/03/02/ex1new.jpg" style="width: 550px; height: 216px;" />
<pre>
<strong>Input:</strong> flowers = [[1,6],[3,7],[9,12],[4,13]], people = [2,3,7,11]
<strong>Output:</strong> [1,2,2,2]
<strong>Explanation: </strong>The figure above shows the times when the flowers are in full bloom and when the people arrive.
For each person, we return the number of flowers in full bloom during their arrival.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/03/02/ex2new.jpg" style="width: 450px; height: 195px;" />
<pre>
<strong>Input:</strong> flowers = [[1,10],[3,3]], people = [3,3,2]
<strong>Output:</strong> [2,2,1]
<strong>Explanation:</strong> The figure above shows the times when the flowers are in full bloom and when the people arrive.
For each person, we return the number of flowers in full bloom during their arrival.
</pre>

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

<ul>
	<li><code>1 &lt;= flowers.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>flowers[i].length == 2</code></li>
	<li><code>1 &lt;= start<sub>i</sub> &lt;= end<sub>i</sub> &lt;= 10<sup>9</sup></code></li>
	<li><code>1 &lt;= people.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= people[i] &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution:
    def fullBloomFlowers(self, flowers: List[List[int]], people: List[int]) -> List[int]:
        # Input: Flower bloom times, people arrival times
        # Output: For each person, number of flowers blooming at that time

        # Algo: Line sweep
            # first, create a priority queue, insert all the flowers and then the people
            # then, maintain num bloom, result, and keep popping until pq is done
        # elements are ordered first by a, then b in (a, b)
            # to ensure people get counted at edges of bloom:
                # (time, 0) = bloom start
                # (time, 1) = person
                # (time, 2) = bloom end

        # (0) Set-up
        heap = []
        # (1) Create line sweep
        for start, end in flowers:
            heap.append((start, -1))
            heap.append((end, float('inf')))
        for index, arrivalTime in enumerate(people):
            heap.append((arrivalTime, index))
        heapq.heapify(heap) # O(N)

        # (2) Iterate through and return
        currentBloom = 0
        result = [0]*len(people)
        while heap:
            time, category = heapq.heappop(heap)
            if category == -1:
                currentBloom += 1
            elif category == float('inf'):
                currentBloom -= 1
            else:
                result[category] = currentBloom
        return result

        


        
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