<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]:
        answer = [0 for _ in range(len(people))]
        # order of putitng on heap: flower start, person, flower end
        heap = []
        for i in range(len(flowers)):
            s, e = flowers[i]
            heappush(heap, (s, 1, i)) # start has priority of 1
            heappush(heap, (e, 3, i)) # start has priority of 3
        
        for i in range(len(people)):
            arrival_time = people[i]
            heappush(heap, (arrival_time, 2, i))
        
        # process the heap
        num_flowers = 0
        while heap:
            time, prio, i = heappop(heap)
            if prio == 1:
                num_flowers += 1
            elif prio == 2:
                answer[i] = num_flowers
            elif prio == 3:
                num_flowers -= 1

        return answer

# example 1:
# heap = (1, 1, 0) (2, 2, 0) (3, 1, 1) (3, 2, 1) (4, 1, 3) (6, 3, 0) (7, 2, 2) (7, 3, 1) (9, 1, 2) (11, 2, 3) (12, 3, 2) (13, 3, 3)
# num_flowers = 0 1 2 3 2 1 2 1 0
# answer = [1, 2, 2, 2]
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