<p>You are given an array <code>nums</code> of positive integers. In one operation, you can choose <strong>any</strong> number from <code>nums</code> and reduce it to <strong>exactly</strong> half the number. (Note that you may choose this reduced number in future operations.)</p>

<p>Return<em> the <strong>minimum</strong> number of operations to reduce the sum of </em><code>nums</code><em> by <strong>at least</strong> half.</em></p>

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

<pre>
<strong>Input:</strong> nums = [5,19,8,1]
<strong>Output:</strong> 3
<strong>Explanation:</strong> The initial sum of nums is equal to 5 + 19 + 8 + 1 = 33.
The following is one of the ways to reduce the sum by at least half:
Pick the number 19 and reduce it to 9.5.
Pick the number 9.5 and reduce it to 4.75.
Pick the number 8 and reduce it to 4.
The final array is [5, 4.75, 4, 1] with a total sum of 5 + 4.75 + 4 + 1 = 14.75. 
The sum of nums has been reduced by 33 - 14.75 = 18.25, which is at least half of the initial sum, 18.25 &gt;= 33/2 = 16.5.
Overall, 3 operations were used so we return 3.
It can be shown that we cannot reduce the sum by at least half in less than 3 operations.
</pre>

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

<pre>
<strong>Input:</strong> nums = [3,8,20]
<strong>Output:</strong> 3
<strong>Explanation:</strong> The initial sum of nums is equal to 3 + 8 + 20 = 31.
The following is one of the ways to reduce the sum by at least half:
Pick the number 20 and reduce it to 10.
Pick the number 10 and reduce it to 5.
Pick the number 3 and reduce it to 1.5.
The final array is [1.5, 8, 5] with a total sum of 1.5 + 8 + 5 = 14.5. 
The sum of nums has been reduced by 31 - 14.5 = 16.5, which is at least half of the initial sum, 16.5 &gt;= 31/2 = 15.5.
Overall, 3 operations were used so we return 3.
It can be shown that we cannot reduce the sum by at least half in less than 3 operations.
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>7</sup></code></li>
</ul>

from heapq import *

class Solution:
    def halveArray(self, nums: List[int]) -> int:

        nums = [-1 * num for num in nums]
        heapify(nums)
        s = sum(nums)
        half_sum = s / 2

        ans = 0
        while half_sum > s:
            num = heappop(nums) / 2
            s -= num
            heappush(nums, num)
            ans += 1

        return ans
        
736