minimum-operations-to-halve-array-sum

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Algorithms

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

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

&nbsp;
Example 1:

<pre>
Input: nums = [5,19,8,1]
Output: 3
Explanation: 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>

Example 2:

<pre>
Input: nums = [3,8,20]
Output: 3
Explanation: 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>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= nums.length &lt;= 105</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 107</code></li>
</ul>

halveArray

Minimum Operations to Halve Array Sum

Remove Stones to Minimize the Total

remove-stones-to-minimize-the-total

移除石子使总数最小

Minimum Operations to Exceed Threshold Value II

minimum-operations-to-exceed-threshold-value-ii

超过阈值的最少操作数 II

Greedy

Array

Heap (Priority Queue)

给你一个正整数数组&nbsp;<code>nums</code>&nbsp;。每一次操作中，你可以从&nbsp;<code>nums</code>&nbsp;中选择 任意&nbsp;一个数并将它减小到 恰好&nbsp;一半。（注意，在后续操作中你可以对减半过的数继续执行操作）

请你返回将 <code>nums</code>&nbsp;数组和 至少&nbsp;减少一半的 最少&nbsp;操作数。

&nbsp;

示例 1：

<pre>
输入：nums = [5,19,8,1]
输出：3
解释：初始 nums 的和为 5 + 19 + 8 + 1 = 33 。
以下是将数组和减少至少一半的一种方法：
选择数字 19 并减小为 9.5 。
选择数字 9.5 并减小为 4.75 。
选择数字 8 并减小为 4 。
最终数组为 [5, 4.75, 4, 1] ，和为 5 + 4.75 + 4 + 1 = 14.75 。
nums 的和减小了 33 - 14.75 = 18.25 ，减小的部分超过了初始数组和的一半，18.25 &gt;= 33/2 = 16.5 。
我们需要 3 个操作实现题目要求，所以返回 3 。
可以证明，无法通过少于 3 个操作使数组和减少至少一半。
</pre>

示例 2：

<pre>
输入：nums = [3,8,20]
输出：3
解释：初始 nums 的和为 3 + 8 + 20 = 31 。
以下是将数组和减少至少一半的一种方法：
选择数字 20 并减小为 10 。
选择数字 10 并减小为 5 。
选择数字 3 并减小为 1.5 。
最终数组为 [1.5, 8, 5] ，和为 1.5 + 8 + 5 = 14.5 。
nums 的和减小了 31 - 14.5 = 16.5 ，减小的部分超过了初始数组和的一半， 16.5 &gt;= 31/2 = 15.5 。
我们需要 3 个操作实现题目要求，所以返回 3 。
可以证明，无法通过少于 3 个操作使数组和减少至少一半。
</pre>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= nums.length &lt;= 105</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 107</code></li>
</ul>