maximum-number-of-groups-entering-a-competition

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Algorithms

You are given a positive integer array <code>grades</code> which represents the grades of students in a university. You would like to enter all these students into a competition in ordered non-empty groups, such that the ordering meets the following conditions:

<ul>
	<li>The sum of the grades of students in the <code>ith</code> group is less than the sum of the grades of students in the <code>(i + 1)th</code> group, for all groups (except the last).</li>
	<li>The total number of students in the <code>ith</code> group is less than the total number of students in the <code>(i + 1)th</code> group, for all groups (except the last).</li>
</ul>

Return the maximum number of groups that can be formed.

&nbsp;
Example 1:

<pre>
Input: grades = [10,6,12,7,3,5]
Output: 3
Explanation: The following is a possible way to form 3 groups of students:
- 1st group has the students with grades = [12]. Sum of grades: 12. Student count: 1
- 2nd group has the students with grades = [6,7]. Sum of grades: 6 + 7 = 13. Student count: 2
- 3rd group has the students with grades = [10,3,5]. Sum of grades: 10 + 3 + 5 = 18. Student count: 3
It can be shown that it is not possible to form more than 3 groups.
</pre>

Example 2:

<pre>
Input: grades = [8,8]
Output: 1
Explanation: We can only form 1 group, since forming 2 groups would lead to an equal number of students in both groups.
</pre>

&nbsp;
Constraints:

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

maximumGroups

Maximum Number of Groups Entering a Competition

Maximum Height by Stacking Cuboids 

maximum-height-by-stacking-cuboids

堆叠长方体的最大高度

Greedy

Array

Math

Binary Search

给你一个正整数数组 <code>grades</code> ，表示大学中一些学生的成绩。你打算将 所有 学生分为一些 有序 的非空分组，其中分组间的顺序满足以下全部条件：

<ul>
	<li>第 <code>i</code> 个分组中的学生总成绩 小于 第 <code>(i + 1)</code> 个分组中的学生总成绩，对所有组均成立（除了最后一组）。</li>
	<li>第 <code>i</code> 个分组中的学生总数 小于 第 <code>(i + 1)</code> 个分组中的学生总数，对所有组均成立（除了最后一组）。</li>
</ul>

返回可以形成的 最大 组数。

&nbsp;

示例 1：

<pre>输入：grades = [10,6,12,7,3,5]
输出：3
解释：下面是形成 3 个分组的一种可行方法：
- 第 1 个分组的学生成绩为 grades = [12] ，总成绩：12 ，学生数：1
- 第 2 个分组的学生成绩为 grades = [6,7] ，总成绩：6 + 7 = 13 ，学生数：2
- 第 3 个分组的学生成绩为 grades = [10,3,5] ，总成绩：10 + 3 + 5 = 18 ，学生数：3 
可以证明无法形成超过 3 个分组。
</pre>

示例 2：

<pre>输入：grades = [8,8]
输出：1
解释：只能形成 1 个分组，因为如果要形成 2 个分组的话，会导致每个分组中的学生数目相等。
</pre>

&nbsp;

提示：

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