leetcode-problemset/leetcode/originData/maximum-number-of-groups-entering-a-competition.json

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            "title": "Maximum Number of Groups Entering a Competition",
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            "content": "<p>You are given a positive integer array <code>grades</code> which represents the grades of students in a university. You would like to enter <strong>all</strong> these students into a competition in <strong>ordered</strong> non-empty groups, such that the ordering meets the following conditions:</p>\n\n<ul>\n\t<li>The sum of the grades of students in the <code>i<sup>th</sup></code> group is <strong>less than</strong> the sum of the grades of students in the <code>(i + 1)<sup>th</sup></code> group, for all groups (except the last).</li>\n\t<li>The total number of students in the <code>i<sup>th</sup></code> group is <strong>less than</strong> the total number of students in the <code>(i + 1)<sup>th</sup></code> group, for all groups (except the last).</li>\n</ul>\n\n<p>Return <em>the <strong>maximum</strong> number of groups that can be formed</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> grades = [10,6,12,7,3,5]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> The following is a possible way to form 3 groups of students:\n- 1<sup>st</sup> group has the students with grades = [12]. Sum of grades: 12. Student count: 1\n- 2<sup>nd</sup> group has the students with grades = [6,7]. Sum of grades: 6 + 7 = 13. Student count: 2\n- 3<sup>rd</sup> group has the students with grades = [10,3,5]. Sum of grades: 10 + 3 + 5 = 18. Student count: 3\nIt can be shown that it is not possible to form more than 3 groups.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> grades = [8,8]\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> We can only form 1 group, since forming 2 groups would lead to an equal number of students in both groups.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= grades.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= grades[i] &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
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            "hints": [
                "Would it be easier to place the students into valid groups after sorting them based on their grades in ascending order?",
                "Notice that, after sorting, we can separate them into groups of sizes 1, 2, 3, and so on.",
                "If the last group is invalid, we can merge it with the previous group.",
                "This creates the maximum number of groups because we always greedily form the smallest possible group."
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