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            "title": "The Score of Students Solving Math Expression",
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            "content": "<p>You are given a string <code>s</code> that contains digits <code>0-9</code>, addition symbols <code>&#39;+&#39;</code>, and multiplication symbols <code>&#39;*&#39;</code> <strong>only</strong>, representing a <strong>valid</strong> math expression of <strong>single digit numbers</strong> (e.g., <code>3+5*2</code>). This expression was given to <code>n</code> elementary school students. The students were instructed to get the answer of the expression by following this <strong>order of operations</strong>:</p>\n\n<ol>\n\t<li>Compute <strong>multiplication</strong>, reading from <strong>left to right</strong>; Then,</li>\n\t<li>Compute <strong>addition</strong>, reading from <strong>left to right</strong>.</li>\n</ol>\n\n<p>You are given an integer array <code>answers</code> of length <code>n</code>, which are the submitted answers of the students in no particular order. You are asked to grade the <code>answers</code>, by following these <strong>rules</strong>:</p>\n\n<ul>\n\t<li>If an answer <strong>equals</strong> the correct answer of the expression, this student will be rewarded <code>5</code> points;</li>\n\t<li>Otherwise, if the answer <strong>could be interpreted</strong> as if the student applied the operators <strong>in the wrong order</strong> but had <strong>correct arithmetic</strong>, this student will be rewarded <code>2</code> points;</li>\n\t<li>Otherwise, this student will be rewarded <code>0</code> points.</li>\n</ul>\n\n<p>Return <em>the sum of the points of the students</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/09/17/student_solving_math.png\" style=\"width: 678px; height: 109px;\" />\n<pre>\n<strong>Input:</strong> s = &quot;7+3*1*2&quot;, answers = [20,13,42]\n<strong>Output:</strong> 7\n<strong>Explanation:</strong> As illustrated above, the correct answer of the expression is 13, therefore one student is rewarded 5 points: [20,<u><strong>13</strong></u>,42]\nA student might have applied the operators in this wrong order: ((7+3)*1)*2 = 20. Therefore one student is rewarded 2 points: [<u><strong>20</strong></u>,13,42]\nThe points for the students are: [2,5,0]. The sum of the points is 2+5+0=7.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> s = &quot;3+5*2&quot;, answers = [13,0,10,13,13,16,16]\n<strong>Output:</strong> 19\n<strong>Explanation:</strong> The correct answer of the expression is 13, therefore three students are rewarded 5 points each: [<strong><u>13</u></strong>,0,10,<strong><u>13</u></strong>,<strong><u>13</u></strong>,16,16]\nA student might have applied the operators in this wrong order: ((3+5)*2 = 16. Therefore two students are rewarded 2 points: [13,0,10,13,13,<strong><u>16</u></strong>,<strong><u>16</u></strong>]\nThe points for the students are: [5,0,0,5,5,2,2]. The sum of the points is 5+0+0+5+5+2+2=19.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> s = &quot;6+0*1&quot;, answers = [12,9,6,4,8,6]\n<strong>Output:</strong> 10\n<strong>Explanation:</strong> The correct answer of the expression is 6.\nIf a student had incorrectly done (6+0)*1, the answer would also be 6.\nBy the rules of grading, the students will still be rewarded 5 points (as they got the correct answer), not 2 points.\nThe points for the students are: [0,0,5,0,0,5]. The sum of the points is 10.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>3 &lt;= s.length &lt;= 31</code></li>\n\t<li><code>s</code> represents a valid expression that contains only digits <code>0-9</code>, <code>&#39;+&#39;</code>, and <code>&#39;*&#39;</code> only.</li>\n\t<li>All the integer operands in the expression are in the <strong>inclusive</strong> range <code>[0, 9]</code>.</li>\n\t<li><code>1 &lt;=</code> The count of all operators (<code>&#39;+&#39;</code> and <code>&#39;*&#39;</code>) in the math expression <code>&lt;= 15</code></li>\n\t<li>Test data are generated such that the correct answer of the expression is in the range of <code>[0, 1000]</code>.</li>\n\t<li><code>n == answers.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 10<sup>4</sup></code></li>\n\t<li><code>0 &lt;= answers[i] &lt;= 1000</code></li>\n</ul>\n",
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            "hints": [
                "The number of operators in the equation is less. Could you find the right answer then generate all possible answers using different orders of operations?",
                "Divide the equation into blocks separated by the operators, and use memoization on the results of blocks for optimization.",
                "Use set and the max limit of the answer for further optimization."
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