feat: add solution 2019. The Score of Students Solving Math Expression

Author: tzuyi0817

solutions/2019. The Score of Students Solving Math Expression/README.md

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+# [2019. The Score of Students Solving Math Expression](https://leetcode.com/problems/the-score-of-students-solving-math-expression)
+
+## Description
+
+<div class="elfjS" data-track-load="description_content"><p>You are given a string <code>s</code> that contains digits <code>0-9</code>, addition symbols <code>'+'</code>, and multiplication symbols <code>'*'</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>
+
+<ol>
+	<li>Compute <strong>multiplication</strong>, reading from <strong>left to right</strong>; Then,</li>
+	<li>Compute <strong>addition</strong>, reading from <strong>left to right</strong>.</li>
+</ol>
+
+<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>
+
+<ul>
+	<li>If an answer <strong>equals</strong> the correct answer of the expression, this student will be rewarded <code>5</code> points;</li>
+	<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>
+	<li>Otherwise, this student will be rewarded <code>0</code> points.</li>
+</ul>
+
+<p>Return <em>the sum of the points of the students</em>.</p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+<img alt="" src="https://assets.leetcode.com/uploads/2021/09/17/student_solving_math.png" style="width: 678px; height: 109px;">
+<pre><strong>Input:</strong> s = "7+3*1*2", answers = [20,13,42]
+<strong>Output:</strong> 7
+<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]
+A 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]
+The points for the students are: [2,5,0]. The sum of the points is 2+5+0=7.
+</pre>
+
+<p><strong class="example">Example 2:</strong></p>
+
+<pre><strong>Input:</strong> s = "3+5*2", answers = [13,0,10,13,13,16,16]
+<strong>Output:</strong> 19
+<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]
+A 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>]
+The 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.
+</pre>
+
+<p><strong class="example">Example 3:</strong></p>
+
+<pre><strong>Input:</strong> s = "6+0*1", answers = [12,9,6,4,8,6]
+<strong>Output:</strong> 10
+<strong>Explanation:</strong> The correct answer of the expression is 6.
+If a student had incorrectly done (6+0)*1, the answer would also be 6.
+By the rules of grading, the students will still be rewarded 5 points (as they got the correct answer), not 2 points.
+The points for the students are: [0,0,5,0,0,5]. The sum of the points is 10.
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>3 &lt;= s.length &lt;= 31</code></li>
+	<li><code>s</code> represents a valid expression that contains only digits <code>0-9</code>, <code>'+'</code>, and <code>'*'</code> only.</li>
+	<li>All the integer operands in the expression are in the <strong>inclusive</strong> range <code>[0, 9]</code>.</li>
+	<li><code>1 &lt;=</code> The count of all operators (<code>'+'</code> and <code>'*'</code>) in the math expression <code>&lt;= 15</code></li>
+	<li>Test data are generated such that the correct answer of the expression is in the range of <code>[0, 1000]</code>.</li>
+	<li>Test data are generated such that value never exceeds 10<sup>9</sup> in intermediate steps of multiplication.</li>
+	<li><code>n == answers.length</code></li>
+	<li><code>1 &lt;= n &lt;= 10<sup>4</sup></code></li>
+	<li><code>0 &lt;= answers[i] &lt;= 1000</code></li>
+</ul>
+</div>
+
+<p>&nbsp;</p>
+
+## Solutions
+
+**Solution: `Dynamic Programming`**
+
+- Time complexity: <em>O(n<sup>3</sup>limit<sup>2</sup>)</em>
+- Space complexity: <em>O(n<sup>2</sup>limit<sup>2</sup>)</em>
+
+<p>&nbsp;</p>
+
+### **JavaScript**
+
+```js
+/**
+ * @param {string} s
+ * @param {number[]} answers
+ * @return {number}
+ */
+const scoreOfStudents = function (s, answers) {
+  const n = s.length;
+  const ANSWER_LIMIT = 1000;
+
+  const compute = () => {
+    const solves = s.split('+');
+
+    return solves.reduce((result, solve) => {
+      let current = Number(solve[0]);
+
+      for (let index = 2; index < solve.length; index += 2) {
+        current *= solve[index];
+      }
+
+      return result + current;
+    }, 0);
+  };
+
+  const correctAnswer = compute();
+  const dp = Array.from({ length: n }, () => new Array(n).fill(-1));
+
+  const getScores = (left, right) => {
+    if (left === right) {
+      const num = Number(s[left]);
+
+      dp[left][right] = new Set([num]);
+
+      return dp[left][right];
+    }
+
+    if (dp[left][right] !== -1) return dp[left][right];
+
+    const result = new Set();
+
+    for (let index = left + 1; index < right; index += 2) {
+      const leftScores = getScores(left, index - 1);
+      const rightScores = getScores(index + 1, right);
+
+      for (const scoreA of leftScores) {
+        for (const scoreB of rightScores) {
+          const operation = s[index];
+          const score = operation === '+' ? scoreA + scoreB : scoreA * scoreB;
+
+          if (score > ANSWER_LIMIT) continue;
+
+          result.add(score);
+        }
+      }
+    }
+
+    dp[left][right] = result;
+
+    return result;
+  };
+
+  const scores = getScores(0, n - 1);
+
+  return answers.reduce((result, answer) => {
+    if (answer === correctAnswer) return result + 5;
+    if (scores.has(answer)) return result + 2;
+
+    return result;
+  }, 0);
+};
+```

solutions/2019. The Score of Students Solving Math Expression/solution.js

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+/**
+ * @param {string} s
+ * @param {number[]} answers
+ * @return {number}
+ */
+const scoreOfStudents = function (s, answers) {
+  const n = s.length;
+  const ANSWER_LIMIT = 1000;
+
+  const compute = () => {
+    const solves = s.split('+');
+
+    return solves.reduce((result, solve) => {
+      let current = Number(solve[0]);
+
+      for (let index = 2; index < solve.length; index += 2) {
+        current *= solve[index];
+      }
+
+      return result + current;
+    }, 0);
+  };
+
+  const correctAnswer = compute();
+  const dp = Array.from({ length: n }, () => new Array(n).fill(-1));
+
+  const getScores = (left, right) => {
+    if (left === right) {
+      const num = Number(s[left]);
+
+      dp[left][right] = new Set([num]);
+
+      return dp[left][right];
+    }
+
+    if (dp[left][right] !== -1) return dp[left][right];
+
+    const result = new Set();
+
+    for (let index = left + 1; index < right; index += 2) {
+      const leftScores = getScores(left, index - 1);
+      const rightScores = getScores(index + 1, right);
+
+      for (const scoreA of leftScores) {
+        for (const scoreB of rightScores) {
+          const operation = s[index];
+          const score = operation === '+' ? scoreA + scoreB : scoreA * scoreB;
+
+          if (score > ANSWER_LIMIT) continue;
+
+          result.add(score);
+        }
+      }
+    }
+
+    dp[left][right] = result;
+
+    return result;
+  };
+
+  const scores = getScores(0, n - 1);
+
+  return answers.reduce((result, answer) => {
+    if (answer === correctAnswer) return result + 5;
+    if (scores.has(answer)) return result + 2;
+
+    return result;
+  }, 0);
+};