# 2019. The Score of Students Solving Math Expression

<https://leetcode.com/problems/the-score-of-students-solving-math-expression>

## Description

You are given a string `s` that contains digits `0-9`, addition symbols `'+'`, and multiplication symbols `'*'` **only**, representing a **valid** math expression of **single digit numbers** (e.g., `3+5*2`). This expression was given to `n` elementary school students. The students were instructed to get the answer of the expression by following this **order of operations**:

1. Compute **multiplication**, reading from **left to right**; Then,
2. Compute **addition**, reading from **left to right**.

You are given an integer array `answers` of length `n`, which are the submitted answers of the students in no particular order. You are asked to grade the `answers`, by following these **rules**:

* If an answer **equals** the correct answer of the expression, this student will be rewarded `5` points;
* Otherwise, if the answer **could be interpreted** as if the student used the **incorrect order of operations**, **once** or **multiple** times, this student will be rewarded `2` points;
* Otherwise, this student will be rewarded `0` points.

Return *the sum of the points of the students*.

**Example 1:**

![](https://assets.leetcode.com/uploads/2021/09/17/student_solving_math.png)

```
**Input:** s = "7+3*1*2", answers = [20,13,42]
**Output:** 7
**Explanation:** As illustrated above, the correct answer of the expression is 13, therefore one student is rewarded 5 points: [20,**13**,42]
A student might have used this incorrect order of operations: 7+3=10, 10*1=10, 10*2=20. Therefore one student is rewarded 2 points: [**20**,13,42]
The points for the students are: [2,5,0]. The sum of the points is 2+5+0=7.
```

**Example 2:**

```
**Input:** s = "3+5*2", answers = [13,0,10,13,13,16,16]
**Output:** 19
**Explanation:** The correct answer of the expression is 13, therefore three students are rewarded 5 points each: [**13**,0,10,**13**,**13**,16,16]
A student might have used this incorrect order of operations: 3+5=8, 8*2=16. Therefore two students are rewarded 2 points: [13,0,10,13,13,**16**,**16**]
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.
```

**Example 3:**

```
**Input:** s = "6+0*1", answers = [12,9,6,4,8,6]
**Output:** 10
**Explanation:** The correct answer of the expression is 6.
If a student had used some incorrect order of operations, 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.
```

**Constraints:**

* `3 <= s.length <= 31`
* `s` represents a valid expression that contains only digits `0-9`, `'+'`, and `'*'` only.
* All the integer operands in the expression are in the **inclusive** range `[0, 9]`.
* `1 <=` The count of all operators (`'+'` and `'*'`) in the math expression `<= 15`
* Test data are generated such that the correct answer of the expression is in the range of `[0, 1000]`.
* `n == answers.length`
* `1 <= n <= 104`
* `0 <= answers[i] <= 1000`

## ac

```java
```