The Score of Students Solving Math Expression

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Problem Statement

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+52 ). 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 :

Compute multiplication , reading from left to right ; Then,

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 applied the operators in the wrong order but had correct arithmetic , this student will be rewarded 2 points;

Otherwise, this student will be rewarded 0 points.

Return the sum of the points of the students .

Examples

Example 1

Input: s = "7+3*1*2", answers = [20,13,42]
Output: 7
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 applied the operators in this wrong order: ((7+3)*1)*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
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 applied the operators in this wrong order: ((3+5)*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
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.

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] .

Test data are generated such that value never exceeds 10 ^9 in intermediate steps of multiplication.

n == answers.length

1 <= n <= 10 ^4

0 <= answers[i] <= 1000

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Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicHash Table