The Score of Students Solving Math Expression

The Score of Students Solving Math Expression

What is this problem about?

Imagine you are grading a math competition. The students are given a string expression containing single-digit numbers and the operators '+' and '*'. The correct way to solve the expression is using the standard order of operations (multiplication before addition). However, some students might solve it differently (e.g., left to right). Students get 5 points for the correct answer, 2 points for any answer that could be obtained by some valid grouping of parentheses, and 0 points otherwise. Given the expression and the students' answers, you need to calculate the total score.

Why is this asked in interviews?

This the Score of Students Solving Math Expression interview question is a hard-level challenge from Flipkart. It tests a wide range of skills: parsing expressions, calculating the "real" value, and using dynamic programming (or memoization) to find all possible values from different groupings. This is similar to the "Matrix Chain Multiplication" or "Different Ways to Add Parentheses" problems, which are core concepts in algorithm design.

Algorithmic pattern used

This problem follows the Array, Math, Memoization, String, Stack, Dynamic Programming interview pattern.

1. Calculate the "true" score using a stack or by processing '*' before '+'.
2. Use interval DP to find all possible results: dp[i][j] is a set of all possible values that can be formed by the sub-expression from index i to j.
3. For each split point k between i and j:
   • Combine results from dp[i][k] and dp[k+1][j] using the operator at index k.
4. Use a bitset or a hash set to store the possible values (since the results are constrained to be <= 1000).
5. For each student answer, check if it equals the true score (5 pts) or if it exists in the set of possible scores (2 pts).

Example explanation

Expression: "1+2*3"

• Correct score: 1 + (2*3) = 7.
• Possible scores:
  • (1+2)*3 = 9
  • 1+(2*3) = 7 Possible values are {7, 9}. Student answers: [7, 9, 5].
• 7 gets 5 points.
• 9 gets 2 points.
• 5 gets 0 points. Total = 7.

Common mistakes candidates make

In "The Score of Students Solving Math Expression coding problem," a common mistake is not using memoization for the interval DP, leading to exponential time complexity. Another error is not filtering out intermediate values greater than 1000, which is often allowed by the problem constraints to keep the state space manageable. Finally, forgetting that multiplication has higher precedence than addition when calculating the correct score is a simple but costly mistake.

Interview preparation tip

Master interval DP, as it is the standard approach for "all possible ways to parenthesize" problems. Practice converting recursive solutions with memoization into iterative DP if you prefer. Also, become comfortable with basic expression parsing using stacks.