Build the Equation - Solution & Explanation

Problem Overview: Each row represents a polynomial term with a coefficient (factor) and exponent (power). Your job is to convert these rows into a single formatted equation string such as 3x^2+2x-5, ordered by descending power and formatted according to algebra rules.

Approach 1: CASE Formatting + GROUP_CONCAT (O(n log n) time, O(n) space)

The clean SQL solution formats every term independently and then concatenates them into a single string. Use CASE expressions to convert each row into its textual representation: factor only when power = 0, factorx when power = 1, and factorx^power otherwise. Handle positive signs by prefixing '+' when the factor is positive so that intermediate terms concatenate correctly.

Once every row is converted into a formatted term, combine them using MySQL’s GROUP_CONCAT. Apply ORDER BY power DESC inside the aggregation so the highest power appears first, matching the standard polynomial format. Finally, remove a possible leading '+' from the final string with TRIM or SUBSTRING. The database scans all rows and performs a sort during aggregation, giving O(n log n) time and O(n) output space.

This approach relies entirely on SQL string manipulation and aggregation features, which is exactly what interviewers want to see in a database problem. The key insight is treating each polynomial term as a formatted string before aggregation rather than trying to build the equation incrementally.

Approach 2: Incremental Concatenation with Variables (O(n log n) time, O(n) space)

Another option uses MySQL user-defined variables to iteratively build the equation string. First sort rows by power DESC. Then iterate through the ordered rows while appending formatted terms to a variable using CONCAT. Each row still uses CASE logic to format the correct representation (x, x^power, or constant).

This method mimics procedural string building inside SQL. While it works, it is more verbose and less portable across SQL engines. Modern SQL solutions generally prefer aggregation functions like GROUP_CONCAT because they express the transformation declaratively and integrate naturally with SQL query patterns.

Recommended for interviews: The CASE + GROUP_CONCAT approach is the expected solution. It shows you understand SQL aggregation, conditional formatting, and ordering inside aggregation. A procedural variable approach demonstrates the same idea but is less idiomatic. Interviewers usually want to see strong string manipulation combined with SQL aggregation.