Build the Equation - Practice Coding Problems

Build the Equation - Problem

Database Hard

You're tasked with creating a polynomial equation formatter that takes mathematical terms and builds a properly formatted equation for a powerful equation solver.

Given a table of polynomial terms, each with a power and factor, you need to construct an equation in the specific format: LHS = 0

Formatting Rules:

Sign: '+' or '-' based on factor's sign
Factor: Use absolute value of the factor
Power formatting:
- Power = 0: Just the factor (e.g., "+3", "-7")
- Power = 1: Factor + X (e.g., "+3X", "-5X")
- Power > 1: Factor + X^power (e.g., "+2X^3", "-4X^7")
Order: Terms must be sorted by power in descending order

Example: Terms with powers [2,0,1] and factors [1,-3,4] should produce: +1X^2+4X-3=0

Input & Output

example_1.sql — Basic Polynomial

$ Input: Terms table: +-------+--------+ | power | factor | +-------+--------+ | 2 | 1 | | 1 | -4 | | 0 | 2 | +-------+--------+

› Output: +1X^2-4X+2=0

💡 Note: Terms sorted by power descending: 2,1,0. Formatted as: +1X^2 (power>1), -4X (power=1), +2 (power=0)

example_2.sql — Single Term

$ Input: Terms table: +-------+--------+ | power | factor | +-------+--------+ | 0 | -3 | +-------+--------+

› Output: -3=0

💡 Note: Single term with power=0, so format is just the signed factor: -3

example_3.sql — Linear Equation

$ Input: Terms table: +-------+--------+ | power | factor | +-------+--------+ | 1 | 5 | | 0 | -2 | +-------+--------+

› Output: +5X-2=0

💡 Note: Linear equation with power=1 term (+5X) and constant term (-2)

Visualization

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Understanding the Visualization

Gather Terms

Collect all polynomial terms with their powers and factors

Sort by Power

Arrange terms in descending order of power (highest first)

Format Terms

Apply specific formatting rules based on power value

Build Equation

Concatenate formatted terms and add '=0' to complete equation

Key Takeaway

🎯 Key Insight: Use SQL's GROUP_CONCAT with ORDER BY to sort terms by power descending, then apply CASE statements to format each term correctly based on its power value.

Time & Space Complexity

Time Complexity

⏱️

O(n log n)

Sorting the terms by power dominates the time complexity

⚡ Linearithmic

Space Complexity

O(n)

Space needed to store all terms and build the result string

⚡ Linearithmic Space

Constraints

power is an integer in the range [0, 100]
factor is an integer in the range [-100, 100] and cannot be zero
Each power value is unique in the table
The table contains at least 1 row

Asked in

a Amazon 35 ⊞ Microsoft 28 G Google 22 f Meta 18

This is a SQL database problem that requires sorting terms by power in descending order and formatting each term based on specific rules. The optimal approach uses GROUP_CONCAT with ORDER BY to sort and concatenate terms in a single query, with CASE statements to handle different power formatting rules (constant, linear, and polynomial terms).

Common Approaches

Approach	Time	Space	Notes
✓ Brute Force (Simple Sort and Format)	O(n log n)	O(n)	Sort all terms by power, then format each term individually

Brute Force (Simple Sort and Format) — Algorithm Steps

Query all terms from the database
Sort terms by power in descending order
For each term, determine the correct format based on power
Handle sign, factor absolute value, and power notation
Concatenate all formatted terms with '=0'

Visualization

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Step-by-Step Walkthrough

Retrieve Terms

Get all terms from database

Sort by Power

Order terms by power descending

Format Each Term

Apply formatting rules based on power

Concatenate

Join all terms and add =0

Code -

solution.c — C

// SQL Solution for Build the Equation
// This is a database problem, so we use SQL

/*
SELECT CONCAT(
    GROUP_CONCAT(
        CASE 
            WHEN power = 0 THEN 
                CASE WHEN factor > 0 THEN CONCAT('+', ABS(factor)) 
                     ELSE CONCAT('-', ABS(factor)) END
            WHEN power = 1 THEN 
                CASE WHEN factor > 0 THEN CONCAT('+', ABS(factor), 'X') 
                     ELSE CONCAT('-', ABS(factor), 'X') END
            ELSE 
                CASE WHEN factor > 0 THEN CONCAT('+', ABS(factor), 'X^', power) 
                     ELSE CONCAT('-', ABS(factor), 'X^', power) END
        END
        ORDER BY power DESC
        SEPARATOR ''
    ),
    '=0'
) AS equation
FROM Terms;
*/

Time & Space Complexity

Time Complexity

⏱️

O(n log n)

Sorting the terms by power dominates the time complexity

⚡ Linearithmic

Space Complexity

O(n)

Space needed to store all terms and build the result string

⚡ Linearithmic Space

Constraints

power is an integer in the range [0, 100]
factor is an integer in the range [-100, 100] and cannot be zero
Each power value is unique in the table
The table contains at least 1 row

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Input & Output

Visualization

Time & Space Complexity

Related Problems

Constraints

Common Approaches

Brute Force (Simple Sort and Format) — Algorithm Steps

Visualization

Code -

Time & Space Complexity

Constraints

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