Build the Equation

Build the Equation - Problem

Database Hard

You have a very powerful program that can solve any equation of one variable in the world. Given a table Terms containing polynomial terms, you need to build a properly formatted equation.

Table: Terms

Column Name	Type
power	int
factor	int

Requirements:

The equation format is: LHS = 0
Each term follows: <sign><fact>X^<pow>
<sign> is either "+" or "-"
<fact> is the absolute value of the factor
If power = 1, omit "^1" (e.g., "+3X")
If power = 0, omit "X" entirely (e.g., "-3")
Order terms by power in descending order

Table Schema

Terms

Column Name	Type	Description
`power` PK	int	The exponent of X in the term (0-100)
`factor`	int	The coefficient of the term (-100 to 100, non-zero)

Primary Key: power

Note: Each row represents one term in a polynomial equation. Power values are unique.

Input & Output

Example 1 — Standard Polynomial

Input Table:

power	factor
2	1
1	-4
0	2

Output:

equation
+1X^2-4X+2=0

💡 Note:

The polynomial has three terms: X² (power=2, factor=1), -4X (power=1, factor=-4), and +2 (power=0, factor=2). Terms are ordered by descending power: 2, 1, 0.

Example 2 — Single Term

Input Table:

power	factor
0	1

Output:

equation
+1=0

💡 Note:

A constant term with power=0 results in just the factor value without X. The equation becomes '+1=0'.

Example 3 — Negative Leading Coefficient

Input Table:

power	factor
4	-5
2	3
1	1

Output:

equation
-5X^4+3X^2+1X=0

💡 Note:

Shows negative leading coefficient (-5X⁴), power=1 formatted as X (not X^1), and proper ordering by descending power.

Constraints

power is an integer in the range [0, 100]
factor is an integer in the range [-100, 100] and cannot be zero
power column contains unique values

Visualization

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Asked in

M Microsoft 28 O Oracle 22

Use STRING_AGG with CASE statements to format each term properly, handling special cases for power 0 and 1, then concatenate in descending power order.

Table Schema

Terms

Column Name	Type	Description
`power` PK	int	The exponent of X in the term (0-100)
`factor`	int	The coefficient of the term (-100 to 100, non-zero)

Primary Key: power

Note: Each row represents one term in a polynomial equation. Power values are unique.

Common Approaches

✓ String Concatenation with CASE Logic

⏱️ Time: O(n log n) Space: O(n)

Format each term individually using CASE logic for different power scenarios, then use string aggregation to combine all terms into the final equation.

String Concatenation with CASE Logic — Algorithm Steps

Step 1: Use CASE to determine sign (+ or -) based on factor
Step 2: Apply CASE logic for power formatting (handle 0, 1, and >1)
Step 3: Concatenate terms in descending power order
Step 4: Add '=0' to complete the equation

Visualization

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Step-by-Step Walkthrough

Format

Apply CASE logic to each term

Order

Sort by power descending

Combine

STRING_AGG concatenates all terms

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

O(n log n)

Sorting by power descending

⚡ Linearithmic

Space Complexity

O(n)

String concatenation storage

⚡ Linearithmic Space

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Table Schema

Input & Output

Constraints

Visualization

Related Problems

Table Schema

Common Approaches

String Concatenation with CASE Logic — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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