00:00:00

Description

Editorial

Polynomial Equation String Builder

HARD30 pts

A symbolic algebra service stores one polynomial term per row and needs a canonical equation string that can be fed to a downstream solver.

Table: Terms

power: non-negative exponent of the term
factor: signed coefficient of the term (never zero)

Each row describes one term of a polynomial in variable X.

Build a single equation string that follows this canonical protocol:

Put all terms on the left-hand side and append "=0".
Every term must be formatted as: <sign><abs(factor)>X^<power>.
Special formatting exceptions:
- If power = 1, omit "^1" (example: +3X)
- If power = 0, omit both "X" and exponent (example: -8)
Terms must appear in descending order of power.

Task: Return exactly one row containing exactly one column:

equation

Supported submission environments:

SQL (SQLite 3.27.2)
Pandas (Python)

Example

Input

Terms:
| power | factor |
|-------|--------|
| 2     | 1      |
| 1     | -4     |
| 0     | 2      |

Output

[
  {"equation":"+1X^2-4X+2=0"}
]

Explanation

The terms are already in descending power order: 2, 1, 0. Power 1 omits exponent and power 0 omits variable part.

Example

Input

Terms:
| power | factor |
|-------|--------|
| 4     | -4     |
| 2     | 1      |
| 1     | -1     |

Output

[
  {"equation":"-4X^4+1X^2-1X=0"}
]

Explanation

No constant term exists here. Power 1 is rendered as -1X.

Example

Input

Terms:
| power | factor |
|-------|--------|
| 0     | -7     |
| 3     | 2      |
| 1     | 5      |

Output

[
  {"equation":"+2X^3+5X-7=0"}
]

Explanation

Rows must be reordered by descending power (3, 1, 0) before concatenation.

Accepted0/0·0% Acceptance

Constraints

1 <= number of rows in Terms <= 101
Terms.power values are unique in each test case
0 <= power <= 100
-100 <= factor <= 100
factor != 0
Return one row and one column named equation
Format signs, coefficients, and power suffixes exactly as specified
Sort powers in descending order in the generated equation
Use SQLite 3.27.2 semantics for SQL submissions
For Pandas submissions, return a DataFrame with one column: equation

Code

Visualizer

Solutions

14px

Test Cases3

Results

Submissions

Terms =

[{"power":2,"factor":1},{"power":1,"factor":-4},{"power":0,"factor":2}]

Loading problem...

101

00:00:00

Description

Editorial

Polynomial Equation String Builder

HARD30 pts

A symbolic algebra service stores one polynomial term per row and needs a canonical equation string that can be fed to a downstream solver.

Table: Terms

power: non-negative exponent of the term
factor: signed coefficient of the term (never zero)

Each row describes one term of a polynomial in variable X.

Build a single equation string that follows this canonical protocol:

Put all terms on the left-hand side and append "=0".
Every term must be formatted as: <sign><abs(factor)>X^<power>.
Special formatting exceptions:
- If power = 1, omit "^1" (example: +3X)
- If power = 0, omit both "X" and exponent (example: -8)
Terms must appear in descending order of power.

Task: Return exactly one row containing exactly one column:

equation

Supported submission environments:

SQL (SQLite 3.27.2)
Pandas (Python)

Example

Input

Terms:
| power | factor |
|-------|--------|
| 2     | 1      |
| 1     | -4     |
| 0     | 2      |

Output

[
  {"equation":"+1X^2-4X+2=0"}
]

Explanation

The terms are already in descending power order: 2, 1, 0. Power 1 omits exponent and power 0 omits variable part.

Example

Input

Terms:
| power | factor |
|-------|--------|
| 4     | -4     |
| 2     | 1      |
| 1     | -1     |

Output

[
  {"equation":"-4X^4+1X^2-1X=0"}
]

Explanation

No constant term exists here. Power 1 is rendered as -1X.

Example

Input

Terms:
| power | factor |
|-------|--------|
| 0     | -7     |
| 3     | 2      |
| 1     | 5      |

Output

[
  {"equation":"+2X^3+5X-7=0"}
]

Explanation

Rows must be reordered by descending power (3, 1, 0) before concatenation.

Accepted0/0·0% Acceptance

Constraints

1 <= number of rows in Terms <= 101
Terms.power values are unique in each test case
0 <= power <= 100
-100 <= factor <= 100
factor != 0
Return one row and one column named equation
Format signs, coefficients, and power suffixes exactly as specified
Sort powers in descending order in the generated equation
Use SQLite 3.27.2 semantics for SQL submissions
For Pandas submissions, return a DataFrame with one column: equation

Code

Visualizer

Solutions

14px

Test Cases3

Results

Submissions

Terms =

[{"power":2,"factor":1},{"power":1,"factor":-4},{"power":0,"factor":2}]

Polynomial Equation String Builder

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Polynomial Equation String Builder

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