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Problem
Table: Terms
+-------------+------+
| Column Name | Type |
+-------------+------+
| power | int |
| factor | int |
+-------------+------+
power is the column with unique values for this table.
Each row of this table contains information about one term of the equation.
power is an integer in the range [0, 100].
factor is an integer in the range [-100, 100] and cannot be zero.
Problem Definition
You have a very powerful program that can solve any equation of one variable in the world. The equation passed to the program must be formatted as follows:
- The left-hand side (LHS) should contain all the terms.
- The right-hand side (RHS) should be zero.
- Each term of the LHS should follow the format
"<sign><fact>X^<pow>"
where:<sign>
is either"+"
or"-"
.<fact>
is the absolute value of thefactor
.<pow>
is the value of thepower
.
- If the power is
1
, do not add"^<pow>"
.- For example, if
power = 1
andfactor = 3
, the term will be"+3X"
.
- For example, if
- If the power is
0
, add neither"X"
nor"^<pow>"
.- For example, if
power = 0
andfactor = -3
, the term will be"-3"
.
- For example, if
- The powers in the LHS should be sorted in descending order.
Write a solution to build the equation.
Example
Output
Try It Yourself
Solution
To construct the equation by pivoting the Terms
table according to the specified formatting rules, we can follow a systematic approach. This involves organizing the terms based on their powers, formatting each term appropriately, and then concatenating them to form the final equation.
Approach Overview
-
Order Terms by Power Descending:
- Sort the terms in descending order of their
power
to ensure the highest power appears first in the equation.
- Sort the terms in descending order of their
-
Assign Row Numbers Within Each Power:
- Assign a sequential row number to each term to handle cases where multiple terms have the same power.
-
Format Each Term:
- Determine the sign (
+
or-
) based on thefactor
. - Format the term according to the rules:
- If
power > 1
, format as"<sign><abs(factor)>X^<power>"
. - If
power = 1
, format as"<sign><abs(factor)>X"
. - If
power = 0
, format as"<sign><abs(factor)>"
.
- If
- Determine the sign (
-
Concatenate Formatted Terms:
- Combine all formatted terms in the correct order and append
=0
to complete the equation.
- Combine all formatted terms in the correct order and append
SQL Query
WITH ordered_terms AS ( SELECT power, factor, ROW_NUMBER() OVER (ORDER BY power DESC) AS rn FROM Terms ), eqn_reps AS ( SELECT power, factor, rn, CASE WHEN factor > 0 THEN '+' WHEN factor < 0 THEN '-' ELSE '' END AS sgn_rep, CASE WHEN power > 1 THEN CONCAT(ABS(factor), 'X^', power) WHEN power = 1 THEN CONCAT(ABS(factor), 'X') ELSE CONCAT(ABS(factor)) END AS power_rep FROM ordered_terms ) SELECT CONCAT( GROUP_CONCAT(CONCAT(e.sgn_rep, e.power_rep) ORDER BY e.power DESC SEPARATOR ''), '=0' ) AS equation FROM eqn_reps e;
Step-by-Step Approach
Step 1: Order Terms by Power Descending and Assign Row Numbers
Sort the terms in descending order of their power
and assign a row number to each term. This ensures that higher-powered terms appear first in the equation.
SQL Query:
WITH ordered_terms AS ( SELECT power, factor, ROW_NUMBER() OVER (ORDER BY power DESC) AS rn FROM Terms ) SELECT * FROM ordered_terms;
Explanation:
ROW_NUMBER() OVER (ORDER BY power DESC) AS rn
:- Assigns a unique sequential number to each term based on the descending order of
power
.
- Assigns a unique sequential number to each term based on the descending order of
WITH ordered_terms AS (...)
:- Creates a Common Table Expression (CTE) named
ordered_terms
to hold the sorted terms with their assigned row numbers.
- Creates a Common Table Expression (CTE) named
Intermediate Output After Step 1 (ordered_terms
):
sql +-------+--------+----+ | power | factor | rn | +-------+--------+----+ | 2 | 1 | 1 | | 1 | -4 | 2 | | 0 | 2 | 3 | +-------+--------+----+
Step 2: Format Each Term with Appropriate Sign and Structure
Determine the sign (+
or -
) for each term based on the factor
and format the term according to the rules specified.
SQL Query:
WITH ordered_terms AS ( SELECT power, factor, ROW_NUMBER() OVER (ORDER BY power DESC) AS rn FROM Terms ), eqn_reps AS ( SELECT power, factor, rn, CASE WHEN factor > 0 THEN '+' WHEN factor < 0 THEN '-' ELSE '' END AS sgn_rep, CASE WHEN power > 1 THEN CONCAT(ABS(factor), 'X^', power) WHEN power = 1 THEN CONCAT(ABS(factor), 'X') ELSE CONCAT(ABS(factor)) END AS power_rep FROM ordered_terms ) SELECT * FROM eqn_reps;
Explanation:
sgn_rep
:- Assigns a
'+'
iffactor > 0
,'-'
iffactor < 0
, and''
otherwise.
- Assigns a
power_rep
:- Formats the term based on
power
:- If
power > 1
, formats as"<abs(factor)>X^<power>"
. - If
power = 1
, formats as"<abs(factor)>X"
. - If
power = 0
, formats as"<abs(factor)>"
.
- If
- Formats the term based on
Intermediate Output After Step 2 (eqn_reps
):
sql +-------+--------+----+--------+-----------+ | power | factor | rn | sgn_rep| power_rep | +-------+--------+----+--------+-----------+ | 2 | 1 | 1 | + | 1X^2 | | 1 | -4 | 2 | - | 4X | | 0 | 2 | 3 | + | 2 | +-------+--------+----+--------+-----------+
Step 3: Concatenate Formatted Terms and Append '=0'
Combine all formatted terms in the correct order and append =0
to complete the equation.
SQL Query:
WITH ordered_terms AS ( SELECT power, factor, ROW_NUMBER() OVER (ORDER BY power DESC) AS rn FROM Terms ), eqn_reps AS ( SELECT power, factor, rn, CASE WHEN factor > 0 THEN '+' WHEN factor < 0 THEN '-' ELSE '' END AS sgn_rep, CASE WHEN power > 1 THEN CONCAT(ABS(factor), 'X^', power) WHEN power = 1 THEN CONCAT(ABS(factor), 'X') ELSE CONCAT(ABS(factor)) END AS power_rep FROM ordered_terms ) SELECT CONCAT( GROUP_CONCAT(CONCAT(e.sgn_rep, e.power_rep) ORDER BY e.power DESC SEPARATOR ''), '=0' ) AS equation FROM eqn_reps e;
Explanation:
GROUP_CONCAT(CONCAT(e.sgn_rep, e.power_rep) ORDER BY e.power DESC SEPARATOR '')
:- Concatenates all formatted terms (
sgn_rep
+power_rep
) in descending order ofpower
without any separators.
- Concatenates all formatted terms (
CONCAT(..., '=0') AS equation
:- Appends
=0
to the concatenated terms to complete the equation.
- Appends
Final Output:
sql +--------------+ | equation | +--------------+ | +1X^2-4X+2=0 | +--------------+
Explanation of Output:
- Formatted Terms:
+1X^2
-4X
+2
- Concatenated Equation:
+1X^2-4X+2=0
.....
.....
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