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.

 

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 the factor.
  • <pow> is the value of the power.
• If the power is 1, do not add "^<pow>".
  • For example, if power = 1 and factor = 3, the term will be "+3X".
• If the power is 0, add neither "X" nor "^<pow>".
  • For example, if power = 0 and factor = -3, the term will be "-3".
• The powers in the LHS should be sorted in descending order.

Write a solution to build the equation.

The result format is in the following example.

 

Example 1:

Input: 
Terms table:
+-------+--------+
| power | factor |
+-------+--------+
| 2     | 1      |
| 1     | -4     |
| 0     | 2      |
+-------+--------+
Output: 
+--------------+
| equation     |
+--------------+
| +1X^2-4X+2=0 |
+--------------+

Example 2:

Input: 
Terms table:
+-------+--------+
| power | factor |
+-------+--------+
| 4     | -4     |
| 2     | 1      |
| 1     | -1     |
+-------+--------+
Output: 
+-----------------+
| equation        |
+-----------------+
| -4X^4+1X^2-1X=0 |
+-----------------+

 

Follow up: What will be changed in your solution if the power is not a primary key but each power should be unique in the answer?