QuadraticRoots | Topcoder Archive

Problem Statement

A quadratic equation has the format ax^2 + bx + c = 0 where a != 0. To solve this equation the quadratic formula is used:

x = (-b (+|-) sqrt(b^2 - 4ac)) / 2a ,

where (+|-) means plus or minus, sqrt means square root, and x is the solution.

Given a list of values for a, b and c your method will return a sorted int[] of all integer solutions to the corresponding quadratic equations. The sorted values should be in ascending order with no repeats. For example, if

    a = {1} ,
    b = {2,3} ,
and c = {2,1} ,

your method would have to solve the quadratic equations corresponding to all combinations of values from a, b and c. This would amount to solving:

 x^2 + 2x + 2 = 0  (Solutions : not integers)
 x^2 + 2x + 1 = 0  (Solutions : -1)
 x^2 + 3x + 2 = 0  (Solutions : -2,-1)  
 x^2 + 3x + 1 = 0  (Solutions : not integers)  .

Notice that all combinations have been tried. The return value would be {-2,-1}.

Definition

Class:: QuadraticRoots
Method:: findRoots
Parameters:: int[], int[], int[]
Returns:: int[]
Method signature:: int[] findRoots(int[] a, int[] b, int[] c)
(be sure your method is public)

Constraints

a, b, and c will each contain between 1 and 50 elements inclusive.
Each element of a will be nonzero, between -10000 and 10000 inclusive.
Each element of b and c will be between -10000 and 10000 inclusive.
The returned int[] will contain at most 100 elements.

Examples

```
{1}
```
```
{2,3}
```
```
{2,1}
```
```
Returns: { -2,  -1 }
```
Example from above.

{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}

{1}

{1}

Returns: { }

No roots here.

{1}

{0}

{-1,-2,-3,-4,-5,-6,-7,-8,-9,-10,-11,-12,-13,-14,-15,-16}

Returns: { -4,  -3,  -2,  -1,  1,  2,  3,  4 }

{1,1,2,2,3,3,4,4}

{1,1,2,2,3,3,4,4}

{1,1,2,2,3,3,4,4}

Returns: { -3,  -2,  -1 }

Tons of repeats.

{1,10000,-10000}

{0,1,10000,-10000}

{0,1,10000,-10000}

Returns: { -10000,  -100,  -1,  0,  1,  100,  10000 }

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