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}.
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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) |
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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. |
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Examples |
| 0) | |
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| 1) | |
| | {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15} | {1} | {1} |
| Returns: { } | |
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| 2) | |
| | {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 } | |
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| 3) | |
| | {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 } | |
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| 4) | |
| | {1,10000,-10000} | {0,1,10000,-10000} | {0,1,10000,-10000} |
| Returns: { -10000, -100, -1, 0, 1, 100, 10000 } | |
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