Problem Statement |
| | Young Andrew has just learned about quadratic equations. He was quite amazed by the fact that their
solutions could look like (5+sqrt(3))/4, so he wants to dig into this issue. More specifically, given five numbers x, y, d, z and k, he wants to find the number of equations a*t2+b*t+c=0 such that (x+y*sqrt(d))/z is a solution of the equation (i.e., when substituting it for t the equation holds) and a, b and c are integers, -k <= a, b, c <= k. Notice that the equations he's looking for are not necessarily quadratic, i.e., a is allowed to be zero, as is b and/or c. |
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Definition |
| | | Class: | QuadraticEquations | | Method: | howMany | | Parameters: | int, int, int, int, int | | Returns: | long | | Method signature: | long howMany(int x, int y, int d, int z, int k) | | (be sure your method is public) |
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Constraints |
| - | x, y and z will be between -1000 and 1000, inclusive. |
| - | z will not be equal to 0. |
| - | d will be between 1 and 1000, inclusive. |
| - | k will be between 0 and 1000000 (106), inclusive. |
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Examples |
| 0) | |
| | | Returns: 3 | | The three possible equations are:
0*x2+0*x+0=0, 8*x2-20*x+11=0, -8*x2+20*x-11=0 |
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| 1) | |
| | | Returns: 1 | | The equation 0*x2+0*x+0=0 always holds. |
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| 2) | |
| | | Returns: 7 | | The value described is simply 2. The equations are 0*x2+0*x+0=0, 0*x2+1*x-2=0, 0*x2-1*x+2=0, 1*x2-1*x-2=0, -1*x2+1*x+2=0, 1*x2-2*x+0=0, -1*x2+2*x+0=0. |
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| 3) | |
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| 4) | |
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| 5) | |
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