Question18-countSquarePairs.txt

Question 18
Define a square pair to be the tuple <x,y> where x and y are positive, non-zero integers,
x<y and x+y is a perfect square. A perfect square is an integer whose square root is also
an integer, e.g 4,9,16 are perfect squares but 3,10,and 17 are not.

Write a function named countSquarePairs that takes an array and returns the number of square
pairs that can be constructed from the elements in the array.
For example, if  the array is {11,5,4,20} the function would return 3 because the only square
pairs that can be constructed from those numbers are <5,11>,<5,20> and <4,5>.
You may assume that there exists a function named isPerfectSquare that returns 1 if
its argument is a perfect square and 0 otherwise. isPerfectSquare(4) returns 1 and
isPerfectSquare(8) returns 0.
If you are programming in Java or C#, the function signature is
int countSquarePairs(int[] a)
You may assume that there are no duplicate values in the array. ie you don't have to deal
with an array like {2,7,2,2}.

examples:
 -------------------|--------|-----------------------------------------------------------------------
| if a is           | return | reason                                                                |
|-------------------|--------|-----------------------------------------------------------------------|
| {9,0,2,-5,7}      | 2      | The square pairs are <2,7> and <7,9>. Note that <-5,9> and <0,9> are  |
|                   |        | not square pairs, even though they sum to perfect squares, because    |
|                   |        | both members of a square pair have to be greater than 0. Also <7,2>   |
|                   |        | and <9,7> are not square pairs because the first number has to be less|
|                   |        | than the second number.                                               |
|-------------------|--------|-----------------------------------------------------------------------|
| {9}               | 0      | The array must have at least 2 elements                               |
 -------------------|--------|-----------------------------------------------------------------------