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Range is working slow. So for solution on python requre more advanced approaches. Also you can reduce search diapason, enough iterate one coordinate quartal for each vertex.
or just replace cpython with pypy, because in this case (lots of arithmetic operations) pypy is much faster. Tried to launch object_oriented_program's solution with test
935 938
:python 2.7 — 1500 ms
pypy 2.5 — 77 ms
i.e. 20 times faster.
Greetings. Your solution is 2000**2 + 2000*2 which is 8*10^6 operations. Python can hardly make more than 7*10^6 operations per second, so your solution must be just above the threshold of 1 second.
You can simply iterate over < 0, a > not < - a, a > and if you get match, add (i, j) and (i, - j) Also, count once and keep a * a, i * iandb * b in separate variables.