Question

I’m programming physics for a small 2D game, and I need to check every object on the screen against every other object on the screen. That’s O(N^2), and I don’t really like that.

What I had in mind:

for (var i = 0; i < objects.length; i ++)
    for (var j = 0; j < objects.length; j ++)
        if (collide(objects[i], objects[j])) doStuff(objects[i], objects[j]);

This is unnecessary, and I will check the same objects against one another multiple times. How can I avoid that? I thought of having a matrix, which would be n*n (given that n is the number of objects), and then each time I visit a pair of objects I would to this:

visited[i][j] = 1;
visited[j][i] = 1;

And then, I would always know which pair of objects I visited.

This would work, however, I would, again, need to set all of those cells, n*n times, just to set them all to 0 at start! Maybe, I could set everything to [], but this still doesn’t seem like a viable solution to me. Is there something better?

Obviously, my language of choice is Javascript, but I know C, C++ and Python relatively fluently, so you can answer in them (although Javascript, C and C++ have almost the same syntax).

Answer 1

You won’t avoid O(n^2), but you can cut it down by half:

for (var i = 0; i < objects.length; i ++)
    for (var j = i; j < objects.length; j ++)
        if (collide(objects[i], objects[j])) doStuff(objects[i], objects[j]);

Assuming collision is symmetric. If it’s also reflexive, and testing for collision is expensive, you can move doStuff(object[i], object[i]) out of the inner loop to avoid testing for collision and start the inner loop from i+1