Atcoder Typical 90 - Not Too Bright (★2)

It’s the day after Valentines Day, and my gf is still not in the same country… That’s a one sad sad sentence.

Forget about it and grind!

Today’s question is hard to understand.

If we were given the height and the width of a display, return how many of the LEDs on that display can be lit at the same time under a specific condition: If there exists a 2x2 region of 4 LEDs, no more than 1 LED can be lit.

Understanding this condition was the tricky bit of today’s problem. If we had a 2x3 matrix, then we’d have a display like the following:

1
# . #
2
. . .

But not a display like this:

1
# . #
2
. # .

Since the condition does not hold. That means for a given row, we can have alternative LEDs lit at the same time. Then with each row, we also need to alternate from a row with lit LEDs and no lit LEDs. But writing a solution for only this would not be enough.

This is where it took me a while to realize that if the height or width is just 1, then this condition can’t hold in the first place. A 2x2 section must exit for this condition to even exist. So for this special case, we can have any and all the LEDs lit at the same time!

So what do we get?

With this process of checking our conditions, we can get the following solution. We can do a quick check for the height and width to check the edge case, followed by the actual calculation under the condition.

1
H, W = map(int, input().split())
2
if H == 1 or W == 1:
3
    print(W if H == 1 else H)
4
else:
5
    perH = (H-1)//2 + 1
6
    perC = (W-1)//2 + 1
7
    print(perH * perC)

Both time and space complexity for this is a constant O(1) since the only variables saved are for the height and width, and no operations relative the input size are used.