First clear solution for Dangerous Bishops by StefanPochmann - python coding challenges

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First solution in Clear category for Dangerous Bishops by StefanPochmann

def safe_squares(n, bishops):
    D, E = set(), set()
    for i, j in bishops:
        D.add(i + j)
        E.add(i - j)
    return sum(
        i + j not in D and
        i - j not in E
        for i in range(n)
        for j in range(n)
    )

May 22, 2024

Comments:

Selindian on May 27, 2024, 8:59 a.m.
I tried hard, but I don't get it. You are not using the classical board coordinates, thats for sure. I tried to understand your code using the example `4, [(2, 3), (0, 1)]`. I'll simplify it a little here: <ol> <li>`D, E` of this example are `{1, 5} {-1}`</li> <li>`i, j` results then in a list like `[(0, 0), (1, -1), (2, -2), (3, -3), (1, 1), (2, 0), (3, -1), (4, -2), (2, 2), (3, 1), (4, 0), (5, -1), (3, 3), (4, 2), (5, 1), (6, 0)]`</li> <li>The expression results in `[True, False, True, True, False, True, False, True, True, True, True, False, True, True, False, True]`</li> </ol> In total you return the sum of all Trues. So far so good. Although I can now understand what the code does, I unfortunately don't understand the idea behind it. For me, these are strange bishop/board coordinates. Can you please explain the approach behind it or at least point me in the right direction?

StefanPochmann on May 27, 2024, 11:37 a.m.
`i + j` and `i - j` just tell you the diagonals. For example when `i - j` is `0`, then the cell (i,j) is on the diagonal from top-left to bottom-right corner of the board. If it's `1`, then it's on the diagonal below that one. And `i + j` tells you which bottom-left-to-top-right diagonal it's on. So `D` and `E` are the sets of "/" diagonals and "\" diagonals where the bishops are. And then I just count all cells not on those diagonals.

Selindian on June 3, 2024, 10 p.m.
I took a pencil and paper and drew the example. Together with your explanation, it makes perfect sense to calculate the diagonals in this way. But for me the drawing with the calculations was really necessary to understand it properly. Thank you very much.

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