Dangerous Bishops

Dangerous Bishops

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The generalized square chessboard has been taken over by an army of bishops, each bishop represented as a two-tuple (row, col) (0-base indexing) of the coordinates of the square that the bishop stands on. Given the board size n and the list of bishops on that board, count the number of safe squares that are not covered by any bishop.

Let's look at the case 4, [(2, 3), (0, 1)], which is 11.

example

Click this line if you need a hint

To check whether two squares (r1, c1) and (r2, c2) are reachable from each other in a single bishop move, the expression abs(r1-r2)==abs(c1-c2) checks that the horizontal distance between those squares equals their vertical distance, which is both necessary and sufficient for those squares to lie on the same diagonal. This way you don’t have to separately rewrite the essentially identical block of logic four times, but one test handles all four diagonal directions in one swoop.

Input: Two arguments. Integer (int) and list of tuples of two integers.

Output: Integer.

Examples:

assert safe_squares(10, []) == 100
assert safe_squares(4, [(2, 3), (0, 1)]) == 11
assert safe_squares(8, [(1, 1), (3, 5), (7, 0), (7, 6)]) == 29

The mission was taken from Python CCPS 109. It is taught for Ryerson Chang School of Continuing Education by Ilkka Kokkarinen

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