Comments on Knight safe squares
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Knight safe squares
Given a chess board with some knights on it, say how many squares are neither attacked by a knight nor containing a knight.
Input
- An 8 by 8 grid where each square is either a knight or empty
- The input can contain any number of knights from 0 to 64
- You may choose to take input with any 2 distinct characters (or numbers or Booleans - there is no restriction to string input) representing a knight and an empty square
- You may take input in the format of your choice provided it does not provide additional information that would help solve the challenge
- For example, if you find it more convenient you could take input as a single 64 bit integer, where each bit is 1 for a knight and 0 for an empty square
Output
- A number from 0 to 64, indicating the number of squares that satisfy both of:
- The square does not contain a knight
- The square is not a knight's move away from a knight.
A knight's move is either of:-
2 squares horizontally (left or right) and 1 square vertically (up or down)
-
1 square horizontally (left or right) and 2 squares vertically (up or down)
(thanks to Wikipedia)
-
Example
The following example input has knights represented by N and empty squares represented by *.
********
********
**N*****
********
********
********
******N*
N*******
Here it is again with attacked empty squares marked as a. The required output is the number of remaining squares (the number of squares still showing *).
*a*a****
a***a***
**N*****
a***a***
*a*a*a*a
*a**a***
**a***N*
N***a***
So for this example, the output would be 47.
Test cases
String input test cases
Test case inputs are given as 8 strings of 8 characters, followed by the output as an integer. Knights are represented by N and empty squares are represented by *.
[
[
"********",
"********",
"********",
"********",
"********",
"********",
"********",
"********",
],
64
],
[
[
"NNNNNNNN",
"NNNNNNNN",
"NNNNNNNN",
"NNNNNNNN",
"NNNNNNNN",
"NNNNNNNN",
"NNNNNNNN",
"NNNNNNNN",
],
0
],
[
[
"N*N*N*N*",
"*N*N*N*N",
"N*N*N*N*",
"*N*N*N*N",
"N*N*N*N*",
"*N*N*N*N",
"N*N*N*N*",
"*N*N*N*N",
],
0
],
[
[
"N***N***",
"*N***N**",
"**N***N*",
"***N***N",
"N***N***",
"*N***N**",
"**N***N*",
"***N***N",
],
16
],
[
[
"N*******",
"********",
"********",
"********",
"********",
"********",
"********",
"********",
],
61
],
[
[
"******N*",
"********",
"********",
"********",
"********",
"********",
"********",
"********",
],
60
],
[
[
"********",
"********",
"********",
"********",
"********",
"********",
"********",
"*****N**",
],
59
],
[
[
"********",
"********",
"********",
"********",
"********",
"********",
"*N******",
"********",
],
59
],
[
[
"********",
"**N*****",
"********",
"********",
"********",
"********",
"********",
"********",
],
57
],
[
[
"********",
"********",
"**N*****",
"********",
"********",
"********",
"********",
"********",
],
55
],
[
[
"********",
"********",
"****N***",
"********",
"***N****",
"********",
"********",
"********",
],
48
],
[
[
"********",
"********",
"***N****",
"*****N**",
"**N*****",
"****N***",
"********",
"********",
],
36
],
[
[
"NNNNNNNN",
"NNN*N*NN",
"NN*NNN*N",
"NNNN*NNN",
"NN*NNN*N",
"NNN*N*NN",
"NNNNNNNN",
"NNNNNNNN",
],
1
],
[
[
"NNNNNNNN",
"NNN*N*NN",
"N***NN*N",
"*NNN*NNN",
"NN*NNN*N",
"*NN***NN",
"N*N*NNNN",
"NNNNNNNN",
],
2
],
[
[
"*NNNNNNN",
"NN*NNNNN",
"N*NNNNNN",
"NNNNNNNN",
"NNNNNNNN",
"NNNNNNNN",
"NNNNNNNN",
"NNNNNNNN",
],
1
],
[
[
"NNNNNN*N",
"NNNN*NNN",
"NNNNN*N*",
"NNNNNNNN",
"NNNNNNNN",
"NNNNNNNN",
"NNNNNNNN",
"NNNNNNNN",
],
1
],
[
[
"NNNNNNNN",
"NNNNNNNN",
"NNNNNNNN",
"NNNNNNNN",
"NNNNNNNN",
"NNNN*N*N",
"NNN*NNN*",
"NNNNN*NN",
],
1
],
[
[
"NNNNNNNN",
"NNNNNNNN",
"NNNNNNNN",
"NNNNNNNN",
"*N*NNNNN",
"NNN*NNNN",
"N*NNNNNN",
"NNN*NNNN",
],
1
],
[
[
"*NNN*NNN",
"NN*NNNNN",
"*NNN*NNN",
"N*N*NNNN",
"NNNNNNNN",
"NNNNNNNN",
"NNNNNNNN",
"NNNNNNNN",
],
1
],
[
[
"N*N*NNNN",
"*NNN*NNN",
"NN*NNNNN",
"*NNN*NNN",
"N*N*NNNN",
"NNNNNNNN",
"NNNNNNNN",
"NNNNNNNN",
],
1
],
[
[
"********",
"********",
"**N*****",
"********",
"********",
"********",
"******N*",
"N*******",
],
47
]
Integer input test cases
If you choose to take input as a 64 bit unsigned integer, with each square being represented by a single bit, these are the equivalent of the test cases shown above, but with integer input.
Input which treats 1 bits as knights will be called one_knight_input, and input which treats 0 bits as knights will be called zero_knight_input. Since both of these are valid input types, both are included in the test cases so you can choose which to use.
Each test case is in the format one_knight_input : zero_knight_input : output.
0 : 18446744073709551615 : 64
18446744073709551615 : 0 : 0
12273903644374837845 : 6172840429334713770 : 0
9819010546270478865 : 8627733527439072750 : 16
9223372036854775808 : 9223372036854775807 : 61
144115188075855872 : 18302628885633695743 : 60
4 : 18446744073709551611 : 59
16384 : 18446744073709535231 : 59
9007199254740992 : 18437736874454810623 : 57
35184372088832 : 18446708889337462783 : 55
8796361457664 : 18446735277348093951 : 48
17609903308800 : 18446726463806242815 : 36
18441077155848519679 : 5666917861031936 : 1
18440988645153550335 : 5755428556001280 : 2
9214294468855857151 : 9232449604853694464 : 1
18300371588261871615 : 146372485447680000 : 1
18446744073708891899 : 659716 : 1
18446744071024132079 : 2685419536 : 1
8637754208117850111 : 9808989865591701504 : 1
12643820184012849151 : 5802923889696702464 : 1
35184372089472 : 18446708889337462143 : 47
Explanations are optional, but I'm more likely to upvote answers that have one.
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