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Rev

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Is there a single straight line in the matrix?

_{Inspired by Wzl}

Determine if a given square binary matrix has exactly one row or column consisting of entirely 1s, and the rest of the matrix is 0s.

For example, these are all true:

0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1
0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1

And these are all false:

0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0
1 1 1 1 1 1 1 0 1 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0

The reasons for the false ones:

More than one row
More than one row or column
There are 1s outside the "all 1s column"
There isn't a row or column of all 1s (describes the last 4)

You should take a square binary matrix of side length \$n \ge 2\$, in any reasonable format, and output 2 distinct, consistent values to indicate whether it has a single straight line. This is code-golf, so the shortest code in bytes wins.

Keep your golfing in your code, not your inputs/outputs. I'm very liberal with the I/O formats, including but not limited to:

A multiline string
A list of lines
A 2D list (or matrix) consisting of two distinct consistent values (e.g. 0/1, space/'*', 5/'(')
A flat array, and \$n\$, as separate arguments

Two distinct consistent values (e.g. 1/0) to indicate the output
Erroring/not erroring
Two families of values, one of which consists of values that are truthy in your language and the other falsey (for example, natural numbers and zero)

etc.

As a broad, general rule, so long as the input can be clearly understood and the outputs clearly distinguished, it's fair game.

Test cases

Input	Output
`000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 111111111`	true
`00000 11111 00000 00000 00000`	true
`1000 1000 1000 1000`	true
`01 01`	true
`0000000 1111111 0000000 1111111 0000000 0000000 0000000`	false
`01000 11111 01000 01000 01000`	false
`0100 1101 0100 0100`	false
`1000 0100 0010 0001`	false
`000 101 000`	false
`000 000 000`	false
`001 100 010`	false
`01 00`	false

Answer*

If this is an answer to a challenge…

…Be sure to follow the challenge specification. However, please refrain from exploiting obvious loopholes. Answers abusing any of the standard loopholes are considered invalid. If you think a specification is unclear or underspecified, comment on the question instead.
…Try to optimize your score. For instance, answers to code-golf challenges should attempt to be as short as possible. You can always include a readable version of the code in addition to the competitive one. Explanations of your answer make it more interesting to read and are very much encouraged.
…Include a short header which indicates the language(s) of your code and its score, as defined by the challenge.

More generally…

…Please make sure to answer the question and provide sufficient detail.
…Avoid asking for help, clarification or responding to other answers (use comments instead).

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\$\begingroup\$ Fails with inputs like 1101 0010 0000 0000. \$\endgroup\$

Bubbler
– Bubbler

2021年06月17日 04:35:13 +00:00
Commented Jun 17, 2021 at 4:35
\$\begingroup\$ Ugh, nice catch. \$\endgroup\$

Jonah
– Jonah

2021年06月17日 04:35:53 +00:00
Commented Jun 17, 2021 at 4:35
\$\begingroup\$ @Bubbler Fixed. I really wanted to find a solution with using diagonal /. sums, which produce a string of # ones and zero elsewhere iff valid input. But golfing that condition was cumbersome. Maybe you can make it work. \$\endgroup\$

Jonah
– Jonah

2021年06月17日 05:00:28 +00:00
Commented Jun 17, 2021 at 5:00
\$\begingroup\$ Why do you need to square element wise? The matrix always has 0 or 1 in it, and squaring either of those (or any product involving those) does nothing \$\endgroup\$

caird coinheringaahing
– caird coinheringaahing ♦

2021年06月17日 13:56:57 +00:00
Commented Jun 17, 2021 at 13:56
2

\$\begingroup\$ Fails with 1100 1100 0000 0000 – which suggests that it is the same algorithm as theorist's answer, that also fails with this case. :-) \$\endgroup\$

xash
– xash

2021年06月17日 15:16:51 +00:00
Commented Jun 17, 2021 at 15:16

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