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Solve Tango Puzzle

Tango is a puzzle that consists of a 6x6 grid partially filled with moons (M) and suns (S) and two lists of coordinate pairs, which we will call = and ×ばつ . The goal is to fill the rest of the grid following these rules:

Each cell must contain either M or S
There cannot be more than 2 M or S next to each other, either vertically or horizontally
Each row and column must contain the same number of M and S
Cells corresponding to a pair of coordinates in = must be of the same type
Cells corresponding to a pair of coordinates in ×ばつ must be of the opposite type

Input

Partially filled 6x6 grid
List of coordinate pairs (=) indicating the two cells must be equal
List of coordinate pairs (×ばつ) indicating the two cells must be different

You may receive the grid and pairs in any reasonable format.

Output: Solved puzzle

You may assume that each input has exactly one answer and that it can be solved via deduction, i.e. you should never have to make a guess.

Test cases

Notes:

The coordinates are 0-indexed
The leftmost top cell has coordinates (row, col) = (0,0)
. denotes an empty cell
Pairs are provided as follows:

(a,b), (c,d), (e,f), (g,h), ...
pair 1: (a,b) and (c,d)
pair 2: (e,f) and (g,h)
...

Test 1

Input

= (1,1), (2,1), (3,1), (3,2)×ばつ (1,2), (2,2), (1,3), (1,4), (2,3), (2,4), (3,3), (4,3), (3,4), (4,4), (4,1), (4,2) 
.MSSM.
M....M
S....M
S....S
M....S
.SMMS.

Output

MMSSMS
MSSMSM
SSMSMM
SMMSMS
MMSMSS
SSMMSM

Test 2

Input

= (2,2), (2,3), (2,3), (3,3)×ばつ (3,2), (3,3), (2,2), (3,2)
MS....
M...SM
SM..M.
.S..MS
SM...M
....MS

Output

MSMMSS
MSSMSM
SMSSMM
MSMSMS
SMSMSM
SMMSMS

Test 3

Input

= (0,1), (1,1), (1,0), (2,0), (2,5), (3,5), (3,0), (4,0), (4,0), (4,1)×ばつ (0,1), (0,2), (0,3), (0,4), (0,4), (1,4), (1,0), (1,1), (1,4), (1,5), (1,5), (2,5), (2,0), (3,0), (3,5), (4,5), (4,4), (4,5), (4,4), (5,4), (5,3), (5,4), (5,1), (5,2), (4,1), (5,1)
......
......
..S.S.
.M.S..
......
......

Output

SSMSMM
MSSMSM
MMSMSS
SMMSMS
SSMMSM
MMSSMS

Test 4

Input

= (1,2), (2,2), (2,1), (3,1), (3,2), (3,3), (4,0), (5,0), (5,1), (5,2), (5,3), (5,4), (4,5), (5,5)×ばつ (1,3), (2,3), (2,4), (3,4), (4,1), (4,2), (4,3), (4,4)
..SS..
......
......
......
......
......

Output

SMSSMM
MSMMSS
SMMSSM
SMSSMM
MSMMSS
MSSMMS

Answer*

# [05AB1E](https://github.com/Adriandmen/05AB1E/wiki/Commands), 53 [bytes](https://github.com/Adriandmen/05AB1E/wiki/Codepage)

 UþSDg„MSSsãδ.;.ΔS¶¡Ðø«εü3€ËàyD¢Ë«}s˜X6δδβèε2ô€ËNÊ}˜«P

First input \$[=,×]\$ as a pair of lists of pairs of 0-based integers; second input grid as a multi-line string with `0`s for empty cells.

Brute-force approach.

[(Don't) try it online.](https://tio.run/##yy9OTMpM/f8/9PC@YJf0Rw3zfIODiw8vPrdFz1rv3JTgQ9sOLTw84fCOQ6vPbT28x/hR05rD3YcXVLocWnS4@9Dq2uLTcyLMzm0Bwk2HV5zbanR4C1iF3@Gu2tNzDq0O@P8/OjraUMcoVifaCEwa6hiDSROwiDGYBLGNwWwTMGkMFjGBkoZg0ig2VkcBZJQhWIshWBmEBErFcikpKRkAXe5rwOVrAAS@XMFIVDBEMJjLINjXN9gAqBYA) (Will time-out.)

**Explanation:**

Step 1: Get all possible output-grids by replacing the `0`s with "M" or "S":

 U # Pop and store the first (implicit) input-pair in variable `X`
 þ # Keep the digits (the 0s) of the second (implicit) input-string
 S # Convert it to a list of 0s
 D # Duplicate this list
 g # Pop and push the length of the copy
 „MS # Push string "MS"
 S # Convert it to a pair of characters: ["M","S"]
 s # Swap so the length is at the top again
 ã # Cartesian product
 δ # Map over each list of M/S using the remaining list of 0s as argument:
 .; # Replace every first 0 one-by-one with the M/S in the second (implicit) input

[Try just step 1 online.](https://tio.run/##yy9OTMpM/f8/9PC@YJf0Rw3zfIODiw8vPrdFz/r//@joaEMdw1idaCMwaQwljWJjdRRAUkZgKRBpqGMMJk3AIsZg0gSsGMQ2AZPGYBETKGkIJoFGxXIpKSkZAK31NeDyNQACX65gJCoYIhjMZRDs6xtsAFQLAA)

Step 2: Keep the first valid result:

 .Δ # Find the first value that's truthy for:
 S # Convert the string to a list of characters
 ¶¡ # Split it on newlines to a 6x6 matrix
 Ð # Triplicate this matrix
 ø # Zip/transpose the top copy; swapping rows/columns
 « # Merge the top two lists together
 ε # Map over this list of rows+columns:
 ü3 # Get all overlapping triplets of each
 € # Inner map over each inner triplet
 Ë # Check that all characters are the same
 y # Push the current row/column again
 D # Duplicate it
 ¢ # Pop both and count how many times each character occurs
 Ë # Check that all those counts are the same as well
 « # Append the two checks to one-another
 # (only 1 is truthy in 05AB1E, so we're expecting "01" here)
 } # Close the map
 s # Swap to get the matrix again
 ˜ # Flatten it to a list
 X # Push the first input from variable `X`
 δδ # Apply triple-vectorized to the inner-most pairs,
 6 β # Convert these pairs from a base-6 list to a base-10 integer
 è # Use those values to index into the list
 ε # Map over the pair of lists of M/S:
 2ô # Split the current list into pairs
 € # Inner map over each inner pair:
 Ë # Check whether both items are the same
 NÊ # Check for each that it's NOT equal to the 0-based map-index
 }˜ # After the map: flatten the pair of bits
 « # Merge the two lists together
 P # Check that everything is truthy
 # (after which the found result is output implicitly)

[Verify the validator with a single given (valid) grid.](https://tio.run/##yy9OTMpM/f8/NPjQtkMLD084vOPQ6nNbD@8xftS05nD34QWVLocWHe4@tLq2@PScCLNzW4Bw0@EV57YaHd4CVuF3uKv29JxDqwP@/4@OjjbUMYzViTYCk8ZQ0ig2VkcBJGUElgKRhjrGYNIELGIMJk3AikFsEzBpDBYxgZKGYBJoVCyXkpKSr29wsG8wF5j05QKTQAooChIEkcEgQSADqBYA)

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