Ken-Ken Helper

Ken-Ken is a puzzle game similar to Sudoku. It consists board filled with digits 1-9 and can have no two identical digits in the same row or column. The board is then split into jigsaw-like shapes (cages), each with a target number and mathematical operator, for which the digits that fill it (order doesn't matter) must match.

• For addition +, the digits must sum to target.
• For multiplication *, the digits must multiply to target.
• For subtraction -, the digits must have a difference of target. Only cages of size 2 are allowed for subtraction.
• For division /, the digits must have a quotient of target. Only cages of size 2 are allowed for division.
• For no operator "", the digits can fill it for any of the operators. If a cage has more than 2 cells, it can only have operators of + or *.

For example, with and operator of / and target of 4, with a 2x1 cage, possible digits to fill it are 2 and 8.

The cage shape is indicated by 1's. Provided a cage, target, and operator, your goal is to return an array of all possible digit combinations (as a JSON string).

Example

cage = [
  [0, 1],
  [1, 1]
]

target = 24, and operator = "*", the output should be:

"[[1,3,8],[1,4,6],[2,2,6],[2,3,4]]"

Inputs

• cage ([][]integer)

The shape of the cage indicated by 1's and 0's. 1 indicates a cell of the cage.

Guaranteed constraints:

• 1 ≤ cage.length ≤ 3

• 1 ≤ cage[i].length ≤ 6

• 2 ≤ cage size (# of 1's) ≤ 8

• target (integer)

• operator (string)

Operator will be +, -, *, / or ""

To match the tests expected output, sort both the inner and outer arrays and then return as a JSON string.