问题
Following Find string to regular expression programmatically?, we assume that it takes linear time to find a string that matches a regex. My intiution says that we can solve a regex crossword programmatically too, right?
If yes, what will be the time complexity of solving a NxM regex crossword?
Example:
回答1:
It's NP hard, even if you disallow backreferences. There's a simple mapping from the exact set cover problem to this problem.
If you have sets S[1], S[2], ..., S[n] (with union S), and without loss of generality, the sets contain all the numbers 1...N for some N. Represent the S[i] as a string of length N, with 1 in the k'th place if k is in S[i], and 0 otherwise.
Let the columns of your regexp puzzle be all the same -- 0*10*, and the k'th row be "(S[k])|(0*)".
For example, if S[1] = {1, 4}, S[2] = {2}, S[3] = {3}, and S[4] = {2, 3}, then the puzzle would be:
0*10* 0*10* 0*10* 0*10*
1001|0*
0100|0*
0010|0*
0110|0*
A solution to this regexp puzzle is an exact cover of {1, 2, 3, 4} with the S[i].
来源：https://stackoverflow.com/questions/46279406/regex-crossword-solver