How to enumerate all possibilities for brute-force algorithm? -


this question may not specified, think important. when want solve optimization problem , not familiar dynamic programming method, first idea comes mind.

i can give simple examples:

  • get min element of list (very simple)
  • list permutation of set
  • list subset of set

these problem have mature method. there problem not clear:

  • list edit distance of 2 string (i mean not shortest 1 of edit operation)
  • list common subsequence of 2 sequence
  • list possibilities of parenthesizing matrix chain multiplication

i have no idea solving these problems brute-force method. question is:

is there systematic generic method list possibilities brute-force algorithm?

backtracking 1 of general methods finding solutions problem. per wikipedia,

backtracking general algorithm finding (or some) solutions computational problem, incrementally builds candidates solutions, , abandons each partial candidate c ("backtracks") determines c cannot possibly completed valid solution.

the classic textbook example of use of backtracking 8 queens puzzle, asks arrangements of 8 chess queens on standard chessboard no queen attacks other.

two of problems mention,
• list common subsequence of 2 sequence
• list possibilities of parenthesizing matrix chain multiplication
can handled using backtracking. not sure edit-distance question.


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