Modelling Problems and Solutions
How to represent the problem in computer world, and how to represent its solution.
e.g.
Problem: A quadratic equation with one unknown can be represented by an expression:
a*x*x+b*x+c == 0
While its solution can be represented by a number x.
Problem: The chessboard of Eight Queens Problem can be represented by a two dimensional array with [8][8], with a[i][j] == 0 representing no queen and a[i][j]==1 representing a queen on position i,j. While its solution can be represented by a chessboard configuration such that no queen conflict with any other queen.
A General Algoarithm to solve an abstract problem is:
- 1, set S be a solution space, that is the set of all possible solutions;
- 2, for every possible solution s in S,
- 2.1, check whether s is really a solution of the problem
- 2.2, if s is a valid solution of the problem, output the solution s;
- 2.3, if want to find next solution, go to step 2;
- 3, end.
This is a brute-force strategy for searching all possible solutions in solution space.
pros: simple
cons: low efficiency
Examples:
