Auto Math Puzzle Solver

The project 2 of subject COMP30020 Declarative Programming, an auto math puzzle solver written in prolog.

Overview

This program aims to provide a predicate called puzzle_solution/1 to automatically solve the given puzzle efficiently and correctly. puzzle_solution/1 would fill in the puzzle with correct solution if there is a correct solution. Otherwise, puzzle_solution/1 would give false.

Importatn Prolog library predicates

#=/2

label/1

Maths Puzzle

Game Description

A maths puzzle is a square grid of squares, each to be filled in with a single digit 1–9 (zero is not permitted) satisfying these constraints:

each row and each column contains no repeated digits;
all squares on the diagonal line from upper left to lower right contain the same value; and
the heading of reach row and column (leftmost square in a row and topmost square in a column) holds either the sum or the product of all the digits in that row or column.

Note that the row and column headings are not considered to be part of the row or column, and so may be filled with a number larger than a single digit. The upper left corner of the puzzle is not meaningful.

Format

When the puzzle is originally posed, most or all of the squares will be empty, with the headings filled in. The goal of the puzzle is to fill in all the squares according to the rules. A proper maths puzzle will have at most one solution.

Here is an example puzzle as posed (left) and solved (right):

 ____ ____ ____ ____    ____ ____ ____ ____ 
|    | 14 | 10 | 35 |  |    | 14 | 10 | 35 |
| 14 |    |    |    |  | 14 |  7 |  2 |  1 |
| 15 |    |    |    |  | 15 |  3 |  7 |  5 |
| 28 |    |    |    |  | 28 |  1 |  1 |  7 |
 ---- ---- ---- ----    ---- ---- ---- ----

The 'Puzzle' referred to in predicates defined below is an NxN list of lists of equal length that fit the specification above and below.

Input Format

A maths puzzle (Puzzle) will be represented as a lists of lists, each of the same length, representing a single row of the puzzle. The first element of each list is considered to be the header for that row. Each element but the first list in the puzzle is considered to be the header of the corresponding column of the puzzle. The first element of the first element of the list is the corner square of the puzzle, and thus is ignored."

Assumptions

Assumption 1: "When puzzle_solution/1 is called, its argument will be a proper list of proper lists, and all the header squares of the puzzle (plus the ignored corner square) are bound to integers. Some of the other squares in the puzzle may also be bound to integers, but the others will be unbound."

Assumption 2: "This code will only be tested with proper puzzles, which have at most one solution. If the puzzle is not solvable, the predicate should fail, and it should never succeed with a puzzle argument that is not a valid solution."

Result

Correctness : 70/70
Code Quality: 28/30
Total : 98/100

BeginnerRudy/COMP30020-Math_Puzzle_Solver