Description
Mini-Sudoku
A mini-sudoku is an array of 4×4 in which each entry is one of the four numbers 1,2,3,4. To be a valid
Sudoku, each row, each column, and each of the four quadrants must contain different numbers (as
shown in the figure above). Note that this Sudoku is already complete, you only have to check its
validity.
We ask you to write a program that will take as input a completed Sudoku (a 4×4 matrix) and will check
if this one is a valid Sudoku solution (true or false).
Question 1:
The Sudoku must be represented with a list of 4 lists, each list element representing one row of
the matrix.
(define sudoku1 ‘((2 1 4 3) (4 3 2 1) (1 2 3 4) (3 4 1 2)))
(define sudoku2 ‘((2 1 4 3) (4 3 2 1) (1 2 3 3) (3 4 1 2)))
You must solve the problem using the following functions:
a) Write the function different that returns true if all numbers in a list are different. [2]
(different ‘(1 3 6 4 8 0))
#t
Mini-Sudoku CSI 2120 page 2
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(different ‘(1 3 6 4 1 8 0))
#f
b) Write the function extract4Columns that extracts the 4 columns of the 4×4 Sudoku. [2]
(extract4Columns sudoku1)
((2 4 1 3) (1 3 2 4) (4 2 3 1) (3 1 4 2))
c) Write the function extract4Quadrants that extracts the 4 quadrants of the 4×4 Sudoku.
[2]
(extract4Columns sudoku1)
((2 1 4 3) (4 3 2 1) (1 2 3 4) (3 4 1 2))
d) Write the function merge3 that merges three lists. [2]
(merge3 ‘(1 3 6) ‘(5 4) ‘(1 2 3))
(1 3 6 5 4 1 2 3)
e) Write the function checkSudoku that verifies if a sudoku is valid by proceeding as
follows: [2]
• merges together the list of rows of the sudoku with the list of its columns (from
extract4Columns) and the lists of its quadrants (from extract4Quadrants);
• use map in order to call the function different on each element of the merged list;
• use the result of map in order to determine if the sudoku is valid and return the result
(true or false).
(checkSudoku sudoku1)
#t
(checkSudoku sudoku2)
#f
