Computing Science 1P

Computing Science 1P

Large Group Tutorial 19

Simon GayDepartment of Computing Science

University of Glasgow

2006/07

2006/07 Computing Science 1P Tutorial 19 - Simon Gay 2

Remember

No lecture on Friday this week.

After the Easter break, Monday 9th April is also a holiday –no labs that day – go to another lab that week if you needhelp.


Example: Sudoku

You are probably familiar with sudoku puzzles:

Each row, column and 3x3 square must be filled in to containthe digits 1 – 9.


Data Structure for Sudoku

The first step in designing a program to work with sudokupuzzles is to choose a data structure.

We have the usual options…


What kind of data structure?

• Based on lists• Based on dictionaries• Something else• Don't know


Data Structure for Sudoku

A sudoku grid is basically a 9x9 matrix, so the natural datastructure is a list of lists. (Could use a dictionary, but little point.)

We can either use a list of 9 rows, or a list of 9 columns.Each row or column is itself a list of 9 numbers.

It doesn't matter whether we choose rows or columns, as longas we remember which it is.

Whatever we do, dealing with the 3x3 squares will be a littleawkward.


Sudoku as a list of rows[ [0,0,3,0,0,9,4,6,0], [0,0,6,0,0,0,1,0,0], [0,0,0,6,3,2,0,0,0], [5,0,0,0,0,1,0,0,2], [0,2,4,0,0,0,6,8,0], [8,0,0,2,0,0,0,0,7], [0,0,0,5,4,7,0,0,0], [0,0,2,0,0,0,8,0,0], [0,4,5,1,0,0,9,0,0] ]

0 represents an empty square.


Checking a sudoku grid

A key operation in any implementation of sudoku is checkingwhether or not a particular grid is a solved puzzle.

A grid is a solved puzzle if all of the following are true:- each row contains the digits 1 – 9- each column contains the digits 1 – 9 - each 3x3 square contains the digits 1 – 9

Assuming that the whole grid is the correct size, theseconditions obviously also guarantee that the digits 1 – 9 appear once each in every row, column and 3x3 square.


Question for discussion

Can you think of a useful function to define, in order toimplement a test for a solved puzzle?

A grid is a solved puzzle if all of the following are true:- each row contains the digits 1 – 9- each column contains the digits 1 – 9 - each 3x3 square contains the digits 1 – 9


A useful function

Are you thinking what I'm thinking?

My idea is to define a function check which, given a list of numbers, checks whether or not the list contains the numbers 1 – 9 exactly once each.

Exercise (discussion): how would you define check ?

First think of an idea, then think about how to implement theidea. Write a Python definition if you have time.


check – idea 1

Take advantage of the fact that Python provides a sort methodfor lists. If we sort a list, we can then easily check whether itcontains the numbers 1 – 9.

def check(x): x.sort() # into increasing numerical order return x == [1,2,3,4,5,6,7,8,9]


Can you see any problems with check ?

• Yes• No• Don't know


check – idea 1

The problem is that x.sort() modifies x and this changepersists after the function (see Lecture 16).

To use this function we would have to be very careful aboutwhat we give it as a parameter.

A safe alternative:

def check(x): y = x + [] # creates a new list y.sort() # into increasing numerical order return y == [1,2,3,4,5,6,7,8,9]


check – idea 2

Another idea is to check that the list contains 1, check that itcontains 2, and so on; if all of these are true, then return true.

This suggests another function:

def contains(x,v): # return True if v occurs in x, # return False otherwise

Exercise (discussion): define contains


contains

def contains(x,v): for a in x: if a == v: return True return False


check using contains

def check(x): i = 1 result = True while i <= 9: if not(contains(x,i)): result = False i = i + 1 return result


check using contains : alternative

def check(x): i = 1 while i <= 9: if not(contains(x,i)): return False i = i + 1 return True


check using contains : alternative 2

def check(x): for i in range(1,10): if not(contains(x,i)): return False return True


Have we forgotten anything?



check using contains

Our definitions will also return True when called with the list

[1,2,3,4,5,6,7,8,9,1]

We have a choice:

1. Note carefully that check only works when its parameterhas length 9, and make sure we call it properly

2. Modify the definition: def check(x): if len(x) != 9: return False for i in range(1,10): if not(contains(x,i)): return False return True


Checking a sudoku grid

Now that we have the function check, how do we use it tocheck a whole grid?

We need to check the rows, the columns, and the 3x3 squares.In each case we can extract the relevant values from the grid.

So, let's define functions getRow, getCol, getSquare

Recall that the grid is represented by a list of rows.

def getRow(grid,row): return grid[row]


Exercise (discussion)

[ [0,0,3,0,0,9,4,6,0], [0,0,6,0,0,0,1,0,0], [0,0,0,6,3,2,0,0,0], [5,0,0,0,0,1,0,0,2], [0,2,4,0,0,0,6,8,0], [8,0,0,2,0,0,0,0,7], [0,0,0,5,4,7,0,0,0], [0,0,2,0,0,0,8,0,0], [0,4,5,1,0,0,9,0,0] ]

Define getCol(grid,col)


getCol

def getCol(grid,col): c = [] for i in range(9): c = c + [grid[i][col]] return c



[ [0,0,3,0,0,9,4,6,0], [0,0,6,0,0,0,1,0,0], [0,0,0,6,3,2,0,0,0], [5,0,0,0,0,1,0,0,2], [0,2,4,0,0,0,6,8,0], [8,0,0,2,0,0,0,0,7], [0,0,0,5,4,7,0,0,0], [0,0,2,0,0,0,8,0,0], [0,4,5,1,0,0,9,0,0] ]

Define getSquare(grid,row,col)

row=1,col=2


getSquare

def getSquare(grid,row,col): c = [] for i in range(2): for j in range(2): c = c + [grid[row*3+i][col*3+j]] return c

row=1,col=2

6 7 8345



Using check, getRow, getCol, getSquare, define checkGrid.


checkGrid

def checkGrid(grid): for i in range(9): if not(check(getRow(grid,i))): return False for i in range(9): if not(check(getCol(grid,i))): return False for i in range(2): for j in range(2): if not(check(getSquare(grid,i,j))): return False return True


Should we add a check that grid is a 9x9 matrix?


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