1. 2-D Lists Taken from notes by Dr. Neil Moore
CS 115 Lecture
2-D Lists
Taken from notes by Dr. Neil Moore

2. Nested loops
Notice that in program 2 you had essentially a loop inside another loop: the main function had a loop that played the whole game, and outside the loop it had another loop, for playing multiple games.
This is called a nested loop.
Which of the two loops iterates more times?
the inner loop
Once the inner loop finishes (game finishes), go to the next iteration of the outer loop (play another game).
What if something should need to happen before/after each round?
Put it inside the outer loop but not in the inner loop

3. Counting iterations
Let’s use nested loops to print out a multiplication table.
mult-table.py

4. Counting iterations How any times did we print a number?
10 times in the first iteration
10 times in the second iteration
And so on…
10 x 10 = 100 times altogether
When the inner loop’s sequence is the same each time:
Total iterations = outer iterations x inner iterations
If the inner loop doesn’t execute the same number of times each time, add up all the inner iterations to find the total
for i in range(5):
for j in range(i): # note, this is an “i“ not a 1
print(i,j)
How many times does the print execute? = 10 times

5. Two-dimensional lists
Nested loops are particularly useful when we have nested lists
That is, a list that contains other lists.
That is also called a two-dimensional list
Why would we use a 2D list?
For storing a table of data
Anything you would put in a spreadsheet
Weather forecasts: row = city, column = days, data in cells = temperatures
Grade book: row = student, column = assignment, data in cells = grade
Or a game board
For example, an 8x8 chess board
Make a list of 8 rows
Each row is a list of 8 squares
Matrices
Very useful for representing pixels in a graphics window
Used all the time for “big data”

6. Row-major order
In this class we’ll look at a 2-D list as “row-major” order.
That means that the rows are the horizontal elements of the table, and they are numbered from 0 at the first row, increasing down to the bottom row
And columns are the vertical components of the table. Each column is numbered from 0 at the left end, increasing as you move to the right.
When you refer to a single element of a 2-D list, the row is given first, then the column “matrix[3][2]” is in the 4th row and 3rd column
Typically you put the row on the outer loop and the column on the inner loop to process each element of the 2-D list

7. Creating 2D lists There are (at least) two ways to make a 2D list
Hard code it
table = [ [ 1, 2, 3 ], [ 4, 5, 6 ], [ 7, 8, 9 ]]
Row 0 is [ 1, 2, 3 ], etc.
Or build it a row at a time - this method is MUCH more flexible!!
First, create an empty list to hold the rows, table = [ ]
Then create the row lists and append them to the outer list
for rownum in range(5): # 5 rows
row = [0 ] * 3 # 3 columns
table.append(row)
Why not just say this? table = [ [ 0, 0, 0 ] ] * 5
That makes all the rows aliases of each other! You really only have ONE row, not 5!!

8. Accessing 2D lists
Suppose you have a list with 5 rows and 3 columns, called table.
How do we access the element in the second row, first column?
Take it a step at a time (for explanation, not necessary every time):
How do you access the second row? row = table[1]
What type is the second row? a ONE D list
So now to get to the first column in the second row, element = row[0]
Or, to put it together as element = table[1][0]
Summary: to access an element in a 2D list, use
list2D[row][column]
This is a variable name just like x. It can be assigned to, printed, compared to another variable or constant, used in calculations, etc.

9. Traversing a 2D list
To iterate over the contents of a 2D list, we need a nested loop
Outer loop: for each row
Inner loop: for each column in that row
If we only need the elements, not the subscripts:
for row in table: # row is a 1D list
for element in row:
process the element
If we DO need subscripts, use ranges instead
for rowno in range(len(table)): # len = number of rows
for colon in range(len(table[rowno])): #len of one row
process element in position [rowno][colno]

10. Tables with “rough edges”
The previous slides assumed that each row of a table was the same length, “5 rows by 3 columns”. This IS the way 2-d lists are formed in other languages.
But in Python they don’t have to be! Each row can have a different length if you want it to. They all start numbering at the zeroth column, as usual, but one row could be 5 elements, one row could be one element, one could be 20!
This is easily handled by the code that was shown on the previous slide, either version (whether you need the subscripts or you don’t)

11. So be careful!
It is easy to assume that a 2-d list is square (same number of rows and columns)
for i in range(len(table)):
for j in range(len(table)): # NOTE: this is different from the previous slides
print(table[i][j])
This code would work as long as it was a square table!
If you assumed that all rows were the same length,
for j in range(len(table[0])): # NOTE: this is different from above!
This code would work as long as the assumption is true!

12. Changing a 2D list element
If you need to change an element, you need its subscripts!
Suppose you just wanted to set all elements of an existing table to 0
for r in table: # r is a list that is one row
for el in r: # el is one element in the row
el = 0
Does NOT accomplish what you want to do! It just sets a temporary variable el to zero, over and over!
What you need is
for i in range(len(table)):
for j in range(len(table[i])):
table[i][j] = 0
This refers to the actual table element! And is what you want!

13. A large example: tic-tac-toe
We’ll use a 2D list to represent a tic-tac-toe board.
Each element in the list will be “X”, “O” or a space
Use loops to print the board and to check whether someone won
tictactoe.py