# CMU 15-112: Fundamentals of Programming and Computer Science Class Notes: 2d Lists

1. Creating 2d Lists
1. Static Allocation
# create a 2d list with fixed values (static allocation) a = [ [ 2, 3, 4 ] , [ 5, 6, 7 ] ] print(a)

2. Dynamic (Variable-Length) Allocation
1. Wrong: Cannot use * (Shallow Copy)
# Try, and FAIL, to create a variable-sized 2d list rows = 3 cols = 2 a = [  * cols ] * rows # Error: creates shallow copy # Creates one unique row, the rest are aliases! print("This SEEMS ok. At first:") print(" a =", a) a = 42 print("But see what happens after a=42") print(" a =", a)

2. Right: Append Each Row
# Create a variable-sized 2d list rows = 3 cols = 2 a=[] for row in range(rows): a += [*cols] print("This IS ok. At first:") print(" a =", a) a = 42 print("And now see what happens after a=42") print(" a =", a)

3. Even Better: make2dList()
def make2dList(rows, cols): a=[] for row in range(rows): a += [*cols] return a rows = 3 cols = 2 a = make2dList(rows, cols) print("This IS ok. At first:") print(" a =", a) a = 42 print("And now see what happens after a=42") print(" a =", a)

4. Another good option: use a list comprehension
rows = 3 cols = 2 a = [ ( * cols) for row in range(rows) ] print("This IS ok. At first:") print(" a =", a) a = 42 print("And now see what happens after a=42") print(" a =", a)

2. Getting 2d List Dimensions
# Create an "arbitrary" 2d List a = [ [ 2, 3, 5] , [ 1, 4, 7 ] ] print("a = ", a) # Now find its dimensions rows = len(a) cols = len(a) print("rows =", rows) print("cols =", cols)

3. Nested Looping over 2d Lists
# Create an "arbitrary" 2d List a = [ [ 2, 3, 5] , [ 1, 4, 7 ] ] print("Before: a =", a) # Now find its dimensions rows = len(a) cols = len(a) # And now loop over every element # Here, we'll add one to each element, # just to make a change we can easily see for row in range(rows): for col in range(cols): # This code will be run rows*cols times, once for each # element in the 2d list a[row][col] += 1 # Finally, print the results print("After: a =", a)

4. Copying 2d Lists
1. Wrong: Cannot use copy.copy (shallow copy)
import copy # Create a 2d list a = [ [ 1, 2, 3 ] , [ 4, 5, 6 ] ] # Try to copy it b = copy.copy(a) # Error: creates shallow copy # At first, things seem ok print("At first...") print(" a =", a) print(" b =", b) # Now modify a a = 9 print("But after a = 9") print(" a =", a) print(" b =", b)

2. Right: use copy.deepcopy
import copy # Create a 2d list a = [ [ 1, 2, 3 ] , [ 4, 5, 6 ] ] # Try to copy it b = copy.deepcopy(a) # Correct! # At first, things seem ok print("At first...") print(" a =", a) print(" b =", b) # Now modify a a = 9 print("And after a = 9") print(" a =", a) print(" b =", b)

3. Limitations of copy.deepcopy
a = [*2]*3 # makes 3 shallow copies of (aliases of) the same row a = 42 # appears to modify all 3 rows print(a) # prints [[42, 0], [42, 0], [42, 0]] # now do it again with a deepcopy import copy a = [*2]*3 # makes 3 shallow copies of the same row a = copy.deepcopy(a) # meant to make each row distinct a = 42 # so we hope this only modifies first row print(a) # STILL prints [[42, 0], [42, 0], [42, 0]] # now one more time with a simple deepcopy alternative that does # what we thought deepcopy did... def myDeepCopy(a): if (isinstance(a, list) or isinstance(a, tuple)): return [myDeepCopy(element) for element in a] else: return copy.copy(a) a = [*2]*3 # makes 3 shallow copies of the same row a = myDeepCopy(a) # once again, meant to make each row distinct a = 42 # so we hope this only modifies first row print(a) # finally, prints [[42, 0], [0, 0], [0, 0]] # what's going on with deepcopy? Answer: if the original list has aliases, # the deepcopied list will have aliases (of a single copy, not the original). # So copy.deepcopy preserves alias structure!

5. Printing 2d Lists
# Helper function for print2dList. # This finds the maximum length of the string # representation of any item in the 2d list def maxItemLength(a): maxLen = 0 rows = len(a) cols = len(a) for row in range(rows): for col in range(cols): maxLen = max(maxLen, len(str(a[row][col]))) return maxLen # Because Python prints 2d lists on one row, # we might want to write our own function # that prints 2d lists a bit nicer. def print2dList(a): if (a == []): # So we don't crash accessing a print([]) return rows = len(a) cols = len(a) fieldWidth = maxItemLength(a) print("[ ", end="") for row in range(rows): if (row > 0): print("\n ", end="") print("[ ", end="") for col in range(cols): if (col > 0): print(", ", end="") # The next 2 lines print a[row][col] with the given fieldWidth formatSpec = "%" + str(fieldWidth) + "s" print(formatSpec % str(a[row][col]), end="") print(" ]", end="") print("]") # Let's give the new function a try! a = [ [ 1, 2, 3 ] , [ 4, 5, 67 ] ] print2dList(a)

6. Accessing 2d Lists by Row or Column
1. Accessing a whole row
# alias (not a copy!); cheap (no new list created) a = [ [ 1, 2, 3 ] , [ 4, 5, 6 ] ] row = 1 rowList = a[row] print(rowList)

2. Accessing a whole column
# copy (not an alias!); expensive (new list created) a = [ [ 1, 2, 3 ] , [ 4, 5, 6 ] ] col = 1 colList = [ ] for i in range(len(a)): colList += [ a[i][col] ] print(colList)

3. Accessing a whole column with a list comprehension
# still a copy, still expensive, but cheaper and cleaner with a list comprehension! a = [ [ 1, 2, 3 ] , [ 4, 5, 6 ] ] col = 1 colList = [ a[i][col] for i in range(len(a)) ] print(colList)

7. Non-Rectangular ("Ragged") 2d Lists
# 2d lists do not have to be rectangular a = [ [ 1, 2, 3 ] , [ 4, 5 ], [ 6 ], [ 7, 8, 9, 10 ] ] rows = len(a) for row in range(rows): cols = len(a[row]) # now cols depends on each row print("Row", row, "has", cols, "columns: ", end="") for col in range(cols): print(a[row][col], " ", end="") print()

8. 3d Lists
# 2d lists do not really exist in Python. # They are just lists that happen to contain other lists as elements. # And so this can be done for "3d lists", or even "4d" or higher-dimensional lists. # And these can also be non-rectangular, of course! a = [ [ [ 1, 2 ], [ 3, 4 ] ], [ [ 5, 6, 7 ], [ 8, 9 ] ], [ [ 10 ] ] ] for i in range(len(a)): for j in range(len(a[i])): for k in range(len(a[i][j])): print("a[%d][%d][%d] = %d" % (i, j, k, a[i][j][k]))

9. Some Worked Examples Using 2d Lists
See here.