Computer Science 111

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Computer Science 111

• Fundamentals of Programming I
• Nested Loops
• Grids
• Two-Dimensional Lists
• Matrices

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Simple Loops
for i in xrange(upper) sum i
Just count through a sequence of values The
sequences are linear
for element in lyst sum element
for element in myfile sum int(element)
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Nested Loops
for row in xrange(upper1) for column in
xrange(upper2) ltdo something with row
and columngt
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0

• Often used to process grid-like structures
• Game boards
• Bitmaps of images
• Matrices
• Maps and diagrams

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Grid Positions as (row,col) Pairs
for row in xrange(3) for col in xrange(3)
print (row, col), print
In this 3 by 3 imaginary grid, each row has 3
positions and each column has 3 positions
col0 col1 col2 (0,0) (0,1) (0,2)
row0 (1,0) (1,1) (1,2) row1 (2,0) (2,1) (2,2)
row2
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Using a while Loop
row 0 while row lt 3 col 0 while col
lt 3 print (row, col), col 1
print row 1
col0 col1 col2 (0,0) (0,1) (0,2)
row0 (1,0) (1,1) (1,2) row1 (2,0) (2,1) (2,2)
row2
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Representing a Grid as Data

• Use a list of lists
• Sometimes called a two-dimensional list or matrix
• Access each element with a pair of subscripts of
  the form rowcolumn
• Usually process the grid with a nested loop

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What a List of Lists Is Like
Build a 3 by 2 grid of integers (3 rows of 2
columns each)
g 6, 3, 2, 5, 8, 1
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What a List of Lists Is Like
Build a 3 by 2 grid of zeros (3 rows of 2 columns
each)
g 6, 3, 2, 5, 8, 1
Print the number of rows and columns
print len(g), len(g0)
We assume that the grid is rectangular, not ragged
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What a List of Lists Is Like
Build a 3 by 2 grid of zeros (3 rows of 2 columns
each)
g 6, 3, 2, 5, 8, 1
Print the number of rows and columns
print len(g), len(g0)
Print the contents of the grid in two-dimensional
format
for row in g for element in row
print element, print
6 3 2 5 8 1
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What a List of Lists Is Like
Build a 3 by 2 grid of zeros (3 rows of 2 columns
each)
g 6, 3, 2, 5, 8, 1
Print the number of rows and columns
print len(g), len(g0)
Or access elements in g using their index
positions
for row in xrange(len(g)) for col in
xrange(len(grow)) print growcol,
print
6 3 2 5 8 1
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What a List of Lists Is Like
Build a 3 by 2 grid of zeros (3 rows of 2 columns
each)
g 6, 3, 2, 5, 8, 1
Or use a while loop
row 0 while row lt len(g) col 0 while
col lt len(grow) print growcol,
col 1 print row 1
6 3 2 5 8 1
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A Grid Type

• Like the list type or the string type, the grid
  type is actually a set of operations on a set of
  data values (grids)
• Define these operations as functions in a module
• Import the module to use grids
• The module hides the details of the data
  structures and operations used to represent and
  manipulate a grid

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The grid Modules Functions
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Using the grid Module
Create a 3 by 3 grid of ones
from grid import
g makeGrid(3, 3, 1)
g makeGrid(3, 3)
g makeGrid(3)
g makeGrid()
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Print of Rows and Columns
print getRows(g), getCols(g)
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Sum the Elements
sum 0 for row in g for element in row
sum element
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Increment the Elements
for row in xrange(getRows(g)) for col in
xrange(getCols(g)) growcol 1
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Defining makeGrid
def makeGrid(rows 3, cols 3, value 1)
g for row in xrange(rows) lyst
for col in xrange(cols)
lyst.append(value) g.append(lyst)
return g
Build and return a two-dimensional list The
outer list contains the rows (nested lists) Each
row or nested list contains the elements
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Defining getRows and getCols
def getRows(g) return len(g) def
getCols(g) return len(g0)
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Defining gridPrint
def gridPrint(g) for row in g for
element in row print element,
print
Formats data in rows and columns
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Matrix Arithmetic

• A matrix is a two-dimensional grid of numbers
• Two matrices can be added, multiplied, and so
  forth
• The result is a third, new matrix

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Matrix Addition

• The two matrices must be of the same order (width
  and height)
• Obtain the sums of each pair of values at each
  position in the two matrices
• Save the sums in the corresponding positions in
  the result matrix

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In Python
m1 makeGrid(3, 3, 2) m2 makeGrid(3, 3,
3) sum matrixAdd(m1, m2) gridPrint(sum)
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Implementing matrixAdd
def matrixAdd(m1, m2) sum
makeGrid(getRows(m1), getCols(m1)) for row in
xrange(getRows(sum)) for col in
xrange(getCols(sum)) sumrowcol
m1rowcol m2rowcol return sum
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For Friday

• Read Section 7.3 on Image Processing