CS51A - Spring 2022 - Class 18

Example code in this lecture

   matrix.py
   tic_tac_toe.py

Lecture notes

  • Admin
       - Assignment 9 out today

  • representing matrices in python
       - what is a matrix?
          - a two-dimensional structure, e.g.

             0 1 0
             1 8 2
             5 0 3

          - it has rows and columns
          - the 2nd row is:

             1 8 2

          - the second column is:

             1
             8
             0

          - for computer science, we'll start indexing at 0, for the first row is row 0 and the first column, is column 0

       - indexing into matrices
          - individual entries in a matrix can be talked about by specifying a row and a column
          - say the matrix above is called m, what entry does m[1][2] represent?
             - in math, we might write this m(1, 2)

             - 1 = second row, 2 = third column: 2

          - how would get get at the 3 in the above matrix?
             - m[2][2]

       - how can we do this in python?
          - list of lists!

          >>> m = [[0, 1, 0], [1, 8, 2], [5, 0, 3]]
          >>> m
          [[0, 1, 0], [1, 8, 2], [5, 0, 3]]
          >>> m[1][2]
          2
          >>> m[2][2]
          3

          - could have also constructed this as:
          >>> m = []
          >>> m.append([0,1,0])
          >>> m.append([1, 8, 2])
          >>> m.append([5, 0, 3])
          >>> m
          [[0, 1, 0], [1, 8, 2], [5, 0, 3]]
          >>> m[1][2]
          2
          >>> m[2][2]
          3

          - what does m[1] represent?
             - the second row!
                >>> m[1]
                [1, 8, 2]

             - matrices are just a list of lists

  • look at matrix.py code
       - what do zero_matrix and zero_matrix2 do?
          - creates a size by size matrix with all entries zero
          - zero_matrix does this an entry at a time
          - zero_matrix2 does this a row at a time

          >>> zero_matrix(3)
          [[0, 0, 0], [0, 0, 0], [0, 0, 0]]
          >>> zero_matrix(2)
          [[0, 0], [0, 0]]
          >>> zero_matrix(1)
          [[0]]
          >>> m = zero_matrix(2)
          >>> m[1][1] = 100
          >>> m
          [[0, 0], [0, 100]]

       - what does random_matrix do?
          - same thing, but puts random numbers in

          >>> random_matrix(3)
          [[7, 9, 9], [3, 6, 6], [6, 6, 2]]
          >>> random_matrix(3)
          [[9, 5, 8], [1, 2, 3], [8, 9, 8]]
          >>> random_matrix(3)
          [[1, 0, 0], [4, 3, 8], [2, 7, 7]]


       - how would we print out a matrix in a more normal form (a row at a time)?
          - iterate for the rows and print each out
          - look at print_matrix function in matrix.py code

       - what does the identity function do in matrix.py code?
          - creates an identity matrix, all zeros except for ones along the diagonal

       - how would we sum up all the numbers in a matrix?
          - iterate over each entry and add them up
          - look at matrix_sum function in matrix.py code
             - what does len(m) give us?
                - the number of rows (remember, list of lists)
             - what does len(m[row]) give us?
                - the number of columns (in that row, technically)
          - look at matrix_sum2 function in matrix.py code
             - use the sum function to sum up each row and then add that to the total

  • copying a matrix

  • look at tic_tac_toe.py code
       - how would you represent a tic tac toe board?
          - a 3 by 3 matrix
          - each entry has one of three values:
             - empty
             - X
             - O
    •