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evaluate_solutions.md

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Evaluate.py Solutions

  1. Basic Recursion

    a. Evaluate f1a(5, 3) = 243

    f1a(5, 3)                   > 243
- f1a(4, 3)                 > 81
    - f1a(3, 3)             > 27
        - f1a(2, 3)         > 9
            - f1a(1, 3)     > 3
                - f1a(0, 3) > 1

    b. Evaluate f1b(6, 3) = 243

    f1b(6, 3)                   > 243
- f1b(5, 3)                 > 81
    - f1b(4, 3)             > 27
        - f1b(3, 3)         > 9
            - f1b(2, 3)     > 3
                - f1b(1, 3) > 1

    c. Evaluate f1c(7, 3) = 9

    f1c(7, 3)                   > 9
- f1c(5, 3)                 > 3
    - f1c(3, 3)             > 1
        - f1c(2, 3)         > 1
            - f1c(1, 3)     > 1

  2. Basic Loops

    a. Evaluate f2a(7, 3) = 6

    c = 0
    + 0
    + 1
    + 2
    + 3

c = 6

    b. Evaluate f2b(3, 10) = "ZPZPZPZPZP"

    s = ""
  = "3"
  = "33"
  = "333"
  = "3333"
  = "33333"
  = "333333"
  ...
  = "ZPZPZPZPZP"

    c. Evaluate f2c(3, 5) = [3 , 2 , 2 , None, None]

    l = [None, None, None, None, None]
  = [3   , 2   , None, None, None]
  = [3   , 3   , 2   , None, None]
  = [3   , 2   , 2   , None, None]
  = [3   , 3   , 2   , None, None]
  = [3   , 2   , 2   , None, None]
  = [3   , 2   , 2   , None, None]

  3. Recursion with Loops

    a. Evaluate f3a(5, 3) = [0, 0, 0, 0]

    f3a(5, 3)                   > [0, 0, 0, 0]
- f3a(4, 3)                 > [0, 0, 0, 0]
    - f3a(3, 3)             > [0, 0, 0, 0]
        - f3a(2, 2)         > [0, 0, 0]
            - f3a(1, 1)     > [0, 0]
                - f3a(0, 0) > [0]

    b. Evaluate f3b(3, 2) = ['3p', '3r', '3a', '2p', '2r', '1p']

    f3b(3, 2)                   > ['3p', '3r', '3a', '2p', '2r', '1p']
- f3b(2, 2)                 > ['2p', '2r', '1p']
    - f3b(1, 2)             > ['1p']
        - f3b(0, 2)         > []

    c. Evaluate f3c(5, 2) = "hi,hey,bye.hi,hey,bye."

    f3c(5, 2)                   > "hi,hey,bye.hi,hey,bye."
- f3c(4, 1)                 > "hey,bye."
    - f3c(4, 0)             > "bye."