# Lab 7

from turtle import *

# Tests are at the bottom in the run function.

# Provided helper function
# You can, but don't need to, change anything in this function
def intializeTurtle():
    ''' Initialize turtle on canvas before drawing '''

    setup(800,600) # Create a turtle window
    reset() # Show turtle window and turtle
    pencolor('black') # You can change the pencolor, if you so choose

    # Set the speed; 0=No animation, 1=slowest, 6=normal, 10=fast, etc.
    speed(100) # can change this to vary the speed of your turtle

    # Turtle, by default, starts roughly in center of canvas
    pu()

    # Put turtle in bottom left cornerish to better fit the pattern
    setx(-200)
    sety(-200)
    pd()

    # Magical statements to make turtle window come to top of screen.
    getscreen()._root.attributes('-topmost', True)
    getscreen()._root.attributes('-topmost', False)


# ------------------------------------
# Task 1
# ------------------------------------
# Version A: No loops, no recursion
def square(length):
    ''' Draws a square of size length maintains
    heading and position invariant '''
    fd(length)
    lt(90)
    fd(length)
    lt(90)
    fd(length)
    lt(90)
    fd(length) # back to starting location
    lt(90)     # heading in same direction as start


# Version B: For loop, no recursion
def square(length):
    ''' Draws a square of size length maintains heading
    and position invariant '''
    for i in range(1,5): # or for i in range(4)
        fd(length)
        lt(90)


# ------------------------------------
# Task 2
# ------------------------------------
def row(number, size):
    ''' Recursively draw a row of squares (like asteriskLine), maintains a position invariant '''
    if (number > 0):
        square(size)
        fd(size)
        row(number-1,size) # recursive call
        bk(size) # maintain position invariant


# ------------------------------------
# Task 3
# ------------------------------------
def spacedRow(number, size):
    ''' Recursively draw a row of squares with a constant space in between squares
    and maintians a posiion invariant '''
    if (number > 0):
        square(size)
        # move to position to draw the next one
        pu()
        fd(size + size/4)
        pd()
        spacedRow(number-1,size)# recursive call
        # move back to original starting position (maintain position invariant)
        pu()
        bk(size+ size/4)
        pd()


# ------------------------------------
# Task 4
# ------------------------------------
def decreasingRow(number, size):
    ''' Recursively draw a row of squares that get progressively smaller by 1/2 each time
    and maintains a position invariant '''
    if (number > 0):
        square(size)
        fd(size)
        decreasingRow(number-1,size/2.)# recursive call
        bk(size) # maintain position invariant


# ------------------------------------
# Task 5
# ------------------------------------
def nestedSquares(number, size):
    ''' Recursively draw nested squares that get progressively smaller by 1/2 each time
    anchored in the lower left corner '''
    if (number > 0):
        square(size)
        nestedSquares(number-1,size/2.)# recursive call


# ------------------------------------
# Task 6
# ------------------------------------
def diagonal(number, size):
    ''' Recursively draw a row of squares that get progressively smaller by 1/2 each time
    where each successive square is anchored on the upper right corner of the previous square.
    Maintains a position invariant '''
    if (number > 0):
        square(size)
        # move to position to draw next one
        fd(size)
        lt(90)
        fd(size)
        rt(90)
        diagonal(number-1,size/2.)# recursive call
        bk(size) # move back: maintain position invariant -- this block of 4 lines undo the block of 4 lines (fd, lt, fd, rt) before the recursive call
        lt(90)
        bk(size)
        rt(90)


# ------------------------------------
# Task 7
# ------------------------------------
def superDiagonal(number, size):
    ''' Recursively draw a row of squares that get progressively smaller by 1/2 each time
    where each successive square is anchored on the upper right corner of the previous square
    and the upper left corner of the previous square '''
    if (number > 0):
        square(size)
        # back at lower left starting point
        fd(size)
        lt(90)
        fd(size)
        rt(90)
        # recursive call for diagonal stemming from upper right corner
        # Note the 2. allows for more precision, e.g. if size is odd
        # then we get a more accurate half size.
        superDiagonal(number-1,size/2.) #  first recursive call
        bk(size) # maintain position invariant
        lt(90)
        bk(size)
        rt(90)
        # back at lower left corner, facing East
        #  draw the diagonal in the SouthWest direction
        lt(180)
        superDiagonal(number-1,size/2.) # second recursive call
        rt(180)


def run():
    intializeTurtle()

    # tests
    #square(100)
    #row(5, 100)
    #spacedRow(5, 100)
    #decreasingRow(5, 100)
    #nestedSquares(5, 100)
    #diagonal(5, 100)
    #superDiagonal(5, 100)

    done() # Done makes it so we don't have to restart the kernel

# Invoke run() to run your turtle program
run()