8.14. Exercises

  1. Add a print statement to Newton’s sqrt function that prints out better each time it is calculated. Call your modified function with 25 as an argument and record the results.

    System Message: ERROR/3 (/home/bmiller/Runestone/web2py/applications/runestone/books/thinkcspy/_sources/MoreAboutIteration/Exercises.rst, line 33)

    Duplicate ID – see Dictionaries/Exercises, line 52

    .. activecode:: q1_answer
    
        def newtonSqrt(n):
            approx = 0.5 * n
            better = 0.5 * (approx + n/approx)
            while better != approx:
                approx = better
                better = 0.5 * (approx + n/approx)
                print("Approx:", better)
            return approx
    
    
        print("Final approx:", newtonSqrt(25))
    
    Show Comments
  1. Write a function print_triangular_numbers(n) that prints out the first n triangular numbers. A call to print_triangular_numbers(5) would produce the following output:

    1       1
    2       3
    3       6
    4       10
    5       15
    

    (hint: use a web search to find out what a triangular number is.)

  1. Write a function, is_prime, that takes a single integer argument and returns True when the argument is a prime number and False otherwise.

    System Message: ERROR/3 (/home/bmiller/Runestone/web2py/applications/runestone/books/thinkcspy/_sources/MoreAboutIteration/Exercises.rst, line 120)

    Duplicate ID – see Functions/thinkcspyExercises, line 117

    .. activecode:: q3_answer
    
        def is_prime(n):
            for i in range(2, n):
                if n % i == 0:
                    return False
            return True
    
        print(is_prime(25))
        print(is_prime(7))
        print(is_prime(251))
        print(is_prime(20))
    
    Show Comments
  1. Modify the walking turtle program so that rather than a 90 degree left or right turn the angle of the turn is determined randomly at each step.
  1. Modify the turtle walk program so that you have two turtles each with a random starting location. Keep the turtles moving until one of them leaves the screen.

    System Message: ERROR/3 (/home/bmiller/Runestone/web2py/applications/runestone/books/thinkcspy/_sources/MoreAboutIteration/Exercises.rst, line 165)

    Duplicate ID – see Functions/thinkcspyExercises, line 166

    .. activecode:: q5_answer
        :nocodelens:
    
        import random
        import turtle
    
        def moveRandom(wn, t):
            coin = random.randrange(0,2)
            if coin == 0:
                t.left(90)
            else:
                t.right(90)
    
            t.forward(50)
    
        def areColliding(t1, t2):
            if t1.distance(t2) < 2:
                return True
            else:
                return False
    
        def isInScreen(w, t):
            leftBound = - w.window_width() / 2
            rightBound = w.window_width() / 2
            topBound = w.window_height() / 2
            bottomBound = -w.window_height() / 2
    
            turtleX = t.xcor()
            turtleY = t.ycor()
    
            stillIn = True
            if turtleX > rightBound or turtleX < leftBound:
                stillIn = False
            if turtleY > topBound or turtleY < bottomBound:
                stillIn = False
            return stillIn
    
        t1 = turtle.Turtle()
        t2 = turtle.Turtle()
        wn = turtle.Screen()
    
        t1.shape('turtle')
        t2.shape('circle')
    
        leftBound = -wn.window_width() / 2
        rightBound = wn.window_width() / 2
        topBound = wn.window_height() / 2
        bottomBound = -wn.window_height() / 2
    
        t1.up()
        t1.goto(random.randrange(leftBound, rightBound),
                random.randrange(bottomBound, topBound))
        t1.setheading(random.randrange(0, 360))
        t1.down()
    
        t2.up()
        t2.goto(random.randrange(leftBound, rightBound),
                random.randrange(bottomBound, topBound))
        t2.setheading(random.randrange(0, 360))
        t2.down()
    
    
        while isInScreen(wn, t1) and isInScreen(wn, t2):
            moveRandom(wn, t1)
            moveRandom(wn, t2)
    
        wn.exitonclick()
    
    Show Comments
  1. Modify the previous turtle walk program so that the turtle turns around when it hits the wall or when one turtle collides with another turtle (when the positions of the two turtles are closer than some small number).
  1. Write a function to remove all the red from an image.

    For this and the following exercises, use the luther.jpg photo.

    System Message: ERROR/3 (/home/bmiller/Runestone/web2py/applications/runestone/books/thinkcspy/_sources/MoreAboutIteration/Exercises.rst, line 272)

    Duplicate ID – see Functions/thinkcspyExercises, line 252

    .. activecode:: q7_answer
        :nocodelens:
    
        import image
    
        img = image.Image("luther.jpg")
        newimg = image.EmptyImage(img.getWidth(), img.getHeight())
        win = image.ImageWin()
    
        for col in range(img.getWidth()):
            for row in range(img.getHeight()):
                p = img.getPixel(col, row)
    
                newred = 0
                green = p.getGreen()
                blue = p.getBlue()
    
                newpixel = image.Pixel(newred, green, blue)
    
                newimg.setPixel(col, row, newpixel)
    
        newimg.draw(win)
        win.exitonclick()
    
    Show Comments
  1. Write a function to convert the image to grayscale.
  1. Write a function to convert an image to black and white.

    System Message: ERROR/3 (/home/bmiller/Runestone/web2py/applications/runestone/books/thinkcspy/_sources/MoreAboutIteration/Exercises.rst, line 325)

    Duplicate ID – see Functions/thinkcspyExercises, line 314

    .. activecode:: q9_answer
        :nocodelens:
    
        import image
    
        def convertBlackWhite(input_image):
            grayscale_image = image.EmptyImage(input_image.getWidth(), input_image.getHeight())
    
            for col in range(input_image.getWidth()):
                for row in range(input_image.getHeight()):
                    p = input_image.getPixel(col, row)
    
                    red = p.getRed()
                    green = p.getGreen()
                    blue = p.getBlue()
    
                    avg = (red + green + blue) / 3.0
    
                    newpixel = image.Pixel(avg, avg, avg)
                    grayscale_image.setPixel(col, row, newpixel)
    
            blackwhite_image = image.EmptyImage(input_image.getWidth(), input_image.getHeight())
            for col in range(input_image.getWidth()):
                for row in range(input_image.getHeight()):
                    p = grayscale_image.getPixel(col, row)
                    red = p.getRed()
                    if red > 140:
                        val = 255
                    else:
                        val = 0
    
                    newpixel = image.Pixel(val, val, val)
                    blackwhite_image.setPixel(col, row, newpixel)
            return blackwhite_image
    
    
        win = image.ImageWin()
        img = image.Image("luther.jpg")
    
        bw_img = convertBlackWhite(img)
        bw_img.draw(win)
    
        win.exitonclick()
    
    Show Comments
  1. Sepia Tone images are those brownish colored images that may remind you of times past. The formula for creating a sepia tone is as follows:

    newR = (R × 0.393 + G × 0.769 + B × 0.189)
    newG = (R × 0.349 + G × 0.686 + B × 0.168)
    newB = (R × 0.272 + G × 0.534 + B × 0.131)
    

    Write a function to convert an image to sepia tone. Hint: Remember that rgb values must be integers between 0 and 255.

  1. Write a function to uniformly enlarge an image by a factor of 2 (double the size).
    Show Comments
  1. After you have scaled an image too much it looks blocky. One way of reducing the blockiness of the image is to replace each pixel with the average values of the pixels around it. This has the effect of smoothing out the changes in color. Write a function that takes an image as a parameter and smooths the image. Your function should return a new image that is the same as the old but smoothed.
  1. Write a general pixel mapper function that will take an image and a pixel mapping function as parameters. The pixel mapping function should perform a manipulation on a single pixel and return a new pixel.

    System Message: ERROR/3 (/home/bmiller/Runestone/web2py/applications/runestone/books/thinkcspy/_sources/MoreAboutIteration/Exercises.rst, line 473)

    Duplicate ID – see Functions/thinkcspyExercises, line 419

    .. activecode:: q13_answer
        :nocodelens:
    
        import image
    
        def pixelMapper(oldimage, rgbFunction):
            width = oldimage.getWidth()
            height = oldimage.getHeight()
            newim = image.EmptyImage(width, height)
    
            for row in range(height):
                for col in range(width):
                    originalpixel = oldimage.getPixel(col, row)
                    newpixel = rgbFunction(originalpixel)
                    newim.setPixel(col, row, newpixel)
    
            return newim
    
        def graypixel(oldpixel):
            intensitysum = oldpixel.getRed() + oldpixel.getGreen() + oldpixel.getBlue()
            aveRGB = intensitysum // 3
            newPixel = image.Pixel(aveRGB, aveRGB, aveRGB)
            return newPixel
    
        win = image.ImageWin()
        img = image.Image("luther.jpg")
    
        newim = pixelMapper(img, graypixel)
        newim.draw(win)
    
        win.exitonclick()
    
    Show Comments
  1. When you scan in images using a scanner they may have lots of noise due to dust particles on the image itself or the scanner itself, or the images may even be damaged. One way of eliminating this noise is to replace each pixel by the median value of the pixels surrounding it.
  1. Research the Sobel edge detection algorithm and implement it.

    System Message: ERROR/3 (/home/bmiller/Runestone/web2py/applications/runestone/books/thinkcspy/_sources/MoreAboutIteration/Exercises.rst, line 537)

    Duplicate ID – see Functions/thinkcspyExercises, line 487

    .. activecode:: q15_answer
        :nocodelens:
    
        import image
        import math
        import sys
    
        # Code adapted from http://www.cl.cam.ac.uk/projects/raspberrypi/tutorials/image-processing/edge_detection.html
        # Licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License.
    
        # this algorithm takes some time for larger images - this increases the amount of time
        # the program is allowed to run before it times out
        sys.setExecutionLimit(20000)
    
        img = image.Image("luther.jpg")
        newimg = image.EmptyImage(img.getWidth(), img.getHeight())
        win = image.ImageWin()
    
        for x in range(1, img.getWidth()-1):  # ignore the edge pixels for simplicity (1 to width-1)
            for y in range(1, img.getHeight()-1): # ignore edge pixels for simplicity (1 to height-1)
    
                # initialise Gx to 0 and Gy to 0 for every pixel
                Gx = 0
                Gy = 0
    
                # top left pixel
                p = img.getPixel(x-1, y-1)
                r = p.getRed()
                g = p.getGreen()
                b = p.getBlue()
    
                # intensity ranges from 0 to 765 (255 * 3)
                intensity = r + g + b
    
                # accumulate the value into Gx, and Gy
                Gx += -intensity
                Gy += -intensity
    
                # remaining left column
                p = img.getPixel(x-1, y)
                r = p.getRed()
                g = p.getGreen()
                b = p.getBlue()
    
                Gx += -2 * (r + g + b)
    
                p = img.getPixel(x-1, y+1)
                r = p.getRed()
                g = p.getGreen()
                b = p.getBlue()
    
                Gx += -(r + g + b)
                Gy += (r + g + b)
    
                # middle pixels
                p = img.getPixel(x, y-1)
                r = p.getRed()
                g = p.getGreen()
                b = p.getBlue()
    
                Gy += -2 * (r + g + b)
    
                p = img.getPixel(x, y+1)
                r = p.getRed()
                g = p.getGreen()
                b = p.getBlue()
    
                Gy += 2 * (r + g + b)
    
                # right column
                p = img.getPixel(x+1, y-1)
                r = p.getRed()
                g = p.getGreen()
                b = p.getBlue()
    
                Gx += (r + g + b)
                Gy += -(r + g + b)
    
                p = img.getPixel(x+1, y)
                r = p.getRed()
                g = p.getGreen()
                b = p.getBlue()
    
                Gx += 2 * (r + g + b)
    
                p = img.getPixel(x+1, y+1)
                r = p.getRed()
                g = p.getGreen()
                b = p.getBlue()
    
                Gx += (r + g + b)
                Gy += (r + g + b)
    
                # calculate the length of the gradient (Pythagorean theorem)
                length = math.sqrt((Gx * Gx) + (Gy * Gy))
    
                # normalise the length of gradient to the range 0 to 255
                length = length / 4328 * 255
    
                length = int(length)
    
                # draw the length in the edge image
                newpixel = image.Pixel(length, length, length)
                newimg.setPixel(x, y, newpixel)
    
        newimg.draw(win)
        win.exitonclick()
    
    Show Comments
Next Section - 9. Strings