Programming, problem solving, and algorithms

CPSC 203, 2025 W1

September 11, 2025

Announcements

• Setup instructions available.

• Python resources posted to piazza.

• First examlet signup available.

Summary

In this introductory class, we use metaphors and abstractions to characterize problem decomposition, code as a communication mechanism, and computational efficiency. We continue our exploration of the idea of elegance, making connections to problem solving and code. Then, we learn a mechanism for measuring efficiency, and talk briefly about why it’s important to consider. The discussion about efficiency is followed by a diversion into colour representation. Finally, we look at some code! The day concludes with a sequence of Python examples designed to clear the cobwebs on lists – our first data structure!

Learning outcomes

1. Computers interpret electrical signals as bits, and bits can be used to represent numbers, and numbers can be used to represent colours, which suggests that we can represent virtually anything!

Warm Up

Suppose we can knit 10¹² stitches per second…

	10	100	1000	10,000	1012
\(n\)	10-11s	10-10 s	10-9 s	10-8 s	1 s
\(n \log n\)	10-11 s	10-9 s	10-8 s	10-7 s	40 s
\(n^2\)	10-10 s	10-8 s	10-6 s	10-4 s	1012 s
\(n^3\)	10-9 s	10-6 s	10-3 s	1 s	1024 s
\(2^n\)	10-9 s	1018 s	10289 s

The amount of computation we do inside our algorithm actually matters!

Why does this matter?

Annotate:

1. Each stitch takes a tiny tiny fraction of a second 1/10¹² = 10^-12 (fastest machine is 415 x 10¹⁵).
2. \(n\) is size parameter for our computation.
3. \(T(n)\) is the amount of time our computation takes.

Choose one to illustrate if our rag/data size is 1000, and we need to compute n³ steps/stitches (like knitting a cube!!), then the total time is 1000³/10¹² = 10^-3 a thousandth of a second. Nbd.

BUT let’s look at bigger data. 10¹² (~128gb pretty big) 10¹² mm = 1M km, 384,400 km to the moon. 149M km to the sun. So knitting something that big would take 10¹² s = ~32000 years. The sun will long since have burnt out by 10¹⁸ s

Punchline—we don’t want to do \(2^n\) amount of computation, and we need creative approaches for big data.

Recap—we’ve seen a problem whose size we characterize by \(n^2\), we’ll see problems whose time we characterize by \(n\), for sure, and later in the term, we’ll see a problem which is very simply stated, whose size we characterize by \(2^n\). 🙁

NOTE: \(\log\) is \(\log_2\). And \(\log 1000 = 10\).

Representation

Colour interpretation

What’s your favorite colour? Do you have a sense for why it’s your favorite? Does that colour influence your dress/decor/purchases?

Psychological: https://www.buzzfeed.com/mermaidbarbie/which-color-truly-matches-your-personality-24h9koy69s

Cultural: https://en.wikipedia.org/wiki/Color_symbolism

Your turn: Colour—cultural interpretations

Activity—In pairs, choose a colour (primary or secondary) and find something in its cultural symbolism that surprises you. Contradictions are especially interesting. Report your findings to the class (briefly).

05:00

Big design implications for data visualization

Colour—representation

First, some general questions…

What does data look like to a computer?

Is that enough?

1. Positive and negative charges interpreted as 1 and 0.
2. Binary digits = bits

Colour—representation

Can we use bits to represent integers?

3	1	5	7
103	102	101	100

103	102	101	100
23	22	21	20

Talk about the BASE of the number.

Colour—representation

What’s the highest number we can represent with 4 bits?

What’s the highest number we can represent with 5 bits?

How many bits do we need to express 120?

Can we represent any integer this way? YES! Until we run out of memory. But we have more memory than we can even conceive of.

How does this help us with colour?

Colour—representation

Can we use integers to represent colours?

One way: RGB (red, green, blue), where each “component” is in range 0 through 255.

ex. (255, 0, 127) ==

Fun calculator for colour values: https://colorizer.org

How many bits for 256 values? 4 5 6 7 8 9 10

Colour—representation

What colour is

0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1

Easier to read if we use hexadecimal representation:

Each component is represented by 2 hex digits 0123456789abcdef

ex. #674ea7

Hex = base 16

Colour—representation (aside)

What do you observe about the following RGB colours?

Red	Green	Blue
255	0	0
17	0	178
45	0	13
200	0	220
62	0	37
130	0	95

Colour and Code

Make the poppies pop!

PC: https://www.epicgardening.com/spring-wildflowers-from-seed/

Examine each pixel. If its red colour channel is high (over 200, say), then leave it as is. Otherwise, change the pixel to grey by setting all 3 colour channels to the average of their original values.

Colour and Code

from typing import Tuple
import numpy as np
from skimage import io
import matplotlib.pyplot as plt

Pixel = Tuple[np.uint8, np.uint8, np.uint8]  # (r, g, b)

'''Input: Pixel p
   Output: Pixel
   Function: If the pixel has high red value, then don't change it, otherwise
   fade the pixel to grey.  Note, to grey a pixel, set all colour channels to
   the average of the 3.
'''
def boost_red_pixel(p: Pixel) -> Pixel:
    # setup -- extract the colour channels as ints
    red = int(p[0])
    green = int(p[1])
    blue = int(p[2])
    # compute grey 
    grey = (red + green + blue)//3

    # conditionally change the pixel to grey
    if red < 200:
        red = green = blue = grey

    # return updated pixel
    return (red, green, blue)

def fancify(img: np.ndarray) -> np.ndarray:
    H, W = img.shape[:2] # grab the height and width of the image
    out = img.copy()     # write to a copy

    # traverse every pixel in the image and change it!
    for row in range(H):
        for col in range(W):
            out[row, col] = boost_red_pixel(img[row,col])

    # return image with changed pixels
    return out

def main() -> None:
    
    img = io.imread('https://raw.githubusercontent.com/UBC-CS/cpsc203/refs/heads/main/images/poppyfield.jpg')[..., :3]     # keep first 3 channels (RGB)
    
    out = fancify(img)
  
    plt.imshow(out)
    plt.axis('off')
    plt.show()
  
main()

Your turn: Change image or boost

Find an online image you would like to boost and use its URL in the code we just wrote.

How can you adjust the code to manipulate the colours in a different way?