🔧 Lab 11 — Feel the Algorithms With Your Own Hands

Goal: experience the speed differences from the lesson physically — with paper, playing cards, and (optionally) a browser. No installation, no code. Labs 1–3 need nothing but this page and something to write on.

Time: 30–45 minutes.

🏁 Lab 1 — The dictionary race (linear vs. binary search)

You’ll search the same sorted list two ways and count your steps.

Here is your “phone book” — 32 names, alphabetized and numbered:

# Name # Name # Name # Name
1 Abara 9 Elif 17 Kwame 25 Rosa
2 Amara 10 Emeka 18 Lena 26 Sana
3 Bilal 11 Farid 19 Maya 27 Tariq
4 Carmen 12 Grace 20 Nadia 28 Uma
5 Chen 13 Hana 21 Omar 29 Vera
6 Dara 14 Ines 22 Priya 30 Wei
7 Diego 15 Ivan 23 Quinn 31 Yusuf
8 Ebba 16 Jonas 24 Ravi 32 Zara

Your target: find “Tariq”.

  1. Linear search first. Start at #1. Read each name aloud, in order, counting as you go, until you reach Tariq. Write down your count.
  2. Now binary search. Look at the middle of the current range and halve:
    • Whole list is 1–32. Middle is #16 (Jonas). Tariq comes after Jonas alphabetically → throw away 1–16. That was peek 1.
    • Range is now 17–32. Middle is #24 (Ravi). Tariq comes after Ravi → keep 25–32. Peek 2.
    • Keep halving. Count every peek until you land on Tariq.
  3. Write both counts side by side.

✅ What you should see: linear search took 27 steps. Binary search took about 5. Now imagine the list had a million names: linear could take a million steps; binary would take at most 20. You’ve now felt O(n) vs. O(log n).

  1. Bonus: race a family member — one of you searches linearly, the other halves. Loser makes the tea.

🃏 Lab 2 — Sort 8 cards, two ways, and count

You need 8 playing cards with different values — or 8 paper scraps numbered 5, 2, 8, 1, 9, 3, 7, 4. Lay them out in exactly that order for both rounds.

Round A: bubble sort

  1. Compare the first two cards. If the left one is bigger, swap them. That’s 1 comparison — keep a tally.
  2. Move one position right; compare that pair; swap if needed. Continue to the end of the row. (That full sweep is 7 comparisons.)
  3. Go back to the start and sweep again. Repeat sweeps until one full sweep needs zero swaps.
  4. Write down your total comparison tally.

✅ What you should see: the cards end up 1–9 in order, and your tally is somewhere around 20–28 comparisons. Notice how big numbers slowly “bubble” to the right — and how often you re-compared pairs you’d already looked at.

Round B: merge sort

  1. Reset the cards to 5, 2, 8, 1, 9, 3, 7, 4.
  2. Split into two piles of 4: (5, 2, 8, 1) and (9, 3, 7, 4).
  3. Split each pile into pairs: (5,2) (8,1) (9,3) (7,4). Sort each pair — 1 comparison each, so 4 so far.
  4. Merge pairs into sorted 4s: take (2,5) and (1,8), both face up. Repeatedly move the smaller front card to a new pile, counting each comparison. Do the same with (3,9) and (4,7).
  5. Merge the two sorted 4s into one sorted 8 the same way — always compare the two front cards, move the smaller.
  6. Write down the total tally.

✅ What you should see: the same sorted row — for roughly 15–17 comparisons, noticeably fewer than bubble sort. With 8 cards the gap is modest; with 1,000,000 items it’s the gap between ~20 million comparisons and ~1,000,000,000,000.

🧥 Lab 3 — The human hash table (coat-check game)

This one shows why hash-table lookups feel instant.

Family version (3+ people):

  1. Lay out 10 paper “hooks” numbered 0–9 in a row on a table.
  2. One person is the attendant. Their one rule for storing any word: count its letters, keep only the last digit, that’s the hook number. (“UMBRELLA” has 8 letters → hook 8. “TOOTHBRUSH” has 10 → hook 0.)
  3. Players hand the attendant 6 word-cards, one at a time. The attendant applies the rule and places each card on its hook. No memorizing allowed!
  4. Now players ask: “where is TOOTHBRUSH?” The attendant recomputes the rule (10 letters → hook 0) and grabs it directly. No searching through hooks.
  5. Try to cause trouble: hand over two words with the same rule-result (“CAT” and “DOG” — both 3 letters → hook 3). Both cards share hook 3, and the attendant must flip through that one hook’s small stack. Congratulations: you’ve caused a collision, the exact thing real hash tables handle quietly all day.

Solo paper version: draw 10 boxes numbered 0–9. “Store” these words using the same letters-count rule: PEN, WINDOW, BICYCLE, SUN, TEA, ELEPHANT. Then, without looking back at your list, answer: which box holds BICYCLE? Recompute the rule — 7 letters → box 7 — and check. You found it without scanning any other box.

✅ What you should see: finding a word never requires searching — the rule is the address. Also: PEN, SUN and TEA collided in box 3. Real systems use fancier rules so collisions stay rare, but the idea is exactly this.

🖥️ Lab 4 (optional, browser) — Watch the sorts race

If you have a browser handy:

  1. Visit visualgo.net and choose “Sorting”.
  2. Pick Bubble Sort, press play, and watch the bars swap — recognize your Round A?
  3. Now pick Merge Sort on the same data and watch the halving-and-merging.
  4. Alternatively, search YouTube for “15 sorting algorithms in 6 minutes” — a famous visualization where you can hear the difference in speed.

✅ What you should see: bubble sort visibly plodding while merge sort finishes in a fraction of the passes. The animations are the lesson’s tables, brought to life.

🎉 Done!

You have now: raced linear against binary search, sorted the same cards with a slow recipe and a fast one, and run a working hash table using only paper and a counting rule. That’s more hands-on algorithm work than many people do in a first-year university course. Head to the quiz when you’re ready.