Algorithms & Flowcharts — Worked Examples

Algorithms you already follow

You run algorithms every day without calling them that: using an ATM, logging in, buying a snack, crossing at the lights. Each is a sequence of steps with decisions (branches) and sometimes loops (repeating until something is true). Drawing them as flowcharts makes the hidden logic — especially the "what if it goes wrong?" branches — visible. Watch the Yes/No labels: getting a branch backwards is the most common bug.

(a) ATM cash withdrawal

Problem

A customer inserts a card and asks for cash. The machine must check the PIN, check the balance, and only then dispense money.

Pseudocode

ATM_WITHDRAW:
    pin = INPUT
    IF pin is not valid:
        show "Incorrect PIN"
    ELSE:
        amount = INPUT
        IF amount <= balance:
            dispense(amount)
            balance = balance - amount
            print receipt
        ELSE:
            show "Insufficient funds"

In Python

def atm_withdraw(entered_pin, correct_pin, amount, balance):
    if entered_pin != correct_pin:
        return "Incorrect PIN", balance
    if amount > balance:
        return "Insufficient funds", balance
    balance -= amount
    return f"Dispensed {amount}", balance

print(atm_withdraw("1234", "1234", 60, 200))

Output:

('Dispensed 60', 140)

(b) Website login with a maximum of 3 attempts

Problem

Let a user try to log in. Allow at most three wrong passwords, then lock the account.

Pseudocode

LOGIN:
    tries = 0
    WHILE tries < 3:
        pw = INPUT
        IF pw is correct:
            grant access
            STOP
        ELSE:
            tries = tries + 1
    lock account

Trace table

User types "abc", "xyz", then the correct "pass" on the third try:

tries (before)	tries < 3?	password	correct?	result
0	Yes	abc	No	tries → 1
1	Yes	xyz	No	tries → 2
2	Yes	pass	Yes	access granted, stop

In Python

def login(attempts, correct="pass"):
    tries = 0
    while tries < 3:
        pw = attempts[tries]
        if pw == correct:
            return "Access granted"
        tries += 1
    return "Account locked"

print(login(["abc", "xyz", "pass"]))
print(login(["a", "b", "c"]))

Output:

Access granted
Account locked

(c) Vending machine

Problem

A customer selects an item, inserts money a coin at a time, and the machine either gives the item plus change, or refunds if they cancel.

Pseudocode

VENDING_MACHINE:
    price = selected item price
    paid  = 0
    WHILE paid < price:
        coin = INPUT          ' a coin, or "cancel"
        IF coin == "cancel":
            refund(paid)
            STOP
        paid = paid + coin
    dispense item
    IF paid > price:
        give change (paid - price)

In Python

def vend(price, coins):
    paid = 0
    for coin in coins:
        if coin == "cancel":
            return f"Refund {paid}"
        paid += coin
        if paid >= price:
            return f"Dispense item, change {paid - price}"
    return f"Refund {paid}"   # ran out of coins

print(vend(75, [25, 25, 25]))
print(vend(75, [25, "cancel"]))

Output:

Dispense item, change 0
Refund 25

(d) Traffic-light controller cycle

Problem

Control a traffic light that repeats forever: Green, then Amber, then Red, each for a fixed time, then back to Green.

Pseudocode

TRAFFIC_LIGHT:
    REPEAT:
        set light GREEN;  wait 30s
        set light AMBER;  wait 5s
        set light RED;    wait 30s
    UNTIL power is off

In Python

def traffic_cycle(cycles):
    sequence = [("GREEN", 30), ("AMBER", 5), ("RED", 30)]
    log = []
    for _ in range(cycles):          # 'cycles' stands in for "while powered on"
        for colour, seconds in sequence:
            log.append(f"{colour} {seconds}s")
    return log

for step in traffic_cycle(2):
    print(step)

Output:

GREEN 30s
AMBER 5s
RED 30s
GREEN 30s
AMBER 5s
RED 30s