Algorithms

BCS1110

Dr. Ashish Sai

Week 2 Lecture 1
bcs1110.ashish.nl
EPD150 MSM Conference Hall

Algorithms

The problem

• The solution
• Math
• History

The problem

• There are times when the world is one way, and you would like it to be another

The problem (Example 1)

• I am hungry and want a brownie
• But there are no brownies in the house
• I can go online and find a recipe
• Follow it step by step → now there are brownies

The problem (Example 2)

• I need to get somewhere
• I go online and get directions
• If I follow them → I reach my destination

The solution

• Recipes & directions are useful because:
  • Easy to follow
  • Minimal knowledge needed
  • Produce the desired result

The solution

Recipes and directions look different

• Here is a recipe

The solution

• And here are directions for traveling from one place to another

The solution (similarities)

Despite differences, they share:

• Prerequisites (must be true before starting)
• Steps (ordered actions)
• Done state (how to know you’re finished)

Math (deeper questions)

Over time, mathematicians asked:

• What are the minimum prerequisites?
• What are the simplest steps?
• Will the algorithm always finish?
• How can we be sure it gets the right answer?

History (preface & early civs)

• Cursory overview (not exhaustive)
• Early civilizations: Egyptians, Babylonians, Indians
  • Basic ops: , , ,
  • Advanced: factorization, square roots
  • Tools: abacus

Programs → Flowcharts

• Programs not ideal for humans → need another way
• Enter: flowcharts

Flowcharts

• Graphical representation of algorithms
• Easier to read than raw code
• Use boxes, diamonds, arrows, and text

Flowcharts (conventions)

• Conventions:
  • Entry → start point
  • Box → operation (read input, arithmetic, assign)
  • Diamond → decision (yes/no branch)
  • Lines → show flow, can carry conditions/data

Flowcharts (operations)

• The box = operation
  • Simple action: input, calculation, assignment

Flowcharts (decisions)

• The diamond = decision
  • Compare something → branch Yes/No

Flowcharts (lines)

• Lines may include:
  • Condition to be true for path
  • Data passed along that path

Flowcharts (styles & UML)

• Many conventions exist → all similar
• No one “right” layout → goal is communication
• Flowcharts can:
  • Be docs, planning tools, or debugging aids
  • Split large projects among teams
• UML (Unified Modeling Language) = flowchart’s more formal cousin
  • Used in high-precision projects

Pseudocode

• Closer to code but still human-readable
• Looks like code, won’t run
• Flexible, less standardized than flowcharts
• Example:

for i ← 1 to n do
    read x
    s ← s + x
output s

Pseudocode (examples)

Read a, b, c
max ← a
If b > max then max ← b
If c > max then max ← c
Print max

input: n ≥ 0
output: n!
p ← 1
for i ← 2 to n do
    p ← p · i
return p

Pseudocode vs Code

• Ideally, pseudocode code translation is straightforward

for i ← 1 to n do
    read x
    s ← s + x
output s

for (int i=0; i<n; i++) {
    int x = sc.nextInt();
    s = s + x;
}
System.out.println(s);

• Imagine I pick a number between 1 and 100 .
• You can ask: “Is it higher or lower”
• If you guess randomly, it could take 100 tries.

Can you do better?

Why it matters ?

Binary Search

• Searching in a dictionary
• Finding songs in your playlist
• Quickly locating files on a laptop
• Finding players with similar rank in multiplayer games

Problem

• You have a pile of books all jumbled together.
• Goal: Put them in order (alphabetically by title).
• Sorting the whole pile at once is messy.

Why it matters

• Organizing playing cards
• Sorting names at graduation
• Sorting contacts on your phone

Problem

• A fire alarm rings in your ICS class (very unrealistic scenario).
• You want the closest exit.
• What’s the safest way to explore?

Idea

Breadth-First Search (BFS)

• Explore in waves:
  • First check all rooms next to you.
  • Then the rooms next to them.
  • Keep going until you find the exit.
• Guarantees the shortest way out.

Why it matters

• Social networks: “You and Sam are 3 steps apart”
• GPS: finding shortest bus routes
• Emergency drills: nearest exit

Problem

• You’re in a maze.
• You try one path → it’s a dead end.
• What do you do?

Idea

Backtracking

• Explore one path as far as possible.
• If blocked → step back.
• Try another path until you succeed.

Why it matters

• Solving Sudoku
• Escape rooms
• Crossword puzzles
• Autocomplain Autocomplete

Problem

• You’re planning a road trip across Europe .
• You want to stop for gas as few times as possible.
• There are many stations, but you can only drive a limited distance per tank.
• How do you plan?

Idea

Dynamic Programming

• Think of smaller trips first:
  • Best way to drive 100 km.
  • Then 200 km.
  • Then 300 km.
• Reuse these answers to plan the full trip.
  Build up the solution step by step.

Why it matters

• Travel planning
• Budget optimization
• Scheduling projects
• DNA/protein analysis

Problem

You’re playing a dice game.

• The math is messy.

How can you find your chances of winning?

Idea

Monte Carlo

• Play the game many times.
• Count how often you win.
• Probability = wins ÷ trials.

Why it matters

• Casinos & gambling
• Predicting weather
• Stock market risks
• Movie recommendations

• You search “best pizza near me” .
• Thousands of results.
• How does Google decide who’s first?

Idea

PageRank

• Each website votes by linking to others.
• Votes from popular sites count more.
• Pages with most “authority” rise to the top.

Why it matters

• Search engines
• Instagram influencers
• Academic paper citations

What we learned

• Binary Search: halve the problem each time.
• Merge Sort: divide work, then combine.
• BFS: ripple out to find shortest path.
• Backtracking: try → undo → try again.
• Dynamic Programming: build answers from smaller ones.
• Monte Carlo: use randomness to estimate.
• PageRank: trust flows through links.

See you in the next lecture!