Week 2: Iteration & Filtering

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# Week 2: Iteration & Filtering > **BSCS1001 — IIT Madras BS Degree** **Prerequisite:** Topic 03 (Pseudocode Basics) **Cross-links:** BSCS1002-Python (Week 2 — Loops, Conditions) ## 1. Motivation: Beyond Simple Counting In Topic 01, we learned that iteration means "doing something repeatedly." But what exactly can w...

Week 2: Iteration & Filtering

BSCS1001 — IIT Madras BS Degree Prerequisite: Topic 03 (Pseudocode Basics) Cross-links: BSCS1002-Python (Week 2 — Loops, Conditions)

1. Motivation: Beyond Simple Counting

In Topic 01, we learned that iteration means "doing something repeatedly." But what exactly can we do repeatedly? Three fundamental operations form the backbone of almost every algorithm:

Operation	Description	Analogy
Count	How many items?	Counting students in a class
Sum	Add up values	Total marks of all students
Max/Min	Find extreme values	Who scored highest?

These may seem simple, but they are the building blocks of sophisticated data analysis.

💡 Key Insight: The difference between counting, summing, and finding max is just what you do inside the loop. The iteration structure is the same.

2. The Two Core Patterns

Pattern A: Accumulation (Count, Sum)

In accumulation, the variable's new value depends on its previous value plus something new.


pseudo
Variable = Variable + NewValue

Examples:

Count = Count + 1 (add 1 each time)
Sum = Sum + X.Maths (add current value each time)

Pattern B: Tracking (Max, Min)

In tracking, the variable's new value might be replaced if the current item is more extreme.


pseudo
if (X.Value > Variable) {
    Variable = X.Value
}

Examples:

if (X.Maths > Max) { Max = X.Maths } (update max)
if (X.Maths < Min) { Min = X.Maths } (update min) (Diagram)

3. Finding Maximum: The Tracker Pattern

The Algorithm


sql
Max = 0
while (Pile 1 has more cards) {
    Pick a card X from Pile 1
    Move X to Pile 2
    if (X.Maths > Max) {
        Max = X.Maths
    }
}

How It Works

Initialize Max to a very small value (0 if marks are non-negative)
For each card, compare X.Maths with current Max
If X.Maths is larger, update Max
After processing all cards, Max holds the largest value

Flowchart

(Diagram)

Tracing: Find Maximum Marks

Dataset: [45, 78, 62, 91, 53]

Iter	X.Maths	Max Before	Condition (X > Max?)	Max After
1	45	0	45 > 0 ✅ Yes	45
2	78	45	78 > 45 ✅ Yes	78
3	62	78	62 > 78 ❌ No	78
4	91	78	91 > 78 ✅ Yes	91
5	53	91	53 > 91 ❌ No	91

Result: Maximum = 91

What If All Values Are Negative?

If Max = 0 but all marks are negative (e.g., [-5, -10, -3]), the algorithm incorrectly returns 0. Solution: Initialize Max to the first card's value instead:


sql
Max = 0
FirstCard = True
while (Pile 1 has more cards) {
    Pick a card X from Pile 1
    Move X to Pile 2
    if (FirstCard) {
        Max = X.Maths
        FirstCard = False
    }
    else if (X.Maths > Max) {
        Max = X.Maths
    }
}

4. Finding Max with Card ID

Often we need to know which student has the max marks, not just the value.

The Algorithm


sql
MaxM = 0
MaxCard = -1
while (Pile 1 has more cards) {
    Pick a card X from Pile 1
    Move X to Pile 2
    if (X.Maths > MaxM) {
        MaxM = X.Maths
        MaxCard = X.Id
    }
}

Tracing

Dataset:

Card ID	Name	Maths
101	Alice	85
102	Bob	92
103	Charlie	78
104	Diana	95

Iter	X.Id	X.Maths	MaxM Before	Condition	MaxM After	MaxCard
1	101	85	0	85>0 ✅	85	101
2	102	92	85	92>85 ✅	92	102
3	103	78	92	78>92 ❌	92	102
4	104	95	92	95>92 ✅	95	104

Result: Max = 95, achieved by student ID = 104 (Diana)

Why Initialize MaxCard to -1?

Card IDs are typically positive numbers (e.g., 1, 2, 3, ...)
-1 is an impossible card ID, serving as "no card selected yet"
If MaxCard remains -1 after the loop, the dataset was empty

5. Finding Both Max and Min

We can find both in a single pass:


sql
Max = -INFINITY
Min = INFINITY
while (Pile 1 has more cards) {
    Pick a card X from Pile 1
    Move X to Pile 2
    if (X.Maths > Max) {
        Max = X.Maths
    }
    if (X.Maths < Min) {
        Min = X.Maths
    }
}

Tracing

Dataset: [45, 78, 62, 91, 53]

Iter	X	Max Before	Max After	Min Before	Min After
1	45	-∞	45	∞	45
2	78	45	78	45	45
3	62	78	78	45	45
4	91	78	91	45	45
5	53	91	91	45	53? No, 45 < 53 so Min stays 45

Result: Max = 91, Min = 45

Note: Two separate if statements (not if-else) because a single card could be both new max AND new min (if it's the first card).

6. The AND Operator in Filters

Compound Conditions

The AND operator combines two conditions — both must be True for the combined condition to be True.

AND Truth Table

Condition 1	Condition 2	C1 AND C2
False	False	False
False	True	False
True	False	False
True	True	True

Using AND in Filtering


sql
Count = 0
while (Pile 1 has more cards) {
    Pick a card X from Pile 1
    Move X to Pile 2
    if (X.Gender == "M" AND X.Maths > 80) {
        Count = Count + 1
    }
}

This counts boys who scored above 80 in Maths.

Worked Example: AND Filter

Dataset:

Name	Gender	Maths
Alice	F	90
Bob	M	85
Charlie	M	72
Diana	F	78
Ethan	M	95

Filter: X.Gender == "M" AND X.Maths > 80

Card	Gender	Maths	Gender=="M"?	Maths>80?	AND	Increment?
Alice	F	90	No	Yes	No	❌
Bob	M	85	Yes	Yes	Yes	✅ Count=1
Charlie	M	72	Yes	No	No	❌
Diana	F	78	No	No	No	❌
Ethan	M	95	Yes	Yes	Yes	✅ Count=2

Result: Count = 2 (Bob and Ethan)

Comparison: AND vs Sequential Ifs

(Diagram) Both forms are equivalent. AND is more compact.

7. Accumulation through Iteration

Accumulation is the process of building up a value step by step during iteration.

Types of Accumulators

Accumulator	Initial Value	Update Rule	Example
Counter	0	`Count = Count + 1`	Number of students
Sum	0	`Sum = Sum + X.Value`	Total marks
Product	1	`Prod = Prod × X.Value`	(Rare in this course)
List builder	[]	`List = List ++ [X]`	Collecting items (Week 5)

Combining Accumulation with Filtering

We can accumulate while filtering:


sql
TotalBoysMaths = 0
while (Pile 1 has more cards) {
    Pick a card X from Pile 1
    Move X to Pile 2
    if (X.Gender == "M") {
        TotalBoysMaths = TotalBoysMaths + X.Maths
    }
}

This is accumulation with filtering — one of the most common patterns in the course.

Multiple Accumulators

We can track multiple things in a single pass:


sql
BoySum = 0
GirlSum = 0
BoyCount = 0
GirlCount = 0
while (Pile 1 has more cards) {
    Pick a card X from Pile 1
    Move X to Pile 2
    if (X.Gender == "M") {
        BoySum = BoySum + X.Maths
        BoyCount = BoyCount + 1
    }
    else {
        GirlSum = GirlSum + X.Maths
        GirlCount = GirlCount + 1
    }
}
BoyAvg = BoySum / BoyCount
GirlAvg = GirlSum / GirlCount

This computes the average Maths marks for boys and girls separately in a single pass!

8. Comparison: Iteration Patterns

Summary Table

Pattern	Initial Value	Update Condition	Update Action	Use Case
Count	0	Always (every card)	`Count = Count + 1`	How many?
Sum	0	Always (or with filter)	`Sum = Sum + X.Value`	Total?
Average	Sum=0, Count=0	Always	Sum+=X, Count+=1	What's typical?
Max	0 or -∞	When X > Max	`Max = X.Value`	Best score?
Min	∞	When X < Min	`Min = X.Value`	Worst score?
Max with ID	Max=0, ID=-1	When X > Max	`Max = X.Value; ID = X.Id`	Who scored best?

Decision Tree: Which Pattern?

(Diagram)

9. Practice Questions

Basic Questions

Q1. Trace the max-finding algorithm for dataset [12, 45, 7, 38, 22].

Show Answer

Iter	X	Max Before	X > Max?	Max After
1	12	0	12>0 ✅	12
2	45	12	45>12 ✅	45
3	7	45	7>45 ❌	45
4	38	45	38>45 ❌	45
5	22	45	22>45 ❌	45

Max = 45 Q2. What does this pseudocode output for dataset [3, 8, 1, 6]?


sql
Result = 0
while (Pile 1 has more cards) {
    Pick a card X from Pile 1
    Move X to Pile 2
    if (X > Result) {
        Result = X
    }
}

Show Answer

Iter	X	X > Result?	Result
1	3	3 > 0 ✅	3
2	8	8 > 3 ✅	8
3	1	1 > 8 ❌	8
4	6	6 > 8 ❌	8

Result = 8 (the maximum) Q3. Write pseudocode to find the minimum value (instead of maximum). Show Answer


sql
Min = INFINITY   // A very large number
while (Pile 1 has more cards) {
    Pick a card X from Pile 1
    Move X to Pile 2
    if (X < Min) {
        Min = X
    }
}

Q4. Evaluate these AND conditions: (a) True AND False (b) True AND True (c) False AND False (d) (5 > 3) AND (10 < 20)

Show Answer

Expression	Step 1	Step 2	Result
`True AND False`	—	—	False
`True AND True`	—	—	True
`False AND False`	—	—	False
`(5>3) AND (10<20)`	`True AND True`	—	True

Intermediate Questions

Q5. Write pseudocode to find the student with the minimum marks in Physics (return both the marks and the student ID).

Show Answer


sql
MinPhy = INFINITY
MinCard = -1
while (Pile 1 has more cards) {
    Pick a card X from Pile 1
    Move X to Pile 2
    if (X.Physics < MinPhy) {
        MinPhy = X.Physics
        MinCard = X.Id
    }
}

Q6. What is the difference between these two code snippets? Snippet A:


pseudo
if (X.Gender == "M") {
    if (X.Maths > 80) {
        Count = Count + 1
    }
}

Snippet B:


pseudo
if (X.Gender == "M" AND X.Maths > 80) {
    Count = Count + 1
}

Show Answer

They are equivalent. Both count boys who scored above 80. Snippet A uses nested if statements, Snippet B uses a compound condition with AND. The result is identical. Q7. Trace this pseudocode. What does it compute?


sql
Result = 0
Count = 0
while (Pile 1 has more cards) {
    Pick a card X from Pile 1
    Move X to Pile 2
    if (X > 0) {
        Result = Result + X
        Count = Count + 1
    }
}
Result = Result / Count

For dataset: [-5, 10, 0, 20, -3, 15]

Show Answer

Iter	X	X > 0?	Result	Count
1	-5	❌	0	0
2	10	✅	10	1
3	0	❌ (not >0)	10	1
4	20	✅	30	2
5	-3	❌	30	2
6	15	✅	45	3

Final: Result = 45 / 3 = **15**

It computes the average of positive numbers. Q8. The following algorithm has a bug. Find and fix it.


sql
Max = 0
while (Pile 1 has more cards) {
    Pick a card X from Pile 1
    Move X to Pile 2
    if (Max > X.Maths) {
        Max = X.Maths
    }
}

Show Answer

Bug: The condition is reversed! if (Max > X.Maths) updates Max when the current Max is greater than X.Maths, which would track the minimum, not the maximum.

Fix: Change to if (X.Maths > Max).

Also, if all values could be negative, initialize Max to the first value or -INFINITY.

Advanced Questions

Q9. Write pseudocode to find the second highest value in a dataset.

Show Answer


sql
Max = 0
SecondMax = 0
while (Pile 1 has more cards) {
    Pick a card X from Pile 1
    Move X to Pile 2
    if (X > Max) {
        SecondMax = Max
        Max = X
    }
    else if (X > SecondMax) {
        SecondMax = X
    }
}

Logic:

When we find a new maximum, the old maximum becomes the second maximum
Otherwise, check if X beats the current second maximum Q10. Trace the second-max algorithm for dataset [10, 30, 20, 50, 40]. Show Answer

Iter	X	Before: Max, SecMax	Action	After: Max, SecMax
1	10	0, 0	X > Max → SecMax=0, Max=10	10, 0
2	30	10, 0	X > Max → SecMax=10, Max=30	30, 10
3	20	30, 10	X not > Max, X > SecMax (20>10) → SecMax=20	30, 20
4	50	30, 20	X > Max → SecMax=30, Max=50	50, 30
5	40	50, 30	X not > Max, X > SecMax (40>30) → SecMax=40	50, 40

Result: Max = 50, SecondMax = 40 Q11. Write pseudocode that counts how many times each of the values "High", "Medium", "Low" appears in a dataset (but without using dictionaries — just three counters). Show Answer


sql
HighCount = 0
MedCount = 0
LowCount = 0
while (Pile 1 has more cards) {
    Pick a card X from Pile 1
    Move X to Pile 2
    if (X.Category == "High") {
        HighCount = HighCount + 1
    }
    else if (X.Category == "Medium") {
        MedCount = MedCount + 1
    }
    else if (X.Category == "Low") {
        LowCount = LowCount + 1
    }
}

Q12. Design an algorithm that finds both the maximum Maths mark AND which gender achieved it. You need to track the maximum and the gender of the student who achieved it.

Show Answer


sql
MaxM = -1
MaxGender = ""
while (Pile 1 has more cards) {
    Pick a card X from Pile 1
    Move X to Pile 2
    if (X.Maths > MaxM) {
        MaxM = X.Maths
        MaxGender = X.Gender
    }
}
// Now MaxGender tells us if a boy or girl topped Maths

Trace with data:

Card	Gender	Maths	Action	MaxM	MaxGender
1	F	85	New max	85	F
2	M	92	New max	92	M
3	M	78	No	92	M
4	F	95	New max	95	F

Result: Max = 95, achieved by a Female student.

📚 Cross-References

Course	Topic	Connection
BSCS1002 (Python)	Week 2 — Loops	Python `for` and `while` loops
BSCS1002 (Python)	Week 3 — Conditions	Python `if`, `elif`, `else`
BSCS2002 (PDSA)	Week 2 — Max/Min	Formal algorithm analysis

Next Topic: 05 — Procedures & Parameters

Quiz Tip: Single-iteration max/min problems are the most common type in Quiz 1. Practice tracing until it's automatic! Join Discord PreviousPseudocode BasicsNextProcedures & Parameters

What this note is really saying

Week 2: Iteration & Filtering

1. Motivation: Beyond Simple Counting

2. The Two Core Patterns

Pattern A: Accumulation (Count, Sum)

Pattern B: Tracking (Max, Min)

3. Finding Maximum: The Tracker Pattern

The Algorithm

How It Works

Flowchart

Tracing: Find Maximum Marks

What If All Values Are Negative?

4. Finding Max with Card ID

The Algorithm

Tracing

Why Initialize MaxCard to -1?

5. Finding Both Max and Min

Tracing

6. The AND Operator in Filters

Compound Conditions

AND Truth Table

Using AND in Filtering

Worked Example: AND Filter

Comparison: AND vs Sequential Ifs

7. Accumulation through Iteration

Types of Accumulators

Combining Accumulation with Filtering

Multiple Accumulators

8. Comparison: Iteration Patterns

Summary Table

Decision Tree: Which Pattern?

9. Practice Questions

Basic Questions

Intermediate Questions

Advanced Questions

📚 Cross-References

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