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Week 4: Iterations & Ranges

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Week 4: Iterations & Ranges

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2026-09-12

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Programming in Python — Week 4: Iterations & Ranges

The official IITM syllabus lists Week 4: Iterations and Ranges.

This is the point where Python moves from one-time decisions to repeated computation.

TL;DR

Conditionals answer:

Should this block run?

Loops answer:

How many times should this block run?

The main Week 4 ideas are:

for loops
range()
repeated execution
loop variables
accumulation
counting
summation
products
running state
tracing loops
off-by-one errors
nested reasoning with conditionals inside loops

Core model:

\boxed{ \text{initialize state} \rightarrow \text{repeat} \rightarrow \text{update state} \rightarrow \text{finish} }

1. Why loops are needed

Suppose you want to print:


text
Hello

five times.

Without iteration:


python
print("Hello")
print("Hello")
print("Hello")
print("Hello")
print("Hello")

This works, but it does not scale.

With a loop:


python
for i in range(5):
    print("Hello")

The repeated structure is expressed once.

2. Iteration

Iteration means repeated execution of a block of instructions.

Conceptually:


text
repeat:
    do something

In Python, one major mechanism is:


python
for ...

3. Basic `for` loop


python
for i in range(5):
    print(i)

Output:


text
0
1
2
3
4

The body executes once for each value produced by range(5).

4. Loop variable

In:


python
for i in range(5):

i is the loop variable.

Across iterations, it takes values:

0,1,2,3,4.

5. `range(n)`


python
range(n)

produces integer values conceptually:

0,1,2,\dots,n-1.

So the number of values is:

\boxed{n}

for positive integer

n

6. Crucial endpoint rule


python
range(5)

does not include 5.

It gives:


text
0, 1, 2, 3, 4

This exclusive upper bound is one of the most common sources of mistakes.

7. `range(start, stop)`

Example:


python
for i in range(2, 6):
    print(i)

Output:


text
2
3
4
5

General idea:

start,\ start+1,\dots,\ stop-1.

8. Start is included, stop is excluded

For:


python
range(3, 8)

values:

3,4,5,6,7.

So:

\boxed{ 3\leq i<8 }

9. `range(start, stop, step)`

Third argument controls step size.


python
range(2, 10, 2)

produces:


text
2, 4, 6, 8

10. Example with step 3


python
for i in range(1, 10, 3):
    print(i)

Output:


text
1
4
7

Next would be 10, but the stop value is excluded.

11. Negative step

Python can count downward.


python
for i in range(5, 0, -1):
    print(i)

Output:


text
5
4
3
2
1

12. Why `range(5, 0, -1)` stops at 1

The stop value:


text
0

is excluded.

So descending values satisfy:

i>0.

13. Countdown including zero

Use:


python
range(5, -1, -1)

which gives:


text
5
4
3
2
1
0

14. Loop body indentation


python
for i in range(3):
    print(i)
    print("inside")

print("outside")

The first two statements repeat.

The final statement executes once after the loop.

15. Trace loop execution

Program:


python
for i in range(3):
    print(i)

Trace:

Iteration	`i`	Output
1	0	0
2	1	1
3	2	2

Then loop ends.

16. Loop variable changes automatically

You normally do not need:


python
i = i + 1

inside:


python
for i in range(...)

The for loop itself assigns the next value from the range.

17. Repeated arithmetic

Example:


python
for i in range(1, 6):
    print(i * i)

Outputs:

1,4,9,16,25.

The expression is recalculated for each i.

18. Printing 1 through 10

Use:


python
for i in range(1, 11):
    print(i)

Not:


python
range(1, 10)

because 10 would be excluded.

19. Off-by-one errors

An off-by-one error occurs when a loop runs one too many or one too few times.

Example intended:

1,\dots,10

Wrong:


python
range(1, 10)

Correct:


python
range(1, 11)

20. Count number of iterations

For:


python
range(a, b)

with step 1 and

b>a

, number of values is:

b-a.

Example:


python
range(3, 8)

has:

8-3=5

values.

21. Accumulator pattern

One of the most important loop patterns:


python
total = 0

for ...:
    total = total + value

total accumulates information across iterations.

22. Sum 1 through 5


python
total = 0

for i in range(1, 6):
    total = total + i

print(total)

Trace:

0 \to1 \to3 \to6 \to10 \to15.

Final:

\boxed{15}

23. Trace table

`i`	`total` before	`total` after
1	0	1
2	1	3
3	3	6
4	6	10
5	10	15

24. Why initialize sum to zero

For addition:

x+0=x.

So zero is the additive identity.

Starting:


python
total = 0

does not distort the sum.

25. Product accumulator

To multiply values:


python
product = 1

for i in range(1, 5):
    product = product * i

Final:

1\cdot1\cdot2\cdot3\cdot4=24.

26. Why product starts at 1

Because:

x\cdot1=x.

Starting at 0 would make every product remain:

0.

27. Factorial

For positive integer

n

n!=1\cdot2\cdots n.

Python:


python
n = int(input())

fact = 1

for i in range(1, n + 1):
    fact = fact * i

print(fact)

28. Example factorial

For:

n=5,

state:

1 \to1 \to2 \to6 \to24 \to120.

Final:

\boxed{5!=120}

29. Counter pattern

A counter usually starts at:


python
count = 0

and increases when some event occurs:


python
if condition:
    count = count + 1

30. Count even numbers


python
count = 0

for i in range(1, 11):
    if i % 2 == 0:
        count = count + 1

print(count)

Even values:

2,4,6,8,10.

So:

\boxed{count=5}

31. Condition inside loop

This structure:


python
for i in range(...):
    if condition:
        action

means:

repeat the test for every iteration.

This combines Weeks 2–3 conditionals with Week 4 iteration.

32. Filter pattern

Example:


python
for i in range(1, 11):
    if i % 3 == 0:
        print(i)

Outputs:


text
3
6
9

The loop generates candidates; the if filters them.

33. Sum only selected values


python
total = 0

for i in range(1, 11):
    if i % 2 == 0:
        total = total + i

print(total)

This computes:

2+4+6+8+10=30.

34. Running total

A variable like:


python
total

changes over time.

That is a running total.

At iteration

k

, it stores the sum of all relevant values processed so far.

35. Loop invariant intuition

For:


python
total = 0

for i in range(1, n + 1):
    total += i

after processing integer

i

, total equals:

1+2+\cdots+i.

That stable meaning across iterations is an invariant-like way to reason about the loop.

36. Shorthand assignment

Python permits:


python
total += i

instead of:


python
total = total + i

Likewise:


python
count += 1
product *= i

37. For learning, expand mentally

When tracing:


python
x += 3

read it as:


python
x = x + 3

That makes state updates clearer.

38. Sum of squares

Goal:

1^2+2^2+\cdots+n^2.


python
total = 0

for i in range(1, n + 1):
    total += i ** 2

print(total)

39. Count multiples

Count numbers from 1 to 100 divisible by 7:


python
count = 0

for i in range(1, 101):
    if i % 7 == 0:
        count += 1

print(count)

40. Generate multiples directly

Instead of filtering every number:


python
for i in range(7, 101, 7):
    print(i)

This directly generates:

7,14,21,\dots,98.

Sometimes the range itself can encode the pattern.

41. Looping a fixed number of times

If you only care about repetition count:


python
for i in range(5):
    print("Hello")

Here i may not be logically important.

Conventionally, Python programmers sometimes use:


python
for _ in range(5):
    print("Hello")

to indicate the loop variable is intentionally unused.

42. Input repeated several times

Suppose read 5 numbers and sum them:


python
total = 0

for _ in range(5):
    x = int(input())
    total += x

print(total)

The program reads exactly five inputs.

43. Count positive inputs


python
count = 0

for _ in range(5):
    x = int(input())

    if x > 0:
        count += 1

print(count)

The state count survives across iterations.

44. Average of fixed number of inputs


python
total = 0

for _ in range(5):
    x = float(input())
    total += x

average = total / 5

print(average)

45. Generalize to `n` values


python
n = int(input())

total = 0

for _ in range(n):
    x = float(input())
    total += x

average = total / n

print(average)

This assumes:

n>0.

46. Maximum over repeated input

Suppose read

n

numbers.

One robust strategy:


python
n = int(input())

maximum = float(input())

for _ in range(n - 1):
    x = float(input())

    if x > maximum:
        maximum = x

print(maximum)

This uses the first value as the initial maximum.

47. Why not initialize maximum to 0?

Suppose all inputs are:


text
-5
-3
-10

If:


python
maximum = 0

then result incorrectly remains 0 even though 0 was never in the data.

Initialize from actual data when possible.

48. Minimum pattern


python
minimum = float(input())

for _ in range(n - 1):
    x = float(input())

    if x < minimum:
        minimum = x

Same logic with reversed comparison.

49. Multiple accumulators

A loop may update several pieces of state.

Example:


python
total = 0
count_positive = 0

for _ in range(n):
    x = int(input())

    total += x

    if x > 0:
        count_positive += 1

One pass can compute multiple summaries.

50. Sum and count for conditional average

Suppose average of positive values only:


python
total = 0
count = 0

for _ in range(n):
    x = float(input())

    if x > 0:
        total += x
        count += 1

Then if:


python
count > 0

we can compute:


python
average = total / count

51. Why count matters

If only selected values contribute, dividing by total number of inputs is wrong.

Example data:


text
5, -2, 7

Positive sum:

12.

Positive count:

2.

Average:

6.

Not:

12/3=4.

52. Arithmetic progression via `range`


python
range(5, 21, 5)

generates:

5,10,15,20.

So range() can represent arithmetic progressions.

53. `range` and inequalities

For positive step:


python
range(a, b)

roughly corresponds to:

a\leq i<b.

For step:


python
s>0,

values are:

a,\ a+s,\ a+2s,\dots

while remaining below

b

54. Negative-step inequality

For:


python
range(10, 2, -2)

values:

10,8,6,4.

They continue while:

i>2.

Stop value still excluded.

55. Empty range

Example:


python
range(5, 2)

with default positive step.

There are no values because you cannot move upward from 5 and reach something below 2.

So loop body executes zero times.

56. Another empty range


python
range(2, 5, -1)

is empty because step moves downward while stop lies upward.

The step direction must be compatible with the interval.

57. Zero iterations matter

Program:


python
x = 10

for i in range(0):
    x = x + 1

print(x)

Loop runs zero times.

Output:

\boxed{10}

58. State after loop

After:


python
for i in range(5):
    ...

the loop is over once all range values are consumed.

Anything after the loop executes once.

Do not mentally keep repeating later statements.

59. Final value of loop variable

In ordinary Python:


python
for i in range(5):
    pass

after normal completion, i is typically:

4.

But do not rely on this unless the problem specifically asks about it; the important logical role is the sequence during iteration.

60. `break`

Python provides:


python
break

to terminate the nearest loop immediately.

Example:


python
for i in range(10):
    if i == 5:
        break
    print(i)

Output:


text
0
1
2
3
4

61. `break` trace

At:

i=5,

condition:


python
i == 5

is true.

break exits the loop before:


python
print(i)

for that iteration.

62. Search pattern with `break`

Suppose:


python
found = False

for i in range(1, 101):
    if i * i == target:
        found = True
        break

Once the desired item is found, further iterations are unnecessary.

63. `continue`

Python:


python
continue

skips the rest of the current iteration and moves to the next one.

Example:


python
for i in range(5):
    if i == 2:
        continue
    print(i)

Output:


text
0
1
3
4

64. `continue` is not `break`

`continue`

Skip current iteration, loop continues.

`break`

End loop entirely.

This distinction is fundamental.

65. Example with `continue`


python
for i in range(1, 6):
    if i % 2 == 0:
        continue

    print(i)

Output:


text
1
3
5

Even values skip the print.

66. Loop `else` — supporting Python feature

Python permits an else attached to a loop.

Example:


python
for i in range(5):
    if i == target:
        print("Found")
        break
else:
    print("Not found")

The else executes if the loop ends normally without break.

This is useful Python knowledge, though it may not be central to the official Week 4 heading.

67. Searching for a divisor


python
n = int(input())

found_divisor = False

for d in range(2, n):
    if n % d == 0:
        found_divisor = True
        break

This tests candidate divisors.

It illustrates repetition + condition + early exit.

68. Prime-number intuition

For integer:

n>1,

a basic algorithm checks whether any integer:

2\leq d<n

divides

n

exactly.

If one does:


text
not prime

If none does:


text
prime

This is a classic loop problem.

69. Basic prime code


python
n = int(input())

is_prime = n > 1

for d in range(2, n):
    if n % d == 0:
        is_prime = False
        break

if is_prime:
    print("Prime")
else:
    print("Not prime")

70. Boolean flag


python
is_prime

is a flag.

A flag stores whether some event/condition has occurred.

Other examples:


python
found
valid
seen_negative

71. Flag pattern


python
found = False

for ...:
    if desired_condition:
        found = True
        break

if found:
    ...
else:
    ...

This pattern is very common.

72. Repeated digit-like arithmetic

Loops can repeatedly apply arithmetic transformations.

Example:


python
n = 1234

for _ in range(4):
    digit = n % 10
    print(digit)
    n = n // 10

Outputs digits from right to left:


text
4
3
2
1

73. Why `% 10`

For positive integer:

n\bmod10

gives the final decimal digit.

Example:

1234\bmod10=4.

74. Why `// 10`

1234//10=123.

It removes the final decimal digit for positive integers.

This lets a loop repeatedly process digits.

75. Build sum of digits

For a known number of digits or with a later while loop, the pattern is:


python
digit = n % 10
total += digit
n = n // 10

This is another accumulator pattern.

76. Pattern printing intuition

Loops can generate repeated output structures.

Example:


python
for i in range(1, 6):
    print("*" * i)

Output:


text
*
**
***
****
*****

The loop controls size.

77. String repetition

Python:


python
"*" * 4

produces:


text
****

Combining this with a loop generates simple patterns.

78. Multiplication table


python
n = int(input())

for i in range(1, 11):
    print(n * i)

For:

n=7,

outputs:

7,14,21,\dots,70.

79. Repetition can generate instead of store

Notice the multiplication table need not first create a list.

Each result can be computed and printed immediately.

This is streaming-style thinking:


text
generate
→ process
→ output
→ next

Common mistake: accumulator inside loop

Wrong:


python
for i in range(1, 6):
    total = 0
    total += i

total resets every iteration.

After each iteration it contains only the current i.

81. Correct accumulator placement


python
total = 0

for i in range(1, 6):
    total += i

Initialization happens once before repetition.

Common mistake: count reset

Wrong:


python
for i in range(10):
    count = 0

    if condition:
        count += 1

The previous count is destroyed on every iteration.

Common mistake: wrong range endpoint

Want:

1,2,3,4,5.

Wrong:


python
range(1, 5)

Correct:


python
range(1, 6)

Common mistake: wrong negative range

Want:


text
5 4 3 2 1

Wrong:


python
range(5, 1)

because default step is positive.

Correct:


python
range(5, 0, -1)

Common mistake: zero step


python
range(1, 10, 0)

is invalid.

A step cannot be zero because the sequence would never progress.

Common mistake: manually modify

for variable

Example:


python
for i in range(5):
    i = i + 10

This changes i during the current iteration, but the next iteration receives the next value from the range.

Do not treat Python for as a manually controlled counter loop.

Common mistake:

if confused with loop


python
if x < 10:
    x += 1

runs at most once.


python
for ...

repeats according to an iterable/range.

Selection and iteration are different control structures.

Common mistake: count loop iterations incorrectly


python
for i in range(2, 8):

runs for:

2,3,4,5,6,7

which is:

\boxed{6}

iterations.

Not 8.

Common mistake: change state before using old value

Example:


python
total = 0

for i in range(3):
    total = total + i

Trace each assignment sequentially.

Do not calculate all updates as though total remained 0.

Common mistake: divide before loop finishes

Suppose computing average.

Wrong structure:


python
for ...:
    total += x
    average = total / n

This repeatedly computes partial averages.

It may still end with the correct final value in some cases, but the intended algorithm is clearer as:


python
for ...:
    total += x

average = total / n

Common mistake: divide by zero count

For filtered average:


python
average = total / count

only valid when:

count>0.

Always consider the possibility of zero matching elements.

Common mistake:

break exits all loops

break exits only the nearest enclosing loop.

This becomes especially important once nested loops appear.

For Week 4 single loops, just remember it terminates the current loop.

Common mistake:

continue repeats same iteration

No.

continue skips to the next iteration.

It does not restart the same value.

94. Manual loop-tracing workflow

For a loop question:

Write the values produced by range().
Write initial state before the loop.
Process one iteration at a time.
Update variables immediately.
Record output in order.
If break, stop immediately.
If continue, skip remaining body for that iteration.
After final iteration, continue with code after the loop.

95. Trace table template

Program:


python
s = 0

for i in range(1, 5):
    s = s + 2 * i

Use:

`i`	`2*i`	`s` before	`s` after
1	2	0	2
2	4	2	6
3	6	6	12
4	8	12	20

Final:

\boxed{s=20}

96. Slightly harder trace


python
x = 1

for i in range(1, 5):
    if i % 2 == 0:
        x = x * 2
    else:
        x = x + 3

print(x)

Trace:

`i = 1`

odd:

x=1+3=4

`i = 2`

even:

x=4\cdot2=8

`i = 3`

odd:

x=8+3=11

`i = 4`

even:

x=11\cdot2=22

Output:

\boxed{22}

97. Loop as repeated state transformation

A loop can be viewed mathematically as repeatedly transforming state:

S_0\to S_1\to S_2\to\cdots\to S_n.

For a running sum:

S_{k+1}=S_k+x_{k+1}.

This viewpoint is useful for understanding almost every iterative algorithm.

98. Efficiency intuition

Suppose:


python
for i in range(n):
    ...

The body runs about:

n

times.

So the amount of repeated work grows with

n

This later leads naturally to algorithmic complexity ideas.

99. Week 3 → Week 4 transition

Week 3:


text
if condition:
    execute branch

Week 4:


text
for each value:
    execute block

Combined:


python
for i in range(...):
    if condition:
        ...

This is already enough to solve a large class of programming problems.

100. Compact `range()` cheat sheet


python
range(5)
## 0,1,2,3,4


python
range(2, 6)
## 2,3,4,5


python
range(2, 10, 2)
## 2,4,6,8


python
range(5, 0, -1)
## 5,4,3,2,1

Core rule:

\boxed{ \text{start included, stop excluded} }

101. Core loop patterns

Repetition


python
for _ in range(n):
    action

Sum


python
total = 0
for ...:
    total += value

Count


python
count = 0
for ...:
    if condition:
        count += 1

Product


python
product = 1
for ...:
    product *= value

Maximum


python
maximum = first_value
for ...:
    if value > maximum:
        maximum = value

Search


python
found = False
for ...:
    if condition:
        found = True
        break

102. What you should actually master

By the end of Python Week 4, you should be able to:

Explain iteration.
Write and trace for loops.
Understand the loop variable.
Use range(stop).
Use range(start, stop).
Use range(start, stop, step).
Handle positive and negative steps.
Remember that the stop value is excluded.
Detect off-by-one errors.
Count loop iterations.
Build running sums.
Build counters.
Build running products.
Compute factorials.
Combine if with for.
Filter values during iteration.
Read repeated inputs.
Find running max/min.
Use multiple accumulators.
Understand flags.
Use break.
Use continue.
Trace loop state line-by-line.
Avoid resetting accumulators inside loops.
Recognize zero-iteration cases.

If these are comfortable, Programming in Python Week 4 is under control.

Quick Recall & Flashcards

Test your active recall before proceeding to practice problems. Format:

Question :: Answer.

Week 4 Diagnostic: What is the sequence of integers generated by list(range(2, 10, 3))? :: Answer: A — range(start, stop, step) starts at 2, steps by 3, and stops before 10: 2, 5, 8.
Week 4 Diagnostic: How many times will a while loop with condition count < 5 execute if count starts at 0 and increments by 1 each iteration? :: Answer: 5 — Iterations for count = 0, 1, 2, 3, 4 -> 5 times.

Practice & Self-Check

Attempt these diagnostic questions to verify your operational understanding.

Question 1

What is the sequence of integers generated by list(range(2, 10, 3))?

MCQ

3 Unit Assessment

A. [2, 5, 8]

B. [2, 5, 8, 10]

C. [3, 6, 9]

D. [2, 3, 4, 5, 6, 7, 8, 9]

Question 2

How many times will a while loop with condition count < 5 execute if count starts at 0 and increments by 1 each iteration?

NAT

3 Unit Assessment