Week 4 — iterations & ranges

Quiz 2 scope: Weeks 1–8 per IITM May 2026 foundation courses. Source baseline: IITM BS admissions important-dates calendar · May 2026 cycle. Times on assessments are operational conventions — verify hall ticket.

Week map

Classify → Represent → Execute → Trap-check

• Recognize: Ask: How many values does range(3, 8) produce?
• Procedure: range(5) gives 0..4 (five values). range(2,7) gives 2..6. Step defaults to 1; negative step counts down when start > stop.
• Variations / traps: Watch for: range(1, n) vs range(n) off-by-one.

Formula chain (compressed)

for/while → range(start,stop,step) → accumulator → loop invariant.

1. for loop — for x in seq: — known iteration count
2. while loop — while cond: — stop when condition false
3. range — range(n), range(a,b), range(a,b,s) — 0..n-1 or stepped
4. Accumulator — total = total + x — sum/count/product patterns
5. Infinite loop trap — cond never becomes false — check update inside while

Deep study

Programming in Python · Week 4 — Iterations and range

Week map

Loop notation

• for i in range(n): → counted loop → i takes each value produced by range → body runs once per value.
• range(stop) → integers 0, 1, …, stop-1 → range(4) → 0,1,2,3 (four values).
• range(start, stop) → from start inclusive to stop exclusive → range(2,6) → 2,3,4,5.
• range(start, stop, step) → step size → range(0,10,2) → 0,2,4,6,8.

Accumulator

python
Run Inline
total = 0          # neutral for sum
for k in range(5):
    total = total + k
# total = 0+1+2+3+4 = 10

for vs while

• for — known iteration count or explicit sequence.
• while cond: — repeat until cond false; must ensure progress toward termination.

python
Run Inline
n = 8
while n > 0:
    n = n - 3
# n goes 8→5→2→-1, stops; loop ran 3 times

Pattern families

Easy — Count iterations

• How many values does range(a,b) produce? → max(0, b-a) for step 1.
• List indices visited: range(len(s)) for string s.
• Final loop variable value after for (last assigned value remains).

Medium — Accumulator trace

• Sum 1..n, sum of squares, count positives in fixed list.
• Product accumulator starts at 1, not 0.
• Print once after loop vs each iteration.

Hard — Combined condition in loop

• Sum only entries meeting predicate (if x % 2 == 0 inside loop).
• while with compound update; detect infinite loop risk if condition never changes.
• Nested setup for week 5 preview: outer i, inner j — count pairs briefly.

Worked mini-examples

python
Run Inline
s = 0
for i in range(1, 11):
    s += i
# s = 55

python
Run Inline
data = [4, 7, 2, 9, 0, 6]
c = 0
for x in data:
    if x % 2 == 0:
        c += 1
# c = 4

python
Run Inline
val = 20
steps = 0
while val >= 10:
    val = val - 6
    steps += 1
# val = 8, steps = 2

python
Run Inline
t = 0
for j in range(0, 15, 3):
    t += j
# j: 0,3,6,9,12 → t = 30

Traps

• range(1, n) vs range(n) — classic off-by-one.
• Forgetting accumulator initialization (total = 0 missing).
• Modifying loop variable expecting to change how many iterations — range already fixed.
• while True without break path.
• Using = instead of += in accumulation (total = x resets each time).

Diagnostic (try yourself)

1. How many numbers does range(5, 15) generate? List them.
2. What is the final value of sum?

python
Run Inline
sum = 0
for i in range(2, 8):
    sum = sum + i

1. What is printed?

python
Run Inline
prod = 1
for k in range(1, 5):
    prod = prod * 2
print(prod)

1. Write a loop that prints integers 10 down to 1 (inclusive) using range with a negative step.
2. After this loop, what is n?

python
Run Inline
n = 50
while n > 1:
    n = n // 2

ChatGPT prep archive

• Chatty reference archive

Archived import for extra depth — complements the notes above, not official IITM material.

Core concepts

• for loop: iterate over sequence or range(start, stop, step); stop is exclusive.
• while loop: repeat while condition true; needs progress toward false to avoid infinite loop.
• Accumulator: variable updated each iteration (total += x).
• Loop variable takes each value in turn; may be unused with for _ in range(n).

Notation & vocabulary

Pattern families

Easy — Count iterations

Medium — Accumulator trace

Hard — while with guard

Drill these on the pattern atlas — filter to week 4.

Traps

• range(1, n) vs range(n) off-by-one.
• Forgetting to initialize accumulator.
• Modifying loop variable expecting to change range length.
• while True without break exit path.

Retrieval prompts

1. How many values does range(3, 8) produce?
2. Where must an accumulator be initialized?
3. When prefer for over while?

Practice loop

1. Read Deep study (if present) or core concepts once.
2. Recite the formula chain without looking.
3. Open one easy pattern on the interactive atlas for week 4.
4. Attempt without solutions; mark studied after an honest try.
5. Say one trap aloud before closing the tab.

Related

• Full weeks 1–8 prep guide
• Pattern atlas note
• Formula chain desk