Week 5 — iterations continued

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 times runs inner if outer is 3 and inner is 4?
• Procedure: Multiply outer and inner trip counts. Trace one outer step showing full inner run. Useful for tables and coordinate pairs.
• Variations / traps: Watch for: break only leaves inner loop in nested structure.

Formula chain (compressed)

outer×inner loops → O(n²) scans → search flag → min/max over grid.

1. Nested for — for i in ...: for j in ...: — pairs / grid traversal
2. Iteration count — outer × inner body runs — complexity estimate
3. Search flag — found = False; break inner — stop early on match
4. Min/max scan — if x < best: best = x — linear search
5. Indentation — body belongs to nearest for/while — trace nested blocks

Deep study

Programming in Python · Week 5 — Nested iterations

Week map

Nested loop notation

• Outer index → often row or first coordinate → runs its full range once per “round.”
• Inner index → completes entire range for each outer value → total body runs = outer count × inner count.
• break → exits innermost loop only → outer continues unless restructured.

python
Run Inline
count = 0
for i in range(3):
    for j in range(2):
        count += 1
# count = 6  (3 × 2)

Search pattern

python
Run Inline
found = False
for item in seq:
    if item == target:
        found = True
        break

Min/max pattern

python
Run Inline
best = seq[0]
for x in seq[1:]:
    if x > best:
        best = x

Pattern families

Easy — Nested count

Medium — Search and index

Hard — Min/max with updates

Worked mini-examples

python
Run Inline
pairs = []
for i in range(2):
    for j in range(3):
        pairs.append((i, j))
# 6 pairs: (0,0)..(1,2)

python
Run Inline
nums = [4, 7, 2, 9]
target = 7
found = False
for n in nums:
    if n == target:
        found = True
        break
# found is True

python
Run Inline
data = [-3, -8, -1, -5]
m = data[0]
for x in data:
    if x > m:
        m = x
# m = -1

python
Run Inline
for i in range(3):
    for j in range(3):
        if j == 1:
            break
    # inner breaks at j=1; outer continues
# outer runs 3 times; inner runs 2 times each → 6 inner bodies

Traps

• break only leaves inner loop in nested structure.
• Max initialized to 0 fails for all-negative data.
• Off-by-one: range(len) vs direct iteration.
• Inner variable shadows outer (for i inside for i).
• Counting iterations as n + m instead of n × m.

Diagnostic (try yourself)

1. How many times does the body run?

python
Run Inline
for a in range(4):
    for b in range(3):
        pass

1. After nested loops below, what is j?

python
Run Inline
for i in range(2):
    for j in range(5):
        pass

1. Write a loop that sets found = True and breaks when target appears in list items.
2. Find max of [-10, -3, -7] — why should best not start at 0?
3. In a 3×3 nested loop with break when j == 0 in the inner loop, how many inner bodies execute per outer step?

ChatGPT prep archive

• Chatty reference archive

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

Core concepts

• Nested loops: inner completes fully for each outer step; total iterations = product of counts.
• Search: boolean found flag or early break when target located.
• Min/max: initialize with first element or float('inf'); update when comparison holds.
• break exits innermost loop only unless labeled logic restructures.

Notation & vocabulary

Pattern families

Easy — Nested count

Medium — Find in sequence

Hard — Min with updates

Drill these on the pattern atlas — filter to week 5.

Traps

• break only leaves inner loop in nested structure.
• Max initialized to 0 fails for all-negative data.
• Off-by-one when using range(len) vs direct iteration.
• Variable reused name in inner loop shadows outer.

Retrieval prompts

1. How many times runs inner if outer is 3 and inner is 4?
2. Why initialize max carefully for negative inputs?
3. What does break do inside nested loops?

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 5.
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