Trackers & Flags: Remembering What You've Seen

01Why it matters & the intuition

A loop body forgets everything when it finishes an iteration. Any variable declared before the loop is how information survives from one element to the next. Choosing that variable and giving it the right starting value is half of writing any algorithm — Kadane's, sliding window and DP are all built on it.

Think of it like…

A cricket scorer doesn't re-read the whole match after every ball. They keep a few running numbers — total runs, wickets, highest partnership — and update them ball by ball. Your tracker variables are that scorecard.

02The code blocks

Each block: the template in Python and C++, a line-by-line trace (press play and watch the highlighted line and the variables), the mistakes that cost the most debugging time, and a recall drill. Do the drill without scrolling up— that’s what makes it stick.

Block 1

Accumulator & counter

Use it for: Sums, averages, 'how many satisfy X', building totals for prefix sums.

1 · The template

python

total = 0
count = 0
for x in a:
    if x > 0:
        total += x
        count += 1

2 · Watch it run, line by line

trace · pythona = [3, -1, 4]

1/13

▶total = 0
2count = 0
3for x in a:
4    if x > 0:
5        total += x
6        count += 1

Variables

total: 0

-1

line 1 ›Sums start at 0 (the value that changes nothing when added).

3 · Classic mistakes

total = 0 inside the loopIt resets every iteration — initialise once, before the loop.
int total (C++, big inputs)Sums of 10⁵ values up to 10⁹ overflow 32-bit int. Use long long.

4 · Recall it without looking

recall · fill the blank

total = 
for x in a:
    total += x

Block 2

Running best (value + index)

Use it for: Max/min, best day to buy, longest streak so far, closest value, argmax.

1 · The template

python

best = a[0]
best_i = 0
for i in range(1, len(a)):
    if a[i] > best:
        best = a[i]
        best_i = i

2 · Watch it run, line by line

trace · pythona = [-4, -2, -7, -1]

1/13

▶best = a[0]
2best_i = 0
3for i in range(1, len(a)):
4    if a[i] > best:
5        best = a[i]
6        best_i = i

Variables

best: -4

-4

-2

-7

-1

line 1 ›Start with the first real element — not 0. With all-negative data, 0 would 'win' without being in the list.

3 · Classic mistakes

best = 0Wrong when every value is negative. Start from a[0] (or float('-inf') / INT_MIN).
Updating best but not best_iThe two drift apart and you return the wrong position.

4 · Recall it without looking

recall · fill the blanks

best = 
for i in range(, len(a)):
    if a[i] > best:
        best = a[i]

Block 3

Flag + early exit

Use it for: Does any element match? Is the list sorted? Bubble sort's 'no swaps → done'.

1 · The template

python

found = False
for x in a:
    if x == target:
        found = True
        break
print(found)

2 · Watch it run, line by line

trace · pythona = [4, 8, 15, 16, 23], target = 15

1/10

▶found = False
2for x in a:
3    if x == target:
4        found = True
5        break
6print(found)

Variables

target: 15
found: False

line 1 ›Assume 'not found' until proven otherwise.

3 · Classic mistakes

else: found = False (inside the loop)A later non-match overwrites an earlier match. Only ever set the flag one way inside the loop.
return inside a loop that should keep countingbreak / return are for 'answer known now'. For counts, let the loop finish.

4 · Recall it without looking

recall · fill the blank

found = False
for x in a:
    if x == target:
        found = True

Block 4

Count occurrences (dict / map)

Use it for: Frequencies, anagrams, duplicates, majority element, 'first unique character'.

1 · The template

python

counts = {}
for x in a:
    counts[x] = counts.get(x, 0) + 1

2 · Watch it run, line by line

trace · pythona = ['a', 'b', 'a', 'c', 'a']

1/12

▶counts = {}
2for x in a:
3    counts[x] = counts.get(x, 0) + 1

Variables

counts: {}

line 1 ›An empty dictionary: value → how many times seen.

3 · Classic mistakes

counts[x] += 1 (plain dict, first time)KeyError: the key doesn't exist yet. Use .get(x, 0) or collections.defaultdict(int).
if x in list_of_seen:Membership in a list is O(n) — the whole loop becomes O(n²). Use a dict or set.

4 · Recall it without looking

recall · fill the blank

counts = {}
for x in a:
    counts[x] = counts.get(x, ) + 1

03Key ideas

Declare before, update inside, read after

Trackers live outside the loop. Initialise before, update in the body, use the result after the loop ends.

Pick the right starting value

Sum → 0, product → 1, max → a[0] or −∞, min → a[0] or +∞, found → False, count → 0. A wrong start value is a silent bug.

Flags answer yes/no; break saves time

Once the answer is certain, stop. break exits the innermost loop; inside a function, return exits everything.

Dict/map = a tracker per value

When you need a counter for every distinct value, use a dictionary. It's the bridge to the Hashing lessons.

04Cheat sheet

Every block from this lesson on one screen. Keep it open while you do the lab — then try the lab again without it.

python

total = 0                     # sum
count = 0                     # how many
best, best_i = a[0], 0        # running max + where
found = False                 # yes/no

for i in range(len(a)):
    total += a[i]
    if a[i] > 0:
        count += 1
    if a[i] > best:
        best, best_i = a[i], i
    if a[i] == target:
        found = True          # add break if nothing else needs the loop

counts = {}                   # frequency of every value
for x in a:
    counts[x] = counts.get(x, 0) + 1

Tracker	Time	Extra space
Sum / count / running best	O(n)	O(1)
Flag + break	O(n) worst, often much less	O(1)
Counting dict	O(n) average	O(k) for k distinct values

Tracker

Time

Extra space

Sum / count / running best

O(n)

O(1)

Flag + break

O(n) worst, often much less

O(1)

Counting dict

O(n) average

O(k) for k distinct values

06Check your understanding

07Code lab

Write Python(or switch to JavaScript) and run it against real test cases. Python runs inside your browser — nothing is uploaded — and a C++ reference solution is under “Solution”.

Second largest distinct value

Return the second largest distinct value in the list, or None (JS: None) if it doesn't exist. One pass with two trackers — no sorting.

function: second_largestPython starts when you get here

⌘/Ctrl + Enter

01Why it matters & the intuition

02The code blocks

03Key ideas

Declare before, update inside, read after

Pick the right starting value

Flags answer yes/no; break saves time

Dict/map = a tracker per value

04Cheat sheet

05Complexity

06Check your understanding

07Code lab

Second largest distinct value