Phase 8Days 40-44

Two Pointers & Sliding Window

The window / two-pointer engine that solves a huge class of subarray and substring problems in O(n)

Phase Goal

Master the grow-shrink window and know exactly when it applies versus prefix sums.

Progress

Day 40: Two pointers — the technique

Pair with a target sum in a sorted arrayContainer with most waterTrapping rain water (two-pointer view; the stack view comes later)Deciding which pointer to move

Slow/fast write-index compaction (remove or move)Merging and partitioning with two indicesInvariants that guarantee correctnessAvoiding rescans

The monotonic-structure requirement (sorted or additive)Why it fails on unsorted, non-monotone dataComplexity: O(n) after an O(n log n) sortRecognizing the shape

Choose one core problem from LeetCode, Codeforces, AtCoder, or CSES after checking its prerequisites; hide its technique labelSpend 10–20 minutes retrieving one earlier mechanism and one earlier bug before new work; prioritize weak prerequisitesUse a five-task bank: guided warm-up, core, changed constraint, delayed recall, optional stretch; attempt one or two, not all five on a timerBefore a solution, produce a trace or brute-force plan; when stuck take one hint, act on it, then reassessRecord help used, the failing input, the corrected reasoning, and a next review date; start around 1/3/7/14/30 days and adaptReserve a weekly mixed review; after foundation readiness add a short virtual contest and upsolve one task with known prerequisitesProve progress through a delayed blank-editor reconstruction and a changed problem; a same-day quiz is supporting evidence only

Day 41: Fixed-size sliding window

Maximum sum of a size-k subarraySlide by adding the new element and removing the oldMax points from cards (window on the complement)Why recomputing is O(nk) and sliding is O(n)

First negative in every windowCount anagrams of a pattern (fixed window plus frequency compare)Maintaining a frequency array as the window movesComparing frequency arrays in O(26)

Off-by-one on window boundariesForgetting to remove the leaving elementInitializing the first windowEdge case k > n

Day 42: Variable-size sliding window

Grow the right, shrink the left while the window is invalidLongest substring without repeating charactersLongest repeating character replacementThe while-shrink pattern

Max consecutive ones III (at most k zeros)Binary subarray with sum = goal via atMost(goal) - atMost(goal-1)Count nice subarrays (exactly k odds)Number of substrings containing all three characters

Longest subarray with at most K distinct (a map of counts)Fruits into baskets as the K=2 caseSubarrays with exactly K distinct integersWhen a map is needed versus a fixed array

Day 43: Hard window problems

Minimum window substring covering all chars of tThe have / need counter techniqueShrinking to the smallest valid windowThe minimum window subsequence variant

Sliding window maximum with a monotonic dequeWhy a deque gives O(n) instead of O(nk)The full deque treatment comes in the stacks/queues phaseRecognizing when a monotonic structure is needed

Positives-only points to a window; negatives point to prefix+hashFixed versus variable window cuesBuilding a decision checklistComplexity sanity checks

Day 44: Hashing deep dive & problem set

Hashing pairs, tuples, and vectors as map keysCustom hash functions and anti-hash defenseFrequency signatures for groupingWhen to use ordered versus unordered

Longest consecutive sequence (revisit, O(n))Subarray sum = k and XOR = k (revisit with mastery)Group anagrams and isomorphic patternsThe two-sum family

Prefix+hash versus window decision recapCommon hashing TLEs and their fixesPattern log updatePrep for linked lists

Phase Complete!

After this phase, you'll be able to:

Two pointers — the technique
Fixed-size sliding window
Variable-size sliding window
Hard window problems
Hashing deep dive & problem set

After Phase 8, explain a core invariant, reconstruct a solution after a delay, diagnose a bug, and solve one unlabelled variation. Repair a failed prerequisite before advancing; record help separately from independent work.

Back to all phases

Two Pointers & Sliding Window

Phase Goal

Day 40: Two pointers — the technique

Opposite-direction pointers

Same-direction pointers

When two pointers apply

Practice, delayed recall, and independent transfer

Day 41: Fixed-size sliding window

The window sum

Averages & counts

Fixed-window pitfalls

Practice, delayed recall, and independent transfer

Day 42: Variable-size sliding window

The longest-window template

At-most / exactly K

Fruits into baskets & K distinct

Practice, delayed recall, and independent transfer

Day 43: Hard window problems

Minimum window

Window + deque (preview)

Choosing window versus prefix versus two pointer

Practice, delayed recall, and independent transfer

Day 44: Hashing deep dive & problem set

Designing hash keys

Hashing-powered problems

Reflection

Practice, delayed recall, and independent transfer

Phase Complete!