Interview Patterns in Motion

How to read this

• The top row is your input with indices underneath. Arrows mark the pointers (l, r, i); the orange bracket is the current window or range.
• Colors: blue = the pointer's current element, yellow = being compared or inside the window, red = just changed / popped / written, green = part of the answer, gray = ruled out forever.
• The lower half is the pattern's helper: the running sum, the hash map of last positions, the stack, the prefix-sum table with its counts, or the lo/mid/hi number line with the day-by-day packing.
• Every counter panel shows the pattern's work next to the brute-force cost it replaces. The pointers only move forward, which is the amortized argument for O(n).

Try this

1. Two pointers on 1 3 4 6 8 11, target 10: five sum checks find (2, 3) = 4 + 6. Brute force would test up to 15 pairs. Try target 100: l and r meet after 5 checks with no pair.
2. Longest substring on abacdbe: l jumps from 0 to 1 at the second "a", then past the first "b" to 2; the answer is 5 ("acdbe"). Try aaaa (answer 1) and abcdef (answer 6, l never moves).
3. Shortest window ≥ S on 4 1 1 3 2 5, S = 8: best becomes 4, then 3 (3 2 5). Count pointer moves: never more than 2n = 12.
4. Next greater on 3 7 1 4 2 6 → 7 −1 4 6 6 −1. When 6 arrives it pops two indices at once. Try a decreasing array: nothing is popped until the end, and every answer is −1.
5. Prefix sums on 1 2 1 −1 2 1, k = 3: count 5. Binary search on the answer for 4 8 2 5 3 7 1, D = 3: mids 19, 13, 10, 12, 11 and the answer is 12 after only 5 checks; the range [8, 30] holds 23 candidates, and doubling the weights barely adds a check.

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