Fancy Sequence: O(1) lazy trick
A new explainer breaks down LeetCode 1622 (“Fancy Sequence”) and shows how lazy propagation plus modular inverses yields O(1) per operation for add/multiply/getIndex — avoiding costly per-element updates. The Java walkthrough highlights modular division pitfalls and edge-case handling you’ll need to explain in interviews explained.
ExpertFunda published a Java walkthrough titled "Leetcode 1622 Fancy Sequence Explained" on Mar 14, 2026, showing diagrams and a step‑by‑step implementation (50 views at crawl time). (youtube.com) Canonical O(1) solutions store two global accumulators a (multiplier) and b (adder) and append a normalized value x = (val − b) * inv(a) mod M so getIndex simply computes (a * vals[idx] + b) % M, as shown in community code and the WalkCCC reference implementation. (walkccc.me) The modulus used across solutions is 1,000,000,007 (10^9+7), and modular inverses are computed with Fermat’s Little Theorem via fast exponentiation a^(M−2) mod M to get inv(a) in O(log M) time. (walkccc.me) Problem constraints—1 ≤ val, inc, m ≤ 100, 0 ≤ idx ≤ 10^5, and at most 10^5 total calls—drive the need for the lazy/inverse trick to avoid O(n) updates per operation. (leetcode.com) Java/C++ walkthroughs explicitly use 64‑bit types and an iterative modPow (exponentiation by squaring) to avoid overflow and to compute inverses; WalkCCC’s C++ snippet and several Java repos mirror that approach. (walkccc.me) A known pitfall flagged in LeetCode feedback is multAll by 0 (or by 10^9+7) which makes a non‑invertible multiplier and requires special handling such as zeroing the sequence or recording a reset epoch instead of blindly calling inv(a); community guides and the GitHub issue recommend treating m % MOD == 0 as a full‑reset event. (github.com)
