Priyanshu Debnath — Blog https://priyanshudebnath.me/#/blogs Notes on competitive programming, mathematics, and systems programming. Thu, 17 Sep 2026 03:19:30 GMT Bin Packing — Why It's Hard, How to Approximate It, and When It Isn't Hard At All https://priyanshudebnath.me/blog/bin-packing-np-hardness-approximation-algorithms/ https://priyanshudebnath.me/blog/bin-packing-np-hardness-approximation-algorithms/ Tue, 07 Jul 2026 00:00:00 GMT A full pass through bin packing — the formal problem, why the decision version is NP-complete (and why the optimization version is strongly so), every classical approximation algorithm with its proven bound, the special cases that collapse back to polynomial time, and the backtracking/bitmask-DP techniques you'd actually use to solve small instances in a contest. Why My PBDS ordered_multiset Solution TLE'd (and the Fenwick Fix) https://priyanshudebnath.me/blog/pbds-vs-fenwick-cache-tle/ https://priyanshudebnath.me/blog/pbds-vs-fenwick-cache-tle/ Sun, 05 Jul 2026 00:00:00 GMT My approach to Zhily and Barknights was correct from the start, but the PBDS ordered_multiset implementation TLE'd twice. This post covers how Red-Black trees and order statistics work, and why a Fenwick tree passed instead. Stack, Heap, and the Registers That Finally Made Sense https://priyanshudebnath.me/blog/stack-heap-registers/ https://priyanshudebnath.me/blog/stack-heap-registers/ Sat, 04 Jul 2026 00:00:00 GMT Hi, it's my first blog. I went looking for proof that the stack and heap actually exist, and found it.