Freaks City

Problem Statement Given a non-negative integer n where 0 ≤ n ≤ 2×10^9, compute the n-th term of the Fibonacci sequence modulo 10000. The sequence is defined as F(0) = 0, F(1) = 1, and F(n) = F(n-1) + F(n-2) for n > 1. The input consists of multiple test cases, each containing a single integer n. Processing terminates when n = -1. Algorithmic ...

Subtree Budget Allocation and Optimal Path Reconstruction The core challenge revolves around allocating a fixed budget across a binary tree structure to maximize a specific threshold value. The solution begins by analyzing the root's contribution and propagating constraints downward. We define a dynamic programming state dp_max[u][b] representi ...

Problem D: Weighted Permutation Sum Given a sequence of numbers, consider generating all its non-empty subsequences, constructing a permutation by repeatedly removing the last element until one remains, and summing the final remaining numbers across all such processes. The problem requires computing the total sum over all subsequences. For anal ...

The ZKW segment tree is a non-recursive data structure that performs bottom-up updates and queries. It is often used as a replacement for Fenwick trees when range updates and range queries are needed. The key concept is to use two "shrinking" pointers (l and r) that move upward from the leaf level. To range updates with lazy tags, we ...