Fading Coder

One Final Commit for the Last Sprint

Algorithmic Contest Analysis: Range Queries, Grid Optimization, and Combinatorics

Contest OverviewMisreading the first problem caused a 20-minute delay. The second problem presented a psychological barrier despite being solvable for partial points. Skipping the third problem's statement cost easy points, while the fourth problem failed due to inefficient modular inverse preproces...

Maximize Gold Collection by Repositioning a 3-Wide Blocking Door

Single-width adjacent caves in a row each hold some gold coins. A fixed-width stone door, initially blocking three unspecified caves, can be shifted exactly once to cover any set of three consecutive caves. No cave can be accessed before shifting; after shifting, only unblocked caves are collectible...

NOIP 2005 Problem Solutions

Scholarship Allocation A school distributes scholarships after each semester's final exams. There are five scholarship types available: Academician Scholarship: 8000 yuan for students with final exam scores > 80 and atleast one published paper May Fourth Scholarship: 4000 yuan for students with f...

Algorithmic Problem Solving: Tree Queries, Maximum Spanning Tree, and Grid Pattern Counting

Determining Valid Initial Values for Tree Path ConstraintsLet v represent the cumulative change in value from the root to a specific node u. For the initial value x to remain valid when reaching u, it must satisfy the constraint L_u - v <= x <= R_u - v. The cumulative change v can be managed e...

Maximizing GCD after Uniform Increment, Binary Rescue, Tower Rebalancing, Energizer Balancing, and Chessboard Parity Painting

Problem A – Kamilka’s Sheep and the Optimal Boost Given n distinct positive integers a1, a2, …, an, choose a non–negative integer d and add d to every element. After the increment, pick any two resulting values x and y and compute gcd(x, y). The goal is to maximize this greatest common divisor. Key...

Efficient Solutions for AtCoder Beginner Contest 353 Problems

Problem A: Building Height Comparison Given an array of building heights, find the first building taller than the first one. #include <cstdio> const int MAX_SIZE = 105; int heights[MAX_SIZE]; int main() { int n; scanf("%d", &n); int result = -1; for (int i = 1; i <= n; i++) {...

Competitive Programming Solutions: Mathematical Analysis, Matrix Operations, Bracket Sequences, and DAG Construction

Problem A: Minimum Function Summation Given the function f(x) = min_{i∈ℕ⁺}, compute the sum Σ_{i=1}^{n} f(i) modulo 10^9+7 across multiple test cases. Constraints: n ≤ 10^16, T ≤ 10^4. Solution Approach: Analyze the frequency of each value in the sequence f(i). For a particular value x, we need to c...

Algorithmic Solutions for AtCoder Beginner Contest 342

Problem A: Locating the Singleton Character Concept: Given a string containing exactly two distinct lowercase letters, identify the 1-based index of the letter that appears precisely once. Approach: Maintain frequency counters or index lists for each character. Since only two characters exist in the...

Algorithmic Solution for Sequence Similarity Constraints via Suffix Automaton and Binary Lifting Union-Find

The problem requires counting the number of valid sequences \(b\) given constraints \(b_i \in [L_i, R_i]\) and a similarity condition defined by a sequence \(a\). Two sequences \(a\) and \(b\) are defined as "k-similar" if, for every quadruple \((l_1, r_1, l_2, r_2)\) where the intervals \([l_1, r_1...

Solving AtCoder Beginner Contest 058 Problems

A — Checking a Beautiful Arrangement Three pillars stand equally spaced in a line. Their heights are (a), (b), (c) from left to right. The arrangement is beautiful if (b - a = c - b). Determine whether it qualifies. #include <iostream> int main() { int h1, h2, h3; std::cin >> h1 >>...