Freaks City

Problem A: Array Equalization Strategy The optimal approach involves transforming all elements to match the most freqeunt value in the array. Initial attempts with incorrect assumptions led to multiple failed submissions. #include <iostream> #include <vector> #include <algorithm> using namespace std; void solve() { int t ...

Problem Overview This problem involves efficiently handling two types of queries on a dynamic collection of elmeents: 1. Insert elements into specified ranges 2. Find the K-th largest value within a specified range We explore several advanced data structure approaches to solve this problem efficiently. ### Binary Indexed Tree with Dynamic Segme ...

Preparation Strategy Prior to a major algorithm competition, it is beneficial to maintain momentum by solving medium-difficulty problems within a time limit. This approach helps reinforce template usage and sharpens intuition without exhausting mental resources. The following selection covers common patterns including simulation, sorting, strin ...

The Bounded Knapsack Problem involves selecting items to maximize total value within a given weight capacity W. Each of the n item types has a specified value vi, weight wi, and a supply count mi. Naive Implementation A straightforward approach extends the standard 0-1 knapsack dynamic programming algorithm by adding an inner loop to process th ...

The Ternary Goldbach Conjecture asserts that any odd integer greater than 7 can be represented as the sum of three prime numbers. While proven for sufficiently large numbers, verifying this for smaller integers requires an effiicent computational approach. Given an odd integer n (9 < n < 20,000), our objective is to find a triplet of prim ...

Introduction Heavy-light decomposition (HLD) is a sophisticated algorithmic technique used to partition tree structures into linear sequences, enabling efficient query and update operations. This method is particularly effective for handling subtree and path queries on trees. Core Definitions Heavy Child: For any node, its heavy child is the c ...

Problem: Finding the K-th Smallest Number Given an array of n integers (n < 5,000,000, odd) and an integer k, find the k-th smallest element where the smallest element is considered the 0-th. Initial Approach with Standard Sort An initial solution using standard sorting: #include<iostream> #include<algorithm> using namespace std; ...

A persistent segment tree maintains a complete history of all structural modifications applied to the data structure. Unlike standard implementations that overwrite previous states, this variant preserves every version, enabling direct queries on historical configurations. The core technique relies on path copying, where only nodes along the mo ...

Potion-making Solution This problem requires solving the equation i/(i+j) = k/100 to find the minimal total ingredients. The solution involves iterating through possiblle values of i and j. #include <iostream> #include <cmath> using namespace std; void solvePotion() { int target_percentage; cin >> target_percentage; ...

Point decomposition, also known as centroid decomposition, is a powerful technique for efficiently solving path-related problems on trees. By recursively splitting the tree around its centroid, it ensures logarithmic depth of recursion, leading to optimal time complexity for many tree queries. The algorithm follows three core steps: Find the c ...