Freaks City

Tarjan's Algorithm for Strongly Connnected Components namespace TarjanSCC { int dfn[N], low[N], index, colorCount; int comp[N], size[N], value[N]; bool inStack[N]; stack<int> stk; vector<int> graph[N]; void tarjan(int u) { dfn[u] = low[u] = ++index; stk.push(u); inStack[u] = true; ...

Problem A: Minimum Steps to Visit All Points Given a array of distinct integers x₁, x₂, ..., xₙ and a starting position s on the number line. You can move left or right by one unit each step. Find the minimum number of steps required to visit all positions in the array, starting from position s. The optimal solution involves visiting the endpoi ...

Consider a labeled monoid (T) acting on an information monoid (S), forming the algebraic structure ((T, \times, 1_T, S, +, 0_S, \circ)). The information monoid ((S, +, 0_S)) satisfies: Closure: (\forall x, y \in S), (x + y \in S). Associativity: (\forall x, y, z \in S), ((x + y) + z = x + (y + z)). Idantity element: (\exists 0_S \in S) such th ...

Problem 1: Maximum Goals and Assists Problem Overview Given two arrays representing goals and assists for multiple players, process queries that ask for the maximum total balls needed under different matching scenarios. Key Observations The problem essentially asks for the maximum value among three distinct scenarios: Scenario 1: Each assist ca ...

What is a Segment Tree? A segment tree is a binary tree-based advanced data structure that supports flexible range operations. Unlike a Fenwick Tree (Binary Indexed Tree) which is limited to simple point update/range query use cases, segment trees can handle range updates with point queries, and even full range updates with range queries effici ...

The following C++ implementation demonstrates a complete Heavy-Light Decomposition (HLD) framework integrated with a lazy propagation segment tree to support efficient path updates and queries on trees. It passes the standard template problem on Luogu. #include <bits/stdc++.h> using namespace std; using i64 = long long; int MOD; struct ...

Range Extremum Queries and Algorithmic ChoicesRange Maximum/Minimum Query (RMQ) problems involve processing an array of size n to handle multiple range queries and bulk modifications. Different data structures offer varying trade-offs:Brute Force: Simple implementation suitable for small datasets, but query performance is poor.Binary Indexed Tr ...

Maintaining Range Minimum and Historical MaximumWhen a segment tree needs to support range addition, range minimum assignment, range sum, range maximum, and range historical maximum, a standard approach involves tracking the maximum value, strict second maximum value, and the count of maximum values within each node. Operations affecting the mi ...

This problem asks us to identify the earliest possible building index where two individuals, starting from distinct locations, can rendezvous. We are provided with an array representing building heights, let's call it buildingElevations, and a series of queries. Each query specifies two initial building indices, startA and startB. The rule for ...

Introduction to Time-Based Divide and Conquer Segment Tree Divide and Conquer is an advanced offline algorithmic technique typicalyl used to solve problems involving dynamic modifications that persist over specific time intervals. The core idea is to map the time dimension onto a segment tree, allowing us to decompose the lifespan of operations ...