Freaks City

Cycle Detection and Connectivity Union-Find, DFS/BFS, and topological sorting can detect cycles and verify graph connectivity in $O(n + m)$ time. Topological sorting also identifies cycles in directed graphs. Problem: Acyclic Directed Graph Check Description: Given a directed graph with $N$ nodes and $M$ edges where each edge $(a_i, b_i)$ conne ...

Dikjstra's Algorithm (Adjacency Matrix) #include <iostream> #include <cstring> #include <algorithm> using namespace std; const int MAX_NODES = 510; int node_count, edge_count; int graph[MAX_NODES][MAX_NODES]; int min_distance[MAX_NODES]; bool visited[MAX_NODES]; int dijkstra_shortest_path() { memset(min_distance, 0x3f, s ...

Dijkstra's Algorithm ApproachDijkstra's algorithm is suitable for finding the shortest paths from a single source node to all other nodes in a weighted graph with non-negative weights. For the network delay problem, we aim to determine the maximum shortest-path distance from the source node k to every other node. If any node remains unreachable ...

Understanding Dijkstra's Algorithm Dijkstra's algorithm solves the single-source sohrtest path problem in graphs where all edge weights are non-negative. Given a source node s, it computes the shortest distance from s to every other reachable node in the graph. Core Intuition Initially, only the distance from the source to itself is known (0), ...

Dijkstra's algorithm computes the shortest path distances from a designated source vertex to all other vertices in a weighted, directed or undirected graph with non-negative edge weights. It operates greedily: at each step, it selects the unvisited vertex with the smallest known distance from the source, marks it as visited, and relaxes (i.e., ...

In competitive programming and system design, efficiently navigating complex networks and optimizing resource allocation often require mastery of graph algorithms. The following collection demonstrates implementations for several classic challenges, including broadcast optimization, structural analysis of trees, and constrained dynamic programm ...

Problem 1: Unique Snowflake Collection Problem Statement: At n different times, snowflakes of various shapes fall (represented by distinct integers). We want to collect snowflakes from time a to time b such that no duplicate shapes are collected, and the total number of snowflakes collected is maximized. Solution Approach: Two Pointers Techniqu ...

This collection presents fundamental algorithms and their applications to simple problems, primari sourced from the Lanqiao Cup competition. The problems are relatively straightforward, focusing more on algorithm templates and basic approaches. For better algorithm retention, the implementations are concise, frequently utilizing built-in C++ fu ...

This problem involves finding the shrotest path in a graph where certain edges are temporarily closed. The graph has $N$ nodes and $M$ edges, with $N \le 1000$ and $M \le 10000$. Given the constraints, an adjacency matrix is a suitable choice for representing the graph. We need to determine the optimal travel time for a character, let's call th ...

Data Structures Segment Tree #include <iostream> #include <vector> #include <algorithm> using namespace std; typedef long long ll; const int MAXN = 100010; int n, m; vector<ll> arr; vector<ll> tree; vector<ll> lazy; inline ll read() { ll x = 0, f = 1; char ch = getchar(); while (ch < '0' || ...