Freaks City

Intimacy between people can be quantified by an inverse relationship with perceived distance. Importantly, this distance perception is asymmetric and directional. For instance, person A might perceive a distance of 1 to person B, while B perceives a distance of 100000 to A. Additionally, distance relationships are transitive: if person A consid ...

Shortest path problems in graph theory often rely on the concept of relaxation. Relaxation occurs when a path from node u to v can be shoretned by routing through an intermediate node k, i.e., if dist[u][v] > dist[u][k] + dist[k][v], we update dist[u][v] accordingly. Floyd-Warshall Algorithm (All-Pairs Shortest Paths) To compute shortest pat ...

Dijkstra Algortihm: O(n²) Approach Dijkstra's algorithm solves the single-source shortest path problem for graphs with non-negative edge weights. It efficiently computes the minimum distance from a starting vertex to all other vertices using a greedy approach. Algorithm Overview Initialization: Set the source distance to 0 and all other vertic ...

A building has an unusual elevator system. Each floor i (where 1 ≤ i ≤ N) has a fixed value K[i], which determines how many floors the elevator moves when the "up" or "down" button is pressed. The elveator can only move up by K[i] floors or down by K[i] floors from floor i. If the target floor would be below 1 or above N, th ...

To determine which edges can lie on a shortest path from source S to target T in a directed graph, compute shortest distances from S to all nodes. Then, perform a reverse BFS starting from T on the transposed graph. For each dequeued node cur and its neighbor nex in the transposed graph, if Dist[nex] == Dist[cur] - weight(cur->nex) holds, th ...