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Origin of the ProblemIn the early 18th century, a puzzle was discussed in the city of Prussia's Königsberg (now Kaliningrad) concerning people. Königsberg was divided into four land by the Pregel River flowing through its center, and a total of seven bridge connected these landmasses. The residents of City wondered whether it was possible to take a walk that crossed each of these bridges exactly once. The striking feature of the problem was that no specific starting or ending point was specified

The Floyd-Warshall Algorithm is an algorithm designed to find the shortest paths between all pairs of knot in graph theory. This algorithm employs a dynamic programming approach and can operate on graphs with both positive and negative edge weights, provided there are no negative-weight cycles. The algorithm was developed in 1962 by Robert Floyd and Stephen Warshall independent.Working PrincipleThe Floyd-Warshall Algorithm uses a stepwise approach to find the shortest paths between all pairs of

Dijkstra's Algorithm is a shortest path algorithm used in graph theory, developed in 1956 by Dutch computer scientist Edsger W. Dijkstra. This algorithm is used to find the shortest paths from a specific starting node to all other nodes in a graph. It operates on weighted graphs—where edges have specific weights—and is valid only for graphs that do not contain negative-weight edges.Working PrincipleDijkstra's Algorithm employs a greedy approach. At each step, it selects the node with the shortes