In 1736 Euler answered a strolling puzzle posed by the people of Königsberg and accidentally founded an entire branch of mathematics. Those seven bridges cannot be walked once each, because all four landmasses meet an odd number of bridges, whereas a single-stroke route tolerates at most two odd vertices. From that parity remark grew a whole family of problems: colouring regions so no two neighbours match, BFS spreading in distance layers while DFS plunges down one branch and backtracks, and Kruskal picking the cheapest edges that close no cycle to build a minimum spanning tree.
In 1736 Euler answered a strolling puzzle posed by the people of Königsberg and accidentally founded an entire branch of mathematics. Those seven bridges cannot be walked once each, because all four landmasses meet an odd number of bridges, whereas a single-stroke route tolerates at most two odd vertices. From that parity remark grew a whole family of problems: colouring regions so no two neighbours match, BFS spreading in distance layers while DFS plunges down one branch and backtracks, and Kruskal picking the cheapest edges that close no cycle to build a minimum spanning tree.
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