다익스트라 알고리즘

Dijkstra's algorithm

음수가 없는 간선 비용을 더하며 시작점에서 각 정점까지의 최소 비용을 확정한다.

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html
<canvas id="stage"></canvas><div class="controls"><button id="restart" type="button">처음부터</button><button id="step" type="button">한 단계</button><label>속도 <input id="speed" type="range" min="1" max="5" value="3"></label></div>
css
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js
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const title = "다익스트라 · 최단 비용";
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도로마다 통행 시간이 다르면 단순히 몇 개의 도로를 지났는지로 빠른 길을 고를 수 없습니다. 다익스트라는 출발점에서 각 장소까지 현재까지 찾은 가장 싼 비용을 적어가며 지도를 넓혀 갑니다.

시작 거리를 0, 나머지를 무한대로 두고 아직 확정하지 않은 정점 중 거리가 가장 작은 것을 꺼냅니다. 그 정점의 이웃에 대해 '현재 거리 + 간선 가중치'가 더 작으면 거리를 완화(relax)합니다. 우선순위 큐를 쓰면 보통 O((V+E) log V) 시간에 처리합니다. 데모 숫자는 갱신된 출발점 거리입니다.

비용이 음수가 아니어야 꺼낸 거리를 확정할 수 있습니다. 음수 간선이 있으면 다른 알고리즘을 고려하고, 목적지가 하나라면 그 정점이 확정됐을 때 멈출 수 있습니다.

언제 쓰나

도로·네트워크처럼 비음수 비용이 있는 최단 경로에. 가중치가 모두 같으면 BFS가 더 단순합니다.

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