너비 우선 탐색

Breadth-first search

시작점에서 가까운 정점부터 한 겹씩 방문하는 탐색.

다른 이름: BFS
···
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
body{display:block}#stage{position:absolute;inset:0;width:100%;height:100%}.controls{position:absolute;bottom:9px;left:50%;transform:translateX(-50%);display:flex;align-items:center;gap:7px;white-space:nowrap}.controls button,.controls label{font:12px sans-serif;color:var(--fg);background:var(--surface);border:1px solid var(--line);border-radius:6px;padding:5px 8px}.controls button{cursor:pointer}.controls input{width:75px;vertical-align:middle;accent-color:var(--accent)}@media(max-width:500px){.controls{display:none}}
js
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const title = "BFS · 큐로 한 겹씩";
const canvas = document.getElementById('stage');
const ctx = canvas.getContext('2d');
const restart = document.getElementById('restart');
const step = document.getElementById('step');
const speed = document.getElementById('speed');
let index = 0, last = performance.now(), width = 300, height = 200;
function colors(){ const s=getComputedStyle(document.documentElement); const v=(key)=>s.getPropertyValue(key).trim(); return {bg:v('--bg'),fg:v('--fg'),muted:v('--muted'),line:v('--line'),surface:v('--surface'),accent:v('--accent'),accent2:v('--accent-2'),accent3:v('--accent-3')}; }
function resize(){ const dpr=Math.min(devicePixelRatio||1,2); width=innerWidth;height=innerHeight;canvas.width=Math.round(width*dpr);canvas.height=Math.round(height*dpr);ctx.setTransform(dpr,0,0,dpr,0,0);draw(); }
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function dot(x,y,r,color){ctx.fillStyle=color;ctx.beginPath();ctx.arc(x,y,r,0,Math.PI*2);ctx.fill();}
function draw(){
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  if(frame.kind==='graph'){
    const nodes=d.nodes, edges=d.edges, positions=Object.fromEntries(nodes.map(n=>[n.id,{x:left+areaW*(.06+.88*n.x),y:top+span*(.11+.78*n.y)}]));
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    for(let r=0;r<rows;r++)for(let c=0;c<cols;c++){const n=r*cols+c,x=ox+c*cell,y=oy+r*cell,active=bits?d.active?.includes(c):table?d.active?.[0]===r&&d.active?.[1]===c:d.active===n,source=table?d.sources?.some(v=>v[0]===r&&v[1]===c):false,visited=bits?d.bits[c]:table?false:d.visited?.includes(n),front=d.frontier?.includes(n),blocked=d.blocked?.includes(n),path=d.path?.includes(n),queen=d.queens?.[r]===c;
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    const side=Math.min(areaW,span)-8,ox=(width-side)/2,oy=top+(span-side)/2;ctx.strokeStyle=p.muted;ctx.globalAlpha=.5;ctx.strokeRect(ox,oy,side,side);ctx.globalAlpha=1;ctx.beginPath();ctx.arc(ox,oy+side,side,Math.PI*1.5,0);ctx.strokeStyle=p.muted;ctx.stroke();
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}
function advance(){index=(index+1)%frames.length;draw();}
restart.addEventListener('click',()=>{index=0;last=performance.now();draw();});
step.addEventListener('click',()=>{advance();last=performance.now();});
addEventListener('resize',resize);resize();
function loop(now){const delay=900-Number(speed.value)*140;if(now-last>delay){advance();last=now;}requestAnimationFrame(loop);}requestAnimationFrame(loop);

물결이 퍼지듯 시작점의 이웃을 먼저 보고, 그 이웃의 이웃을 봅니다. 데모에서 초록색 대기 정점은 큐에 들어 있고, 강조된 정점은 지금 꺼내 방문하는 대상입니다.

시작 정점을 큐(queue)에 넣고, 앞에서 하나 꺼내며 아직 발견하지 않은 이웃을 뒤에 넣습니다. 넣는 순간 방문 예정으로 표시해야 같은 정점이 여러 번 들어가지 않습니다. 인접 리스트 기준 시간은 O(V+E), 대기 공간은 최악 O(V)입니다.

모든 간선의 비용이 같을 때 최단 간선 수 경로를 찾거나 연결 성분을 훑을 때 씁니다. 가중치가 다르면 BFS 순서가 최소 비용을 보장하지 않습니다.

언제 쓰나

간선 수가 곧 거리일 때 최단 경로. 가중 그래프의 최소 비용은 다익스트라를 보세요.

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