편집 거리

Edit distance

한 문자열을 다른 문자열로 바꾸는 삽입·삭제·치환의 최소 횟수.

다른 이름: Levenshtein distance
···
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 = "편집 거리 · 최소 수정";
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;
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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();
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한 단어를 다른 단어로 고치려면 몇 번 손을 대야 하는지 세는 방법입니다. 데모는 CAT를 CUT으로 바꿀 때 두 접두사 사이의 최소 편집 횟수를 칸마다 계산합니다.

dp[i][j]는 첫 문자열 앞 i글자를 둘째 앞 j글자로 바꾸는 최소 비용입니다. 마지막 글자를 삭제하면 위 칸+1, 삽입하면 왼쪽 칸+1, 같거나 치환하면 대각선 칸+0 또는 +1 중 최솟값을 고릅니다. 첫 행과 열을 빈 문자열과의 거리로 초기화하며 시간은 O(mn)입니다.

오타 후보·DNA 서열·문자열 유사도에 씁니다. 여기서는 세 연산의 비용이 모두 1인 레벤슈타인 거리이며, 철자에 따른 다른 비용이나 글자 맞바꿈까지 허용하면 점화식이 달라집니다.

언제 쓰나

문자열 사이의 수정 비용이 중요할 때. 허용할 편집 연산과 비용을 먼저 정하세요.

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