const{Fragment:i,jsx:s,jsxs:h}=arguments[0];function _createMdxContent(l){const e={a:"a",code:"code",em:"em",figcaption:"figcaption",figure:"figure",h2:"h2",h3:"h3",img:"img",li:"li",ol:"ol",p:"p",pre:"pre",span:"span",strong:"strong",table:"table",tbody:"tbody",td:"td",th:"th",thead:"thead",tr:"tr",ul:"ul",...l.components},{Callout:a,QuickSort:n}=e;return a||_missingMdxReference("Callout",!0),n||_missingMdxReference("QuickSort",!0),h(i,{children:[h(e.p,{children:["Quick Sort는 분할 정복(divide and conquer) 전략으로 동작하는 비교 정렬 알고리즘입니다. 평균 시간 복잡도 ",s(e.span,{className:"katex",children:s(e.span,{className:"katex-html","aria-hidden":"true",children:h(e.span,{className:"base",children:[s(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),s(e.span,{className:"mord mathnormal",style:{marginRight:"0.0278em"},children:"O"}),s(e.span,{className:"mopen",children:"("}),s(e.span,{className:"mord 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비교해보세요."]})}),"\n",s(e.h2,{id:"개요",children:"개요"}),"\n",s(e.p,{children:"Quick Sort의 핵심 아이디어는 간단합니다:"}),"\n",h(e.ol,{children:["\n",h(e.li,{children:["배열에서 ",s(e.strong,{children:"피벗(pivot)"})," 하나를 고릅니다"]}),"\n",s(e.li,{children:"피벗보다 작은 값은 왼쪽, 큰 값은 오른쪽으로 분할합니다"}),"\n",s(e.li,{children:"좌우 각각에 대해 재귀적으로 같은 과정을 반복합니다"}),"\n"]}),"\n",s(e.p,{children:"이 과정을 그림으로 표현하면 다음과 같습니다:"}),"\n",s(e.p,{children:s(e.img,{src:"/images/quicksort-diagram.svg",alt:"Quick Sort 피벗 분할 개념도"})}),"\n",h(e.p,{children:["데이터베이스 인덱스도 유사한 분할 정복 사고방식을 활용합니다. 인덱스 탐색은 ",s(e.a,{href:"/posts/b-tree-structure","data-keyword-link":"true",children:"B-Tree"}),'를 통해 매 단계 탐색 범위를 절반 가까이로 줄이는 방식인데, Quick Sort의 "피벗으로 분할" 아이디어와 직관적으로 닮아있습니다.']}),"\n",s(e.h2,{id:"알고리즘-단계",children:"알고리즘 단계"}),"\n",s(e.p,{children:"Lomuto 파티션 방식을 기준으로 동작을 정리하면:"}),"\n",h(e.ol,{children:["\n",s(e.li,{children:"배열의 마지막 원소를 피벗으로 선택"}),"\n",h(e.li,{children:[s(e.span,{"data-rehype-pretty-code-figure":"",children:s(e.code,{"data-language":"plaintext","data-theme":"one-light one-dark-pro",children:s(e.span,{"data-line":"",children:s(e.span,{children:"i = lo - 1"})})})})," 로 파티션 경계 초기화"]}),"\n",h(e.li,{children:[s(e.span,{"data-rehype-pretty-code-figure":"",children:s(e.code,{"data-language":"plaintext","data-theme":"one-light one-dark-pro",children:s(e.span,{"data-line":"",children:s(e.span,{children:"j"})})})})," 를 ",s(e.span,{"data-rehype-pretty-code-figure":"",children:s(e.code,{"data-language":"plaintext","data-theme":"one-light one-dark-pro",children:s(e.span,{"data-line":"",children:s(e.span,{children:"lo"})})})})," 부터 ",s(e.span,{"data-rehype-pretty-code-figure":"",children:s(e.code,{"data-language":"plaintext","data-theme":"one-light one-dark-pro",children:s(e.span,{"data-line":"",children:s(e.span,{children:"hi - 1"})})})})," 까지 순회하며:","\n",h(e.ul,{children:["\n",h(e.li,{children:[s(e.span,{"data-rehype-pretty-code-figure":"",children:s(e.code,{"data-language":"plaintext","data-theme":"one-light one-dark-pro",children:s(e.span,{"data-line":"",children:s(e.span,{children:"arr[j] <= pivot"})})})})," 이면 ",s(e.span,{"data-rehype-pretty-code-figure":"",children:s(e.code,{"data-language":"plaintext","data-theme":"one-light one-dark-pro",children:s(e.span,{"data-line":"",children:s(e.span,{children:"i"})})})})," 를 1 증가시키고 ",s(e.span,{"data-rehype-pretty-code-figure":"",children:s(e.code,{"data-language":"plaintext","data-theme":"one-light one-dark-pro",children:s(e.span,{"data-line":"",children:s(e.span,{children:"arr[i]"})})})})," 와 ",s(e.span,{"data-rehype-pretty-code-figure":"",children:s(e.code,{"data-language":"plaintext","data-theme":"one-light one-dark-pro",children:s(e.span,{"data-line":"",children:s(e.span,{children:"arr[j]"})})})})," 교환"]}),"\n"]}),"\n"]}),"\n",h(e.li,{children:["마지막으로 ",s(e.span,{"data-rehype-pretty-code-figure":"",children:s(e.code,{"data-language":"plaintext","data-theme":"one-light one-dark-pro",children:s(e.span,{"data-line":"",children:s(e.span,{children:"arr[i+1]"})})})})," 와 ",s(e.span,{"data-rehype-pretty-code-figure":"",children:s(e.code,{"data-language":"plaintext","data-theme":"one-light one-dark-pro",children:s(e.span,{"data-line":"",children:s(e.span,{children:"arr[hi]"})})})}),"(피벗) 교환"]}),"\n",h(e.li,{children:["피벗의 최종 위치 ",s(e.span,{"data-rehype-pretty-code-figure":"",children:s(e.code,{"data-language":"plaintext","data-theme":"one-light one-dark-pro",children:s(e.span,{"data-line":"",children:s(e.span,{children:"i+1"})})})})," 을 기준으로 좌우 서브 배열에 재귀 호출"]}),"\n"]}),"\n",s(e.h3,{id:"의사-코드",children:"의사 코드"}),"\n",h(e.figure,{"data-rehype-pretty-code-figure":"",children:[s(e.figcaption,{"data-rehype-pretty-code-title":"","data-language":"python","data-theme":"one-light 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이해하기 쉽습니다. 아래 컴포넌트로 피벗 선택·비교·교환·확정의 단계별 흐름을 확인하세요. ",s(e.span,{"data-rehype-pretty-code-figure":"",children:s(e.code,{"data-language":"plaintext","data-theme":"one-light one-dark-pro",children:s(e.span,{"data-line":"",children:s(e.span,{children:"Play"})})})})," 버튼으로 자동 재생도 가능합니다."]}),"\n",s(n,{initial:[38,27,43,3,9,82,10]}),"\n",h(e.p,{children:["피벗은 ",s(e.strong,{children:"amber"}),"(주황), 비교 중인 원소는 ",s(e.strong,{children:"blue"}),"(파랑), 확정된 위치는 ",s(e.strong,{children:"emerald"}),"(초록)로 표시됩니다. Step 설명에서 매 동작의 근거를 확인할 수 있습니다."]}),"\n",s(e.h2,{id:"시간-복잡도",children:"시간 복잡도"}),"\n",h(e.table,{children:[s(e.thead,{children:h(e.tr,{children:[s(e.th,{children:"케이스"}),s(e.th,{children:"시간 복잡도"}),s(e.th,{children:"설명"})]})}),h(e.tbody,{children:[h(e.tr,{children:[s(e.td,{children:"최선"}),s(e.td,{children:s(e.span,{className:"katex",children:s(e.span,{className:"katex-html","aria-hidden":"true",children:h(e.span,{className:"base",children:[s(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),s(e.span,{className:"mord mathnormal",style:{marginRight:"0.0278em"},children:"O"}),s(e.span,{className:"mopen",children:"("}),s(e.span,{className:"mord mathnormal",children:"n"}),s(e.span,{className:"mspace",style:{marginRight:"0.1667em"}}),h(e.span,{className:"mop",children:["lo",s(e.span,{style:{marginRight:"0.0139em"},children:"g"})]}),s(e.span,{className:"mspace",style:{marginRight:"0.1667em"}}),s(e.span,{className:"mord mathnormal",children:"n"}),s(e.span,{className:"mclose",children:")"})]})})})}),s(e.td,{children:"피벗이 항상 배열을 균등하게 분할"})]}),h(e.tr,{children:[s(e.td,{children:"평균"}),s(e.td,{children:s(e.span,{className:"katex",children:s(e.span,{className:"katex-html","aria-hidden":"true",children:h(e.span,{className:"base",children:[s(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),s(e.span,{className:"mord mathnormal",style:{marginRight:"0.0278em"},children:"O"}),s(e.span,{className:"mopen",children:"("}),s(e.span,{className:"mord mathnormal",children:"n"}),s(e.span,{className:"mspace",style:{marginRight:"0.1667em"}}),h(e.span,{className:"mop",children:["lo",s(e.span,{style:{marginRight:"0.0139em"},children:"g"})]}),s(e.span,{className:"mspace",style:{marginRight:"0.1667em"}}),s(e.span,{className:"mord mathnormal",children:"n"}),s(e.span,{className:"mclose",children:")"})]})})})}),s(e.td,{children:"랜덤 피벗 선택 시의 기대값"})]}),h(e.tr,{children:[s(e.td,{children:"최악"}),s(e.td,{children:s(e.span,{className:"katex",children:s(e.span,{className:"katex-html","aria-hidden":"true",children:h(e.span,{className:"base",children:[s(e.span,{className:"strut",style:{height:"1.0641em",verticalAlign:"-0.25em"}}),s(e.span,{className:"mord mathnormal",style:{marginRight:"0.0278em"},children:"O"}),s(e.span,{className:"mopen",children:"("}),h(e.span,{className:"mord",children:[s(e.span,{className:"mord mathnormal",children:"n"}),s(e.span,{className:"msupsub",children:s(e.span,{className:"vlist-t",children:s(e.span,{className:"vlist-r",children:s(e.span,{className:"vlist",style:{height:"0.8141em"},children:h(e.span,{style:{top:"-3.063em",marginRight:"0.05em"},children:[s(e.span,{className:"pstrut",style:{height:"2.7em"}}),s(e.span,{className:"sizing reset-size6 size3 mtight",children:s(e.span,{className:"mord mtight",children:"2"})})]})})})})})]}),s(e.span,{className:"mclose",children:")"})]})})})}),s(e.td,{children:"이미 정렬된 배열 + 끝 원소를 피벗으로 선택"})]})]})]}),"\n",h(e.p,{children:["공간 복잡도는 재귀 스택의 깊이에 비례해 ",s(e.span,{className:"katex",children:s(e.span,{className:"katex-html","aria-hidden":"true",children:h(e.span,{className:"base",children:[s(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),s(e.span,{className:"mord mathnormal",style:{marginRight:"0.0278em"},children:"O"}),s(e.span,{className:"mopen",children:"("}),h(e.span,{className:"mop",children:["lo",s(e.span,{style:{marginRight:"0.0139em"},children:"g"})]}),s(e.span,{className:"mspace",style:{marginRight:"0.1667em"}}),s(e.span,{className:"mord mathnormal",children:"n"}),s(e.span,{className:"mclose",children:")"})]})})}),"이며, 최악의 경우 ",s(e.span,{className:"katex",children:s(e.span,{className:"katex-html","aria-hidden":"true",children:h(e.span,{className:"base",children:[s(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),s(e.span,{className:"mord mathnormal",style:{marginRight:"0.0278em"},children:"O"}),s(e.span,{className:"mopen",children:"("}),s(e.span,{className:"mord mathnormal",children:"n"}),s(e.span,{className:"mclose",children:")"})]})})}),"까지 증가할 수 있습니다."]}),"\n",s(e.h2,{id:"sql에서의-정렬",children:"SQL에서의 정렬"}),"\n",h(e.p,{children:["데이터베이스는 ",s(e.span,{"data-rehype-pretty-code-figure":"",children:s(e.code,{"data-language":"plaintext","data-theme":"one-light one-dark-pro",children:s(e.span,{"data-line":"",children:s(e.span,{children:"ORDER BY"})})})})," 절을 처리할 때 내부적으로 정렬 알고리즘을 사용합니다. PostgreSQL의 경우 기본적으로 ",s(e.strong,{children:"외부 병합 정렬"}),"(external merge sort)을 사용하지만, 데이터 크기가 ",s(e.span,{"data-rehype-pretty-code-figure":"",children:s(e.code,{"data-language":"plaintext","data-theme":"one-light one-dark-pro",children:s(e.span,{"data-line":"",children:s(e.span,{children:"work_mem"})})})})," 안에 들어오면 ",s(e.strong,{children:"quicksort"}),"로 전환됩니다."]}),"\n",h(e.figure,{"data-rehype-pretty-code-figure":"",children:[s(e.figcaption,{"data-rehype-pretty-code-title":"","data-language":"sql","data-theme":"one-light one-dark-pro",children:"order_by_example.sql"}),s(e.pre,{className:"has-highlighted",tabIndex:"0","data-language":"sql","data-theme":"one-light one-dark-pro",children:h(e.code,{"data-language":"sql","data-theme":"one-light one-dark-pro",style:{display:"grid"},children:[s(e.span,{"data-line":"",children:s(e.span,{style:{"--shiki-light":"#A0A1A7","--shiki-light-font-style":"italic","--shiki-dark":"#7F848E","--shiki-dark-font-style":"italic"},children:"-- 인덱스가 없는 컬럼을 정렬 → Quick Sort 또는 Merge Sort 사용"})}),"\n",s(e.span,{"data-line":"",children:s(e.span,{style:{"--shiki-light":"#383A42","--shiki-dark":"#ABB2BF"},children:"EXPLAIN ANALYZE"})}),"\n",h(e.span,{"data-line":"",children:[s(e.span,{style:{"--shiki-light":"#A626A4","--shiki-dark":"#C678DD"},children:"SELECT"}),s(e.span,{style:{"--shiki-light":"#383A42","--shiki-dark":"#ABB2BF"},children:" id, "}),s(e.span,{style:{"--shiki-light":"#A626A4","--shiki-dark":"#C678DD"},children:"name"}),s(e.span,{style:{"--shiki-light":"#383A42","--shiki-dark":"#ABB2BF"},children:", created_at"})]}),"\n",h(e.span,{"data-line":"",children:[s(e.span,{style:{"--shiki-light":"#A626A4","--shiki-dark":"#C678DD"},children:"FROM"}),s(e.span,{style:{"--shiki-light":"#383A42","--shiki-dark":"#ABB2BF"},children:" users"})]}),"\n",h(e.span,{className:"highlighted","data-line":"",children:[s(e.span,{style:{"--shiki-light":"#A626A4","--shiki-dark":"#C678DD"},children:"ORDER BY"}),s(e.span,{style:{"--shiki-light":"#383A42","--shiki-dark":"#ABB2BF"},children:" created_at "}),s(e.span,{style:{"--shiki-light":"#A626A4","--shiki-dark":"#C678DD"},children:"DESC"})]}),"\n",h(e.span,{"data-line":"",children:[s(e.span,{style:{"--shiki-light":"#A626A4","--shiki-dark":"#C678DD"},children:"LIMIT"}),s(e.span,{style:{"--shiki-light":"#986801","--shiki-dark":"#D19A66"},children:" 100"}),s(e.span,{style:{"--shiki-light":"#383A42","--shiki-dark":"#ABB2BF"},children:";"})]}),"\n",s(e.span,{"data-line":"",children:" "}),"\n",s(e.span,{"data-line":"",children:s(e.span,{style:{"--shiki-light":"#A0A1A7","--shiki-light-font-style":"italic","--shiki-dark":"#7F848E","--shiki-dark-font-style":"italic"},children:'-- 실행 계획에 "Sort Method: quicksort" 가 나타나면 메모리 내 정렬'})}),"\n",s(e.span,{"data-line":"",children:s(e.span,{style:{"--shiki-light":"#A0A1A7","--shiki-light-font-style":"italic","--shiki-dark":"#7F848E","--shiki-dark-font-style":"italic"},children:'-- "external merge" 가 나타나면 디스크 기반 정렬로 전환된 것'})})]})})]}),"\n",s(a,{type:"warning",title:"인덱스 우선 검토",children:h(e.p,{children:["정렬이 빈번한 쿼리라면 Quick Sort가 호출되지 않도록 ",s(e.strong,{children:"정렬 컬럼에 인덱스를 생성"}),"하는 편이 훨씬 빠릅니다. 정렬된 인덱스를 그대로 읽으면 ",s(e.span,{className:"katex",children:s(e.span,{className:"katex-html","aria-hidden":"true",children:h(e.span,{className:"base",children:[s(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),s(e.span,{className:"mord mathnormal",style:{marginRight:"0.0278em"},children:"O"}),s(e.span,{className:"mopen",children:"("}),s(e.span,{className:"mord mathnormal",children:"n"}),s(e.span,{className:"mspace",style:{marginRight:"0.1667em"}}),h(e.span,{className:"mop",children:["lo",s(e.span,{style:{marginRight:"0.0139em"},children:"g"})]}),s(e.span,{className:"mspace",style:{marginRight:"0.1667em"}}),s(e.span,{className:"mord mathnormal",children:"n"}),s(e.span,{className:"mclose",children:")"})]})})})," 정렬 비용 자체가 사라집니다."]})}),"\n",s(e.h2,{id:"주의사항",children:"주의사항"}),"\n",s(e.p,{children:"Quick Sort를 쓸 때 자주 마주치는 함정들입니다."}),"\n",h(a,{type:"error",title:"이미 정렬된 배열에서의 최악 성능",children:[h(e.p,{children:["끝 원소를 피벗으로 고르는 단순한 구현은 이미 정렬된 배열 또는 역순으로 정렬된 배열에서 ",s(e.span,{className:"katex",children:s(e.span,{className:"katex-html","aria-hidden":"true",children:h(e.span,{className:"base",children:[s(e.span,{className:"strut",style:{height:"1.0641em",verticalAlign:"-0.25em"}}),s(e.span,{className:"mord mathnormal",style:{marginRight:"0.0278em"},children:"O"}),s(e.span,{className:"mopen",children:"("}),h(e.span,{className:"mord",children:[s(e.span,{className:"mord mathnormal",children:"n"}),s(e.span,{className:"msupsub",children:s(e.span,{className:"vlist-t",children:s(e.span,{className:"vlist-r",children:s(e.span,{className:"vlist",style:{height:"0.8141em"},children:h(e.span,{style:{top:"-3.063em",marginRight:"0.05em"},children:[s(e.span,{className:"pstrut",style:{height:"2.7em"}}),s(e.span,{className:"sizing reset-size6 size3 mtight",children:s(e.span,{className:"mord mtight",children:"2"})})]})})})})})]}),s(e.span,{className:"mclose",children:")"})]})})}),"로 성능이 붕괴됩니다. 프로덕션 코드에서는 반드시 다음 중 하나를 사용하세요:"]}),h(e.ul,{children:["\n",h(e.li,{children:[s(e.strong,{children:"Median of three"}),": 첫/중간/끝 원소 중 중앙값을 피벗으로 선택"]}),"\n",h(e.li,{children:[s(e.strong,{children:"Random pivot"}),": 매 파티션에서 랜덤 인덱스 선택"]}),"\n",h(e.li,{children:[s(e.strong,{children:"Introsort"}),": Quick Sort가 재귀 깊이 임계값을 넘으면 Heap Sort로 fallback"]}),"\n"]})]}),"\n",h(a,{type:"success",title:"실무 팁 — 표준 라이브러리 활용",children:[s(e.p,{children:"대부분의 경우 언어 표준 라이브러리의 정렬이 Quick Sort 또는 그 개량판을 내부에서 사용하며, 이미 위의 함정을 모두 해결해뒀습니다."}),h(e.ul,{children:["\n",h(e.li,{children:[s(e.strong,{children:"Java"}),": ",s(e.span,{"data-rehype-pretty-code-figure":"",children:s(e.code,{"data-language":"plaintext","data-theme":"one-light one-dark-pro",children:s(e.span,{"data-line":"",children:s(e.span,{children:"Arrays.sort(int[])"})})})})," → Dual-Pivot Quicksort"]}),"\n",h(e.li,{children:[s(e.strong,{children:"Python"}),": ",s(e.span,{"data-rehype-pretty-code-figure":"",children:s(e.code,{"data-language":"plaintext","data-theme":"one-light one-dark-pro",children:s(e.span,{"data-line":"",children:s(e.span,{children:"list.sort()"})})})})," / ",s(e.span,{"data-rehype-pretty-code-figure":"",children:s(e.code,{"data-language":"plaintext","data-theme":"one-light one-dark-pro",children:s(e.span,{"data-line":"",children:s(e.span,{children:"sorted()"})})})})," → Timsort (Quick Sort 아님)"]}),"\n",h(e.li,{children:[s(e.strong,{children:"Rust"}),": ",s(e.span,{"data-rehype-pretty-code-figure":"",children:s(e.code,{"data-language":"plaintext","data-theme":"one-light one-dark-pro",children:s(e.span,{"data-line":"",children:s(e.span,{children:"slice::sort_unstable()"})})})})," → Pattern-defeating Quicksort (pdqsort)"]}),"\n",h(e.li,{children:[s(e.strong,{children:"Kotlin"}),": JVM의 ",s(e.span,{"data-rehype-pretty-code-figure":"",children:s(e.code,{"data-language":"plaintext","data-theme":"one-light one-dark-pro",children:s(e.span,{"data-line":"",children:s(e.span,{children:"Arrays.sort()"})})})})," 를 그대로 사용"]}),"\n"]}),s(e.p,{children:"특별한 이유(in-place 요구사항, 특정 비교 로직 최적화 등)가 없다면 직접 구현보다 표준 라이브러리를 쓰세요."})]}),"\n",s(a,{type:"info",children:h(e.p,{children:["이 글은 ",s(e.strong,{children:"Backend Notes의 MDX 스타일 가이드"}),"를 겸합니다. 링크·문단·헤딩(h2/h3)·리스트(ol/ul)·인라인 코드·",s(e.span,{"data-rehype-pretty-code-figure":"",children:s(e.code,{"data-language":"plaintext","data-theme":"one-light one-dark-pro",children:s(e.span,{"data-line":"",children:s(e.span,{children:"code"})})})}),"·코드 블록(Python/Kotlin/TypeScript/SQL)·Shiki 라인 하이라이트·이미지·Callout(info/warning/error/success)·키워드 자동 링크·테이블·시각화 컴포넌트까지 모든 요소가 이 한 페이지 안에 포함되어 있습니다."]})}),"\n",s(e.h2,{id:"참고-자료",children:"참고 자료"}),"\n",h(e.ul,{children:["\n",s(e.li,{children:s(e.a,{href:"https://en.wikipedia.org/wiki/Quicksort",children:"Wikipedia — Quicksort"})}),"\n",s(e.li,{children:h(e.a,{href:"https://algs4.cs.princeton.edu/23quicksort/",children:["Sedgewick, Robert. ",s(e.em,{children:"Algorithms"})," (4th ed.)"]})}),"\n",s(e.li,{children:h(e.a,{href:"https://www.postgresql.org/docs/current/runtime-config-resource.html#GUC-WORK-MEM",children:["PostgreSQL Documentation — ",s(e.span,{"data-rehype-pretty-code-figure":"",children:s(e.code,{"data-language":"plaintext","data-theme":"one-light one-dark-pro",children:s(e.span,{"data-line":"",children:s(e.span,{children:"work_mem"})})})})]})}),"\n"]})]})}return{default:function(i={}){const{wrapper:h}=i.components||{};return h?s(h,{...i,children:s(_createMdxContent,{...i})}):_createMdxContent(i)}};function _missingMdxReference(i,s){throw new Error("Expected "+(s?"component":"object")+" `"+i+"` to be defined: you likely forgot to import, pass, or provide it.")}

#Algorithm

Quick Sort (퀵 정렬)