{"id":8013,"date":"2023-10-23T12:43:13","date_gmt":"2023-10-23T05:43:13","guid":{"rendered":"https:\/\/teky.edu.vn\/blog\/?p=8013"},"modified":"2025-04-15T09:46:02","modified_gmt":"2025-04-15T02:46:02","slug":"thuat-toan-quick-sort","status":"publish","type":"post","link":"https:\/\/teky.edu.vn\/blog\/thuat-toan-quick-sort\/","title":{"rendered":"Thu\u1eadt to\u00e1n Quick Sort l\u00e0 g\u00ec? Gi\u1edbi thi\u1ec7u l\u1eadp tr\u00ecnh chi ti\u1ebft nh\u1ea5t"},"content":{"rendered":"\n\n<div class=\"kk-star-ratings kksr-auto kksr-align-left kksr-valign-top\"\n    data-payload='{&quot;align&quot;:&quot;left&quot;,&quot;id&quot;:&quot;8013&quot;,&quot;slug&quot;:&quot;default&quot;,&quot;valign&quot;:&quot;top&quot;,&quot;ignore&quot;:&quot;&quot;,&quot;reference&quot;:&quot;auto&quot;,&quot;class&quot;:&quot;&quot;,&quot;count&quot;:&quot;546&quot;,&quot;legendonly&quot;:&quot;&quot;,&quot;readonly&quot;:&quot;&quot;,&quot;score&quot;:&quot;1.5&quot;,&quot;starsonly&quot;:&quot;&quot;,&quot;best&quot;:&quot;5&quot;,&quot;gap&quot;:&quot;5&quot;,&quot;greet&quot;:&quot;Rate this post&quot;,&quot;legend&quot;:&quot;1.5\\\/5 - (546 b\u00ecnh ch\u1ecdn)&quot;,&quot;size&quot;:&quot;24&quot;,&quot;title&quot;:&quot;Thu\u1eadt to\u00e1n Quick Sort l\u00e0 g\u00ec? Gi\u1edbi thi\u1ec7u l\u1eadp tr\u00ecnh chi ti\u1ebft nh\u1ea5t&quot;,&quot;width&quot;:&quot;41&quot;,&quot;_legend&quot;:&quot;{score}\\\/{best} - ({count} {votes})&quot;,&quot;font_factor&quot;:&quot;1.25&quot;}'>\n            \n<div class=\"kksr-stars\">\n    \n<div class=\"kksr-stars-inactive\">\n            <div class=\"kksr-star\" data-star=\"1\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"2\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"3\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"4\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"5\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n    <\/div>\n    \n<div class=\"kksr-stars-active\" style=\"width: 41px;\">\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n                \n\n<div class=\"kksr-legend\" style=\"font-size: 19.2px;\">\n            1.5\/5 - (546 b\u00ecnh ch\u1ecdn)    <\/div>\n    <\/div>\n<p style=\"text-align: justify;\"><em>Khi nh\u1eafc \u0111\u1ebfn nh\u1eefng thu\u1eadt to\u00e1n \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng ph\u1ed5 bi\u1ebfn trong l\u1eadp tr\u00ecnh th\u00ec kh\u00f4ng th\u1ec3 n\u00e0o thi\u1ebfu Quick Sort. C\u0169ng gi\u1ed1ng nh\u01b0 c\u00e1c thu\u1eadt to\u00e1n kh\u00e1c, Quick Sort kh\u00f4ng h\u1ec1 d\u1ec5 \u201cx\u01a1i\u201d m\u00e0 c\u1ea7n c\u00f3 th\u1eddi gian nghi\u00ean c\u1ee9u k\u1ef9 l\u01b0\u1ee1ng \u0111\u1ec3 ho\u00e0n to\u00e0n n\u1eafm ch\u1eafc n\u00f3 trong b\u00e0n tay. Trong b\u00e0i vi\u1ebft sau, Teky s\u1ebd gi\u00fap b\u1ea1n gi\u1ea3i \u0111\u00e1p m\u1ed9t s\u1ed1 kh\u00e1i ni\u1ec7m c\u01a1 b\u1ea3n xung quanh <strong>thu\u1eadt to\u00e1n Quick Sort.<\/strong> \u0110\u00e2y l\u00e0 s\u1ebd nh\u1eefng ki\u1ebfn th\u1ee9c h\u1eefu \u00edch m\u00e0 b\u1ea5t k\u1ef3 l\u1eadp tr\u00ecnh vi\u00ean n\u00e0o c\u0169ng c\u1ea7n hi\u1ec3u r\u00f5.<\/em><\/p>\n<p><a href=\"https:\/\/lotrinhlaptrinh.teky.vn\/\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-24875\" src=\"https:\/\/teky.edu.vn\/blog\/wp-content\/uploads\/2024\/03\/Sale-Promotion.png\" alt=\"\u01afu \u0111\u00e3i \u0111\u1ebfn 25%\" width=\"600\" height=\"314\" \/><\/a><\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">N\u1ed9i dung <\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/teky.edu.vn\/blog\/thuat-toan-quick-sort\/#Tim_hieu_thuat_toan_Quick_Sort_la_gi\" >T\u00ecm hi\u1ec3u thu\u1eadt to\u00e1n Quick Sort l\u00e0 g\u00ec?<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/teky.edu.vn\/blog\/thuat-toan-quick-sort\/#Gioi_thieu_ve_thuat_toan_sap_xep\" >Gi\u1edbi thi\u1ec7u v\u1ec1 thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/teky.edu.vn\/blog\/thuat-toan-quick-sort\/#Khai_niem_thuat_toan_Quick_Sort\" >Kh\u00e1i ni\u1ec7m thu\u1eadt to\u00e1n Quick Sort<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/teky.edu.vn\/blog\/thuat-toan-quick-sort\/#Y_tuong_cua_thuat_toan_Quick_Sort\" >\u00dd t\u01b0\u1edfng c\u1ee7a thu\u1eadt to\u00e1n Quick Sort<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/teky.edu.vn\/blog\/thuat-toan-quick-sort\/#Cach_trien_khai_thuat_toan_Quick_Sort_Java\" >C\u00e1ch tri\u1ec3n khai thu\u1eadt to\u00e1n Quick Sort Java<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/teky.edu.vn\/blog\/thuat-toan-quick-sort\/#Cach_1_Chon_phan_tu_dau_trong_thuat_toan_Quick_Sort\" >C\u00e1ch 1: Ch\u1ecdn ph\u1ea7n t\u1eed \u0111\u1ea7u trong thu\u1eadt to\u00e1n Quick Sort<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/teky.edu.vn\/blog\/thuat-toan-quick-sort\/#Cach_2_Chon_phan_tu_cuoi\" >C\u00e1ch 2: Ch\u1ecdn ph\u1ea7n t\u1eed cu\u1ed1i<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/teky.edu.vn\/blog\/thuat-toan-quick-sort\/#Cach_3_Chon_phan_tu_giua_trong_thuat_toan_Quick_Sort\" >C\u00e1ch 3: Ch\u1ecdn ph\u1ea7n t\u1eed gi\u1eefa trong thu\u1eadt to\u00e1n Quick Sort<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/teky.edu.vn\/blog\/thuat-toan-quick-sort\/#Giai_thuat_toan_Quick_Sort\" >Gi\u1ea3i thu\u1eadt to\u00e1n Quick Sort<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/teky.edu.vn\/blog\/thuat-toan-quick-sort\/#Do_phuc_tap_cua_thuat_toan_sap_xep_nhanh\" >\u0110\u1ed9 ph\u1ee9c t\u1ea1p c\u1ee7a thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp nhanh<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/teky.edu.vn\/blog\/thuat-toan-quick-sort\/#Ket_luan\" >K\u1ebft lu\u1eadn<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/teky.edu.vn\/blog\/thuat-toan-quick-sort\/#Thong_tin_nen_biet_Hoc_Vien_Cong_Nghe_Teky\" >Th\u00f4ng tin n\u00ean bi\u1ebft H\u1ecdc Vi\u1ec7n C\u00f4ng Ngh\u1ec7 Teky<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/teky.edu.vn\/blog\/thuat-toan-quick-sort\/#Day_la_chuong_trinh_khong_chi_trang_bi_kien_thuc_lap_trinh_ma_con_ren_luyen_nhom_ky_nang_4Cs_Tre_se_duoc\" >\u0110\u00e2y l\u00e0 ch\u01b0\u01a1ng tr\u00ecnh kh\u00f4ng ch\u1ec9 trang b\u1ecb ki\u1ebfn th\u1ee9c l\u1eadp tr\u00ecnh m\u00e0 c\u00f2n r\u00e8n luy\u1ec7n nh\u00f3m k\u1ef9 n\u0103ng 4Cs. Tr\u1ebb s\u1ebd \u0111\u01b0\u1ee3c:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/teky.edu.vn\/blog\/thuat-toan-quick-sort\/#Lien_he_ngay_hoc_vien_cong_nghe_sang_tao_TEKY_de_duoc_tu_van_khoa_hoc\" >Li\u00ean h\u1ec7 ngay h\u1ecdc vi\u1ec7n c\u00f4ng ngh\u1ec7 s\u00e1ng t\u1ea1o TEKY \u0111\u1ec3 \u0111\u01b0\u1ee3c t\u01b0 v\u1ea5n kh\u00f3a h\u1ecdc:<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Tim_hieu_thuat_toan_Quick_Sort_la_gi\"><\/span>T\u00ecm hi\u1ec3u thu\u1eadt to\u00e1n Quick Sort l\u00e0 g\u00ec?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Gioi_thieu_ve_thuat_toan_sap_xep\"><\/span>Gi\u1edbi thi\u1ec7u v\u1ec1 thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">V\u00ec Quick Sort c\u0169ng l\u00e0 m\u1ed9t d\u1ea1ng thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp n\u00ean \u0111\u1ea7u ti\u00ean ch\u00fang ta s\u1ebd \u0111i\u1ec3m nhanh qua c\u00e1c ph\u00e2n lo\u1ea1i ph\u1ed5 bi\u1ebfn.<\/p>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\" aria-level=\"1\">Thu\u1eadt to\u00e1n \u0111\u01a1n gi\u1ea3n v\u1edbi \u0111\u1ed9 ph\u1ee9c t\u1ea1p O(n^2) bao g\u1ed3m: Insertion Sort (s\u1eafp x\u1ebfp ch\u00e8n), Bubble Sort (s\u1eafp x\u1ebfp n\u1ed5i b\u1ecdt), Selection Sort (s\u1eafp x\u1ebfp l\u1ef1a ch\u1ecdn).<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Thu\u1eadt to\u00e1n hi\u1ec7u qu\u1ea3 v\u1edbi \u0111\u1ed9 ph\u1ee9c t\u1ea1p O(nlogn) bao g\u1ed3m: Heap Sort (s\u1eafp x\u1ebfp vun \u0111\u1ed1ng), Merge Sort (s\u1eafp x\u1ebfp tr\u1ed9n), Quick Sort (s\u1eafp x\u1ebfp nhanh).<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Thu\u1eadt to\u00e1n \u0111\u1eb7c bi\u1ec7t v\u1edbi \u0111\u1ed9 ph\u1ee9c t\u1ea1p O(n) bao g\u1ed3m: Counting Sort (s\u1eafp x\u1ebfp \u0111\u1ebfm), Bucket Sort (s\u1eafp x\u1ebfp ph\u00e2n c\u1ee5m), Radix Sort (s\u1eafp x\u1ebfp c\u01a1 s\u1ed1).<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">X\u1eed l\u00fd c\u00e1c t\u1eadp d\u1eef li\u1ec7u l\u1edbn bao g\u1ed3m: External sort (s\u1eafp x\u1ebfp ngo\u00e0i).<\/li>\n<\/ul>\n<figure id=\"attachment_8018\" aria-describedby=\"caption-attachment-8018\" style=\"width: 650px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-8018\" src=\"https:\/\/teky.edu.vn\/blog\/wp-content\/uploads\/2021\/07\/mot-vi-du-ve-thuat-toan-quicksort-java.jpg\" alt=\"M\u1ed9t v\u00ed d\u1ee5 v\u1ec1 thu\u1eadt to\u00e1n Quicksort Java\" width=\"650\" height=\"400\" srcset=\"https:\/\/teky.edu.vn\/blog\/wp-content\/uploads\/2021\/07\/mot-vi-du-ve-thuat-toan-quicksort-java.jpg 650w, https:\/\/teky.edu.vn\/blog\/wp-content\/uploads\/2021\/07\/mot-vi-du-ve-thuat-toan-quicksort-java-400x246.jpg 400w\" sizes=\"auto, (max-width: 650px) 100vw, 650px\" \/><figcaption id=\"caption-attachment-8018\" class=\"wp-caption-text\">M\u1ed9t v\u00ed d\u1ee5 v\u1ec1 thu\u1eadt to\u00e1n Quicksort Java<\/figcaption><\/figure>\n<p style=\"text-align: justify;\">Thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp trong d\u00f9ng \u0111\u1ec3 x\u1eed l\u00fd c\u00e1c t\u1ec7p d\u1eef li\u1ec7u nh\u1ecf. H\u1ecd d\u1eef li\u1ec7u s\u1ebd \u0111\u01b0\u1ee3c \u0111\u01b0a to\u00e0n b\u1ed9 v\u00e0o trong b\u1ed9 nh\u1edb c\u1ee7a m\u00e1y t\u00ednh. C\u00f2n thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp ngo\u00e0i ch\u1ec9 s\u1eed d\u1ee5ng \u0111\u01b0\u1ee3c cho c\u00e1c t\u1ec7p d\u1eef li\u1ec7u l\u1edbn. H\u1ecd d\u1eef li\u1ec7u kh\u00f4ng th\u1ec3 \u0111\u01b0a to\u00e0n b\u1ed9 d\u1eef li\u1ec7u v\u00e0o b\u1ed9 nh\u1edb trong c\u00f9ng m\u1ed9t l\u00fac nh\u01b0ng c\u00f3 th\u1ec3 \u0111\u1ecdc l\u1ea7n l\u01b0\u1ee3t t\u1eebng b\u1ed9 ph\u1eadn t\u1ea1i b\u1ed9 nh\u1edb ngo\u00e0i.<\/p>\n<p>&gt;&gt;&gt; Xem th\u00eam : <a href=\"https:\/\/teky.edu.vn\/blog\/wireframe-la-gi\/\"><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Wireframe l\u00e0 g\u00ec? C\u00f4ng d\u1ee5ng v\u00e0 c\u00e1ch thi\u1ebft l\u1eadp Wireframe ra sao?&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4480,&quot;10&quot;:2,&quot;11&quot;:0,&quot;15&quot;:&quot;Arial&quot;}\">Wireframe l\u00e0 g\u00ec? C\u00f4ng d\u1ee5ng v\u00e0 c\u00e1ch thi\u1ebft l\u1eadp Wireframe ra sao?<\/span><\/a><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Khai_niem_thuat_toan_Quick_Sort\"><\/span>Kh\u00e1i ni\u1ec7m thu\u1eadt to\u00e1n Quick Sort<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">Quick Sort c\u00f3 kh\u00e1i ni\u1ec7m kh\u00e1 t\u01b0\u01a1ng \u0111\u1ed3ng v\u1edbi Merge Sort. T\u1ee9c l\u00e0 \u0111\u1ec1u ho\u1ea1t \u0111\u1ed9ng d\u1ef1a tr\u00ean c\u01a1 ch\u1ebf chia v\u00e0 tr\u1ecb. N\u00f3 s\u1ebd ch\u1ecbu tr\u00e1ch nhi\u1ec7m ph\u00e2n chia d\u1eef li\u1ec7u th\u00e0nh c\u00e1c m\u1ea3ng nh\u1ecf v\u00e0 s\u1eafp x\u1ebfp m\u1ed9t c\u00e1ch nhanh ch\u00f3ng. \u0110\u00f3 c\u0169ng l\u00e0 l\u00fd do t\u1ea1i sao Quick Sort mang \u00fd ngh\u0129a l\u00e0 s\u1eafp x\u1ebfp nhanh.<\/p>\n<p style=\"text-align: justify;\">Quick Sort \u0111\u01b0\u1ee3c chia v\u00e0o ph\u00e2n lo\u1ea1i gi\u1ea3i thu\u1eadt s\u1eafp x\u1ebfp v\u1edbi ph\u1ee9c t\u1ea1p th\u1eddi gian l\u00e0 trung b\u00ecnh O(n log n) v\u00e0 x\u1ea5u nh\u1ea5t O(n2). \u0110\u1ed9 ph\u1ee9c t\u1ea1p d\u1eef li\u1ec7u c\u1ee7a thu\u1eadt to\u00e1n QuickSort t\u00f9y thu\u1ed9c v\u00e0o c\u00e1ch hi\u1ec7n th\u1ef1c. T\u1ea7n su\u1ea5t t\u1ed1i \u01b0u l\u00e0 th\u1ec9nh tho\u1ea3ng.<\/p>\n<p style=\"text-align: justify;\">Thu\u1eadt s\u1eafp x\u1ebfp nhanh Quick Sort s\u1ebd ti\u1ebfn h\u00e0nh chia nh\u1ecf m\u1ea3ng th\u00e0nh hai ph\u1ea7n. Th\u00f4ng qua ph\u01b0\u01a1ng ph\u00e1p so s\u00e1nh t\u1eebng ph\u1ea7n t\u1eed v\u1edbi m\u1ed9t ph\u1ea7n t\u1eed ch\u1ed1t, ta s\u1ebd thu \u0111\u01b0\u1ee3c m\u1ed9t m\u1ea3ng g\u1ed3m nh\u1eefng ph\u1ea7n t\u1eed nh\u1ecf h\u01a1n ho\u1eb7c b\u1eb1ng ph\u1ea7n t\u1eed ch\u1ed1t v\u00e0 m\u1ed9t m\u1ea3ng g\u1ed3m nh\u1eefng ph\u1ea7n t\u1eed l\u1edbn h\u01a1n ph\u1ea7n t\u1eed ch\u1ed1t. M\u1ed7i phi\u00ean b\u1ea3n Quick Sort C++ kh\u00e1c nhau s\u1ebd c\u00f3 m\u1ed9t c\u00e1ch ch\u1ecdn ph\u1ea7n t\u1eed ch\u1ed1t kh\u00e1c nhau. C\u00f3 th\u1ec3 l\u00e0 ph\u1ea7n t\u1eed \u0111\u1ea7u ti\u00ean, cu\u1ed1i c\u00f9ng ho\u1eb7c ph\u1ea7n t\u1eed ng\u1eabu nhi\u00ean, ph\u1ea7n t\u1eed trung v\u1ecb.<\/p>\n<p style=\"text-align: justify;\">Ho\u1ea1t \u0111\u1ed9ng ph\u00e2n chia n\u00e0y di\u1ec5n ra li\u00ean t\u1ee5c v\u00e0 ch\u1ec9 d\u1eebng l\u1ea1i khi \u0111\u1ed9 d\u00e0i c\u1ee7a m\u1ed7i ph\u1ea7n t\u1eed con b\u1eb1ng 1. \u0110\u1ec3 s\u1eafp x\u1ebfp nhanh c\u00e1c ph\u1ea7n t\u1eed con thu \u0111\u01b0\u1ee3c th\u00e0nh m\u1ed9t m\u1ea3ng ho\u00e0n ch\u1ec9nh, ng\u01b0\u1eddi d\u00f9ng s\u1ebd s\u1eed d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p \u0111\u1ec7 quy. T\u1ea5t c\u1ea3 c\u00e1c thao t\u00e1c n\u00e0y \u0111\u1ec1u di\u1ec5n ra trong th\u1eddi gian tuy\u1ebfn t\u00ednh.<\/p>\n<p><a href=\"http:\/\/hoclaptrinhmienphi.teky.vn\/1hhoclaptrinh\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-24877\" src=\"https:\/\/teky.edu.vn\/blog\/wp-content\/uploads\/2024\/03\/Banner-Free-Trial.png\" alt=\"H\u1ecdc th\u1eed mi\u1ec5n ph\u00ed\" width=\"600\" height=\"314\" \/><\/a><\/p>\n<h2 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Y_tuong_cua_thuat_toan_Quick_Sort\"><\/span>\u00dd t\u01b0\u1edfng c\u1ee7a thu\u1eadt to\u00e1n Quick Sort<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Cach_trien_khai_thuat_toan_Quick_Sort_Java\"><\/span>C\u00e1ch tri\u1ec3n khai thu\u1eadt to\u00e1n Quick Sort Java<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">\u0110\u1ea7u ti\u00ean, ta s\u1ebd ti\u1ebfn h\u00e0nh ch\u1ecdn m\u1ed9t pivot. V\u1ec1 c\u00e1ch ch\u1ecdn pivot, c\u00f3 r\u1ea5t nhi\u1ec1u c\u00e1ch \u0111\u1ec3 d\u00f9ng trong nhi\u1ec1u tr\u01b0\u1eddng h\u1ee3p kh\u00e1c nhau. Tuy nhi\u00ean ph\u1ed5 bi\u1ebfn nh\u1ea5t l\u00e0 ch\u1ecdn pivot \u0111\u1ea7u, pivot cu\u1ed1i v\u00e0 pivot gi\u1eefa.<\/p>\n<p style=\"text-align: justify;\">Sau khi \u0111\u00e3 ch\u1ecdn \u0111\u01b0\u1ee3c ph\u1ea7n t\u1eed ng\u01b0\u1eddi d\u00f9ng s\u1ebd c\u1ea7n khai b\u00e1o 2 bi\u1ebfn c\u1ee7a 2 con tr\u1ecf \u0111\u1ec3 duy\u1ec7t 2 ph\u00eda c\u1ee7a ph\u1ea7n t\u1eed pivot. L\u1ea7n l\u01b0\u1ee3t, ta s\u1ebd tr\u1ecf bi\u1ebfn b\u00ean tr\u00e1i \u0111\u1ebfn m\u1ed7i ph\u1ea7n t\u1eed n\u1eb1m b\u00ean tr\u00e1i c\u1ee7a ph\u1ea7n t\u1eed pivot. Ng\u01b0\u1ee3c l\u1ea1i, ta c\u0169ng s\u1ebd tr\u1ecf bi\u1ebfn b\u00ean ph\u1ea3i \u0111\u1ebfn m\u1ed7i ph\u1ea7n t\u1eed n\u1eb1m b\u00ean ph\u1ea3i c\u1ee7a ph\u1ea7n t\u1eed pivot.<\/p>\n<figure id=\"attachment_8017\" aria-describedby=\"caption-attachment-8017\" style=\"width: 650px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-8017\" src=\"https:\/\/teky.edu.vn\/blog\/wp-content\/uploads\/2021\/07\/y-tuong-ve-thuat-toan-quicksort-trong-c.jpg\" alt=\"\u00dd t\u01b0\u1edfng v\u1ec1 thu\u1eadt to\u00e1n Quicksort trong C++\" width=\"650\" height=\"400\" srcset=\"https:\/\/teky.edu.vn\/blog\/wp-content\/uploads\/2021\/07\/y-tuong-ve-thuat-toan-quicksort-trong-c.jpg 650w, https:\/\/teky.edu.vn\/blog\/wp-content\/uploads\/2021\/07\/y-tuong-ve-thuat-toan-quicksort-trong-c-400x246.jpg 400w\" sizes=\"auto, (max-width: 650px) 100vw, 650px\" \/><figcaption id=\"caption-attachment-8017\" class=\"wp-caption-text\">\u00dd t\u01b0\u1edfng v\u1ec1 thu\u1eadt to\u00e1n Quicksort trong C++<\/figcaption><\/figure>\n<p style=\"text-align: justify;\">V\u1edbi m\u1ed7i l\u1ea7n tr\u1ecf nh\u01b0 v\u1eady, ta ti\u1ebfn h\u00e0nh ph\u00e2n lo\u1ea1i c\u00e1c ph\u1ea7n t\u1eed. T\u1ea1i b\u00ean tr\u00e1i, n\u1ebfu bi\u1ebfn tr\u1ecf nh\u1ecf h\u01a1n ph\u1ea7n t\u1eed th\u00ec chuy\u1ec3n gi\u00e1 tr\u1ecb sang ph\u1ea3i. C\u00f2n t\u1ea1i b\u00ean ph\u1ea3i, n\u1ebfu bi\u1ebfn tr\u1ecf nh\u1ecf h\u01a1n ph\u1ea7n t\u1eed th\u00ec chuy\u1ec3n gi\u00e1 tr\u1ecb sang tr\u00e1i. N\u1ebfu bi\u1ebfn tr\u1ecf b\u1eb1ng ph\u1ea7n t\u1eed th\u00ec tr\u00e1o \u0111\u1ed5i gi\u00e1 tr\u1ecb 2 b\u00ean ph\u1ea3i v\u00e0 tr\u00e1i. Cu\u1ed1i c\u00f9ng, khi t\u1ea5t c\u1ea3 ph\u1ea7n t\u1eed tr\u00e1i l\u1edbn h\u01a1n ph\u1ea7n t\u1eed ph\u1ea3i th\u00ec \u0111\u00e2y ch\u00ednh l\u00e0 gi\u00e1 tr\u1ecb ch\u1ed1t m\u1edbi.<\/p>\n<p style=\"text-align: justify;\">L\u00fd thuy\u1ebft c\u01a1 b\u1ea3n l\u00e0 nh\u01b0 v\u1eady nh\u01b0ng v\u1edbi m\u1ed7i c\u00e1ch ch\u1ecdn ph\u1ea7n t\u1eed, qu\u00e1 tr\u00ecnh tri\u1ec3n khai s\u1ebd kh\u00e1c nhau. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 v\u00ed d\u1ee5 v\u1ec1 3 c\u00e1ch ch\u1ecdn ph\u1ea7n t\u1eed ph\u1ed5 bi\u1ebfn nh\u1ea5t.<\/p>\n<p>&gt;&gt;&gt; Xem th\u00eam : <a href=\"https:\/\/teky.edu.vn\/blog\/computer-science-la-gi\/\"><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Computer Science l\u00e0 g\u00ec? Tr\u01b0\u1eddng \u0110\u1ea1i h\u1ecdc n\u00e0o \u0111\u00e0o t\u1ea1o ng\u00e0nh n\u00e0y?&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4480,&quot;10&quot;:2,&quot;11&quot;:0,&quot;15&quot;:&quot;Arial&quot;}\">Computer Science l\u00e0 g\u00ec? Tr\u01b0\u1eddng \u0110\u1ea1i h\u1ecdc n\u00e0o \u0111\u00e0o t\u1ea1o ng\u00e0nh n\u00e0y?<\/span><\/a><\/p>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Cach_1_Chon_phan_tu_dau_trong_thuat_toan_Quick_Sort\"><\/span>C\u00e1ch 1: Ch\u1ecdn ph\u1ea7n t\u1eed \u0111\u1ea7u trong thu\u1eadt to\u00e1n Quick Sort<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">quickSort = (unSortedArr) =&gt; {<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\/\/ n\u1ebfu m\u1ea3ng kh\u00f4ng qu\u00e1 1 ph\u1ea7n t\u1eed th\u00ec m\u1ea3ng \u0111\u00f3 \u0111\u00e3 \u0111\u01b0\u1ee3c s\u1ea3n xu\u1ea5t<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0if (unSortedArr.length &lt; 2) return unSortedArr;<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0const pivot = unSortedArr[0]; \/\/l\u1ea5y ph\u1ea7n t\u1eed \u0111\u1ea7u c\u1ee7a m\u1ea3ng l\u00e0m ph\u1ea7n t\u1eed ch\u1ed1t<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0const leftArr = []; \/\/ m\u1ea3ng ch\u1ee9a ph\u1ea7n t\u1eed nh\u1ecf h\u01a1n pivot<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0const rightArr = []; \/\/ m\u1ea3ng ch\u1ee9a ph\u1ea7n t\u1eed l\u1edbn h\u01a1n pivot<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0let currentItem; \/\/ ph\u1ea7n t\u1eed \u0111ang \u0111\u01b0\u1ee3c x\u00e9t<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\/\/ loop c\u00e1c ph\u1ea7n t\u1eed c\u00f2n l\u1ea1i trong m\u1ea3ng tr\u1eeb ph\u1ea7n t\u1eed ch\u1ed1t.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\/\/ Do pivot l\u00e0 ptu \u0111\u1ea7u ti\u00ean n\u00ean i s\u1ebd b\u1eaft \u0111\u1ea7u t\u1eeb 1<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0for (let i = 1; i &lt; unSortedArr.length; i++) {\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0currentItem = unSortedArr[i];<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0if (currentItem &lt; pivot) {<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0leftArr.push(currentItem);<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0} else {<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0rightArr.push(currentItem);<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0return [&#8230;this.quickSort(leftArr), pivot, &#8230;this.quickSort(rightArr)];<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0}<\/span><\/p>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Cach_2_Chon_phan_tu_cuoi\"><\/span>C\u00e1ch 2: Ch\u1ecdn ph\u1ea7n t\u1eed cu\u1ed1i<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">quickSort = (unSortedArr) =&gt; {<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0if (unSortedArr.length &lt; 2) return unSortedArr;<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0const pivot = unSortedArr[unSortedArr.length &#8211; 1]; \/\/ph\u1ea7n t\u1eed cu\u1ed1i m\u1ea3ng l\u00e0m ch\u1ed1t<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0const leftArr = [];\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0const rightArr = [];\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0let currentItem;<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\/\/ Do pivot l\u00e0 ptu cu\u1ed1i n\u00ean length s\u1ebd tr\u1eeb \u0111i 1\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0for (let i = 0; i &lt; unSortedArr.length &#8211; 1; i++) {<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0currentItem = unSortedArr[i];<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0if (currentItem &lt; pivot) {<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0leftArr.push(currentItem);<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0} else {<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0rightArr.push(currentItem);<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0return [&#8230;this.quickSort(leftArr), pivot, &#8230;this.quickSort(rightArr)];<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0}<\/span><\/p>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Cach_3_Chon_phan_tu_giua_trong_thuat_toan_Quick_Sort\"><\/span><span style=\"color: #000000;\">C\u00e1ch 3: Ch\u1ecdn ph\u1ea7n t\u1eed gi\u1eefa trong thu\u1eadt to\u00e1n Quick Sort<\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">quickSort = (unSortedArr) =&gt; {<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0if (unSortedArr.length &lt; 2) return unSortedArr;<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\/\/ l\u1ea5y ph\u1ea7n t\u1eed gi\u1eefa l\u00e0m ch\u1ed1t<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0const pivotIndex = Math.floor(unSortedArr.length \/ 2);<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0const pivot = unSortedArr[pivotIndex];\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0const leftArr = [];\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0const rightArr = [];\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0let currentItem;<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0unSortedArr.splice(pivotIndex, 1); \/\/ lo\u1ea1i b\u1ecf ptu pivot trong m\u1ea3ng<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0for (let i = 0; i &lt; unSortedArr.length; i++) {<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0currentItem = unSortedArr[i];<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0if (currentItem &lt; pivot) {<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0leftArr.push(currentItem);<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0} else {<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0rightArr.push(currentItem);<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0return [&#8230;this.quickSort(leftArr), pivot, &#8230;this.quickSort(rightArr)];<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0}<\/span><\/p>\n<p>&gt;&gt;&gt; Xem th\u00eam : <a href=\"https:\/\/teky.edu.vn\/blog\/mean-stack-la-gi\/\"><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;MEAN Stack l\u00e0 g\u00ec? Gi\u1ea3i \u0111\u00e1p MEAN Stack t\u1eeb A \u0111\u1ebfn Z&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4480,&quot;10&quot;:2,&quot;11&quot;:0,&quot;15&quot;:&quot;Arial&quot;}\">MEAN Stack l\u00e0 g\u00ec? Gi\u1ea3i \u0111\u00e1p MEAN Stack t\u1eeb A \u0111\u1ebfn Z<\/span><\/a><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Giai_thuat_toan_Quick_Sort\"><\/span>Gi\u1ea3i thu\u1eadt to\u00e1n Quick Sort<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<figure id=\"attachment_8014\" aria-describedby=\"caption-attachment-8014\" style=\"width: 650px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-8014\" src=\"https:\/\/teky.edu.vn\/blog\/wp-content\/uploads\/2021\/07\/cac-buoc-trong-thuat-toan-quicksort-khong-he-kho-nhu-ban-tuong.jpg\" alt=\"C\u00e1c b\u01b0\u1edbc trong thu\u1eadt to\u00e1n Quicksort kh\u00f4ng h\u1ec1 kh\u00f3 nh\u01b0 b\u1ea1n t\u01b0\u1edfng\" width=\"650\" height=\"400\" srcset=\"https:\/\/teky.edu.vn\/blog\/wp-content\/uploads\/2021\/07\/cac-buoc-trong-thuat-toan-quicksort-khong-he-kho-nhu-ban-tuong.jpg 650w, https:\/\/teky.edu.vn\/blog\/wp-content\/uploads\/2021\/07\/cac-buoc-trong-thuat-toan-quicksort-khong-he-kho-nhu-ban-tuong-400x246.jpg 400w\" sizes=\"auto, (max-width: 650px) 100vw, 650px\" \/><figcaption id=\"caption-attachment-8014\" class=\"wp-caption-text\">C\u00e1c b\u01b0\u1edbc trong thu\u1eadt to\u00e1n Quicksort kh\u00f4ng h\u1ec1 kh\u00f3 nh\u01b0 b\u1ea1n t\u01b0\u1edfng<\/figcaption><\/figure>\n<p style=\"text-align: justify;\">D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t v\u00ed d\u1ee5 v\u1ec1 qu\u00e1 tr\u00ecnh gi\u1ea3i thu\u1eadt to\u00e1n Quicksort C++ \u0111\u01b0\u1ee3c vi\u1ebft b\u1eb1ng ng\u00f4n ng\u1eef l\u1eadp tr\u00ecnh Java:<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">public class QuickSort {<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0public static void main(String[] args) {<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0int[] x = {6, 2, 3, 4, 5, 9, 1};<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0printArray(x);<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0int left = 0;<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0int right = x.length &#8211; 1;<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0quickSort(x, left, right);<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0printArray(x);<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0public static void quickSort(int[] arr, int left, int right) {<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0if (arr == null || arr.length == 0)<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0return;<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0if (left &gt;= right)<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0return;<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0int middle = left + (right &#8211; left) \/ 2;<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0int pivot = arr[middle];<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0int i = left, j = right;<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0while (i &lt;= j) {<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0while (arr[i] &lt; pivot) {<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0i++;<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0while (arr[j] &gt; pivot) {<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0j&#8211;;<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0if (i &lt;= j) {<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0int temp = arr[i];<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0arr[i] = arr[j];<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0arr[j] = temp;<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0i++;<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0j&#8211;;<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0if (left &lt; j)<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0quickSort(arr, left, j);<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0if (right &gt; i)<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0quickSort(arr, i, right);<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0public static void printArray(int[] arr) {<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0for(int i = 0; i &lt; arr.length; i++) {<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0System.out.print(arr[i] + &#8221; &#8220;);<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0\u00a0\u00a0System.out.println();<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">\u00a0\u00a0}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #ff0000;\">}<\/span><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Do_phuc_tap_cua_thuat_toan_sap_xep_nhanh\"><\/span>\u0110\u1ed9 ph\u1ee9c t\u1ea1p c\u1ee7a thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp nhanh<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">C\u00f4ng th\u1ee9c t\u00ednh th\u1eddi gian c\u1ee7a thu\u1eadt to\u00e1n Quick Sort \u0111\u01b0\u1ee3c vi\u1ebft nh\u01b0 sau:<\/p>\n<p style=\"text-align: justify;\">T(n) = T(k) + T(n-k-1) + \u03b8(n)<\/p>\n<p style=\"text-align: justify;\">Trong \u0111\u00f3, T(k) v\u00e0 T(n-k-1) th\u1eddi gian d\u00e0nh cho hai cu\u1ed9c g\u1ecdi \u0111\u1ec7 quy. C\u00f2n \u03b8(n) l\u00e0 ti\u1ebfn tr\u00ecnh ph\u00e2n v\u00f9ng. k l\u00e0 s\u1ed1 ph\u1ea7n t\u1eed nh\u1ecf h\u01a1n ph\u1ea7n t\u1eed ch\u1ed1t. Th\u1eddi gian c\u1ee7a thu\u1eadt to\u00e1n Quick Sort c\u00f2n ph\u1ee5 thu\u1ed9c v\u00e0o m\u1ea3ng \u0111\u1ea7u v\u00e0 chi\u1ebfn l\u01b0\u1ee3c chia m\u1ea3ng.<\/p>\n<figure id=\"attachment_8015\" aria-describedby=\"caption-attachment-8015\" style=\"width: 650px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-8015\" src=\"https:\/\/teky.edu.vn\/blog\/wp-content\/uploads\/2021\/07\/cach-trien-khai-thuat-toan-quick-sort.jpg\" alt=\"C\u00e1ch tri\u1ec3n khai thu\u1eadt to\u00e1n Quick Sort\" width=\"650\" height=\"400\" srcset=\"https:\/\/teky.edu.vn\/blog\/wp-content\/uploads\/2021\/07\/cach-trien-khai-thuat-toan-quick-sort.jpg 650w, https:\/\/teky.edu.vn\/blog\/wp-content\/uploads\/2021\/07\/cach-trien-khai-thuat-toan-quick-sort-400x246.jpg 400w\" sizes=\"auto, (max-width: 650px) 100vw, 650px\" \/><figcaption id=\"caption-attachment-8015\" class=\"wp-caption-text\">C\u00e1ch tri\u1ec3n khai thu\u1eadt to\u00e1n Quick Sort<\/figcaption><\/figure>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\" aria-level=\"1\">V\u1edbi ph\u00e2n \u0111o\u1ea1n kh\u00f4ng c\u00e2n b\u1eb1ng: Khi tr\u01b0\u1eddng h\u1ee3p x\u1ea5u nh\u1ea5t x\u1ea3y ra (pivot l\u00e0 ph\u1ea7n t\u1eed \u0111\u1ea7u v\u00e0 d\u00e3y \u0111\u00e3 \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp nhanh), \u0111\u1ed9 ph\u1ee9c t\u1ea1p c\u1ee7a thu\u1eadt to\u00e1n Quick Sort s\u1ebd l\u00e0 O(n^2). T\u1ea1i th\u1eddi \u0111i\u1ec3m \u0111\u00f3, m\u1ea3ng kh\u00f4ng \u0111\u01b0\u1ee3c chia th\u00e0nh b\u1ea5t k\u1ef3 ph\u1ea7n n\u00e0o c\u1ea3, 2 b\u00e0i to\u00e1n con l\u1ea7n l\u01b0\u1ee3t c\u00f3 k\u00edch th\u01b0\u1edbc l\u00e0 n-1 v\u00e0 0.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">V\u1edbi ph\u00e2n \u0111o\u1ea1n ho\u00e0n h\u1ea3o: M\u1ed7i b\u00e0i to\u00e1n con c\u00f3 k\u00edch th\u01b0\u1edbc l\u00e0 n\/2. M\u1ea3ng c\u0169ng \u0111\u01b0\u1ee3c ph\u00e2n th\u00e0nh hai ph\u1ea7n b\u1eb1ng nhau. \u0110\u1ed9 ph\u1ee9c t\u1ea1p l\u00fac n\u00e0y l\u00e0 O(nlogn).<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">V\u1edbi ph\u00e2n \u0111o\u1ea1n c\u00e2n b\u1eb1ng: M\u1ed9t b\u00e0i to\u00e1n con c\u00f3 k\u00edch th\u01b0\u1edbc l\u00e0 n-k, b\u00e0i c\u00f2n l\u1ea1i c\u00f3 k\u00edch th\u01b0\u1edbc l\u00e0 k. \u0110\u1ed9 ph\u1ee9c t\u1ea1p l\u00fac n\u00e0y l\u00e0 O(n).<\/li>\n<li aria-level=\"1\"><a href=\"https:\/\/khuyenmai.teky.vn\/tangsachlaptrinh\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-24876\" src=\"https:\/\/teky.edu.vn\/blog\/wp-content\/uploads\/2024\/03\/Free-Asset.png\" alt=\"T\u1eb7ng s\u00e1ch mi\u1ec5n ph\u00ed\" width=\"600\" height=\"314\" \/><\/a><\/li>\n<\/ul>\n<p><em><strong>&gt;&gt;&gt; Xem th\u00eam:<\/strong> <a class=\"LinkSuggestion__Link-sc-1gewdgc-4 evyocv\" href=\"https:\/\/teky.edu.vn\/blog\/mean-stack-la-gi\/\" target=\"_blank\" rel=\"noopener\">MEAN Stack l\u00e0 g\u00ec? Gi\u1ea3i \u0111\u00e1p MEAN Stack t\u1eeb A \u0111\u1ebfn Z<\/a><\/em><\/p>\n<h2 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Ket_luan\"><\/span>K\u1ebft lu\u1eadn<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\"text-align: justify;\">Th\u00f4ng qua b\u00e0i vi\u1ebft tr\u00ean, Teky \u0111\u00e3 gi\u00fap b\u1ea1n \u0111\u1ecdc hi\u1ec3u th\u00eam v\u1ec1 thu\u1eadt to\u00e1n Quick Sort trong Java. Mong r\u1eb1ng b\u1ea1n \u0111\u1ecdc \u0111\u00e3 n\u1eafm r\u00f5 \u0111\u01b0\u1ee3c nh\u1eefng th\u00f4ng tin c\u01a1 b\u1ea3n xoay quanh thu\u1eadt to\u00e1n n\u00e0y. Ch\u00fac b\u1ea1n nhanh ch\u00f3ng \u1ee9ng d\u1ee5ng \u0111\u01b0\u1ee3c Quicksort Java v\u00e0o trong c\u00f4ng vi\u1ec7c c\u1ee7a m\u00ecnh.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Thong_tin_nen_biet_Hoc_Vien_Cong_Nghe_Teky\"><\/span><span style=\"font-size: 20px; color: #339966;\" data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;C\u00f9ng T\u00ecm Hi\u1ec3u V\u1ec1 Teky H\u1ecdc Vi\u1ec7n 5 sao \u0110\u00e0o T\u1ea1o Tr\u1ebb Em H\u1ecdc L\u1eadp Tr\u00ecnh (4-18 tu\u1ed5i)&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:17153,&quot;3&quot;:{&quot;1&quot;:0},&quot;11&quot;:4,&quot;12&quot;:0,&quot;17&quot;:1}\">Th\u00f4ng tin n\u00ean bi\u1ebft H\u1ecdc Vi\u1ec7n C\u00f4ng Ngh\u1ec7 Teky<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><iframe loading=\"lazy\" title=\"H\u1ecdc l\u1eadp tr\u00ecnh tr\u1ebb em \u1edf \u0111\u00e2u? - Gi\u1edbi thi\u1ec7u h\u1ecdc vi\u1ec7n c\u00f4ng ngh\u1ec7 TEKY h\u00e0ng \u0111\u1ea7u Vi\u1ec7t Nam\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/kGgr0XJAxFM?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<p><strong>TEKY l\u00e0 H\u1ecdc vi\u1ec7n s\u00e1ng t\u1ea1o c\u00f4ng ngh\u1ec7<\/strong> v\u1edbi ch\u01b0\u01a1ng tr\u00ecnh gi\u1ea3ng d\u1ea1y STEAM (Science \u2013 Technology \u2013 Engineering \u2013 Art \u2013 Mathematics) theo chu\u1ea9n M\u1ef9 \u0111\u1ea7u ti\u00ean t\u1ea1i Vi\u1ec7t Nam d\u00e0nh cho tr\u1ebb em t\u1eeb 4 \u0111\u1ebfn 18 tu\u1ed5i.<\/p>\n<p>\u0110\u01b0\u1ee3c th\u00e0nh l\u1eadp v\u00e0o th\u00e1ng 6 n\u0103m 2016, TEKY quy\u1ebft t\u00e2m th\u1ef1c hi\u1ec7n s\u1ee9 m\u1ec7nh mang \u0111\u1ebfn cho th\u1ebf h\u1ec7 tr\u1ebb Vi\u1ec7t Nam ki\u1ebfn th\u1ee9c to\u00e0n di\u1ec7n v\u1ec1 STEAM, \u0111\u1eb7c bi\u1ec7t l\u00e0 c\u00e1c t\u01b0 duy c\u00f4ng ngh\u1ec7, khoa h\u1ecdc m\u00e1y t\u00ednh v\u00e0 k\u1ef9 n\u0103ng th\u1ebf k\u1ef7 21 \u2013 4Cs (Critical Thinking: T\u01b0 duy ph\u1ea3n bi\u1ec7n \u2013 Communication: Giao ti\u1ebfp \u2013 Creativity: S\u00e1ng t\u1ea1o \u2013 Collaboration: L\u00e0m vi\u1ec7c nh\u00f3m).<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Day_la_chuong_trinh_khong_chi_trang_bi_kien_thuc_lap_trinh_ma_con_ren_luyen_nhom_ky_nang_4Cs_Tre_se_duoc\"><\/span>\u0110\u00e2y l\u00e0 ch\u01b0\u01a1ng tr\u00ecnh kh\u00f4ng ch\u1ec9 trang b\u1ecb ki\u1ebfn th\u1ee9c l\u1eadp tr\u00ecnh m\u00e0 c\u00f2n r\u00e8n luy\u1ec7n nh\u00f3m k\u1ef9 n\u0103ng 4Cs. Tr\u1ebb s\u1ebd \u0111\u01b0\u1ee3c:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>\u00a0H\u1ecdc t\u01b0 duy ph\u1ea3n bi\u1ec7n th\u00f4ng qua vi\u1ec7c ph\u00e2n t\u00edch c\u00e1c v\u1ea5n \u0111\u1ec1.<\/li>\n<li>\u00a0H\u1ecdc t\u00ednh s\u00e1ng t\u1ea1o t\u01b0 duy Logic th\u00f4ng qua vi\u1ec7c l\u1eafp \u0111\u1eb7t v\u00e0 l\u1eadp tr\u00ecnh robot th \u00f4ng qua c\u00e1c m\u00f4 h\u00ecnh Lego Mindstorm, app tr\u00f2 ch\u01a1i. Gi\u00fap con h\u1ecdc gi\u1ecfi m\u00f4n To\u00e1n tr\u00ean l\u1edbp<\/li>\n<li>\u00a0K\u1ef9 n\u0103ng h\u1ee3p t\u00e1c th\u00f4ng qua c\u00e1c tr\u00f2 ch\u01a1i team-building, c\u00e1c d\u1ef1 \u00e1n nh\u00f3m tr\u00ean l\u1edbp.<\/li>\n<li>\u00a0Ph\u00e1t huy kh\u1ea3 n\u0103ng giao ti\u1ebfp hi\u1ec7u qu\u1ea3 b\u1eb1ng nhi\u1ec1u b\u00e0i t\u1eadp v\u00e0 ho\u1ea1t \u0111\u1ed9ng h\u1ea5p d\u1eabn.<\/li>\n<\/ul>\n<p><iframe loading=\"lazy\" title=\"Shark Nguy\u1ec5n Ho\u00e0 B\u00ecnh \u0111\u1ed3ng h\u00e0nh c\u00f9ng con h\u1ecdc l\u1eadp tr\u00ecnh t\u1ea1i h\u1ecdc vi\u1ec7n c\u00f4ng ngh\u1ec7 Teky h\u00e0ng \u0111\u1ea7u Vi\u1ec7t Nam\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/q6QbqIs6ll8?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<p>C\u00e1c b\u1ed9 m\u00f4n gi\u1ea3ng d\u1ea1y t\u1ea1i Teky g\u1ed3m: <span style=\"font-weight: 400;\">L\u1eadp tr\u00ecnh v\u00e0 ph\u00e1t tri\u1ec3n \u1ee9ng d\u1ee5ng<\/span><span style=\"font-weight: 400;\">, <\/span><span style=\"font-weight: 400;\">l\u1eadp tr\u00ecnh game<\/span><span style=\"font-weight: 400;\">, <\/span><span style=\"font-weight: 400;\">l\u1eadp tr\u00ecnh web v\u1edbi python<\/span> <span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">L\u1eadp tr\u00ecnh Scratch<\/span> <span style=\"font-weight: 400;\">Robotics<\/span> Engineering, C\u00f4ng ngh\u1ec7 3D v\u00e0 MultiMedia. Ch\u00fang t\u00f4i tin r\u1eb1ng tr\u1ebb em Vi\u1ec7t Nam c\u00f3 c\u01a1 h\u1ed9i ph\u00e1t tri\u1ec3n m\u1ea1nh m\u1ebd trong m\u1ed9t n\u1ec1n kinh t\u1ebf s\u1ed1 v\u00e0 c\u1ea7n \u0111\u01b0\u1ee3c trang b\u1ecb s\u1eb5n s\u00e0ng \u0111\u1ec3 tr\u1edf th\u00e0nh nh\u1eefng doanh nh\u00e2n c\u00f4ng ngh\u1ec7 trong t\u01b0\u01a1ng lai.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Lien_he_ngay_hoc_vien_cong_nghe_sang_tao_TEKY_de_duoc_tu_van_khoa_hoc\"><\/span><span style=\"color: #008000;\"><b>Li\u00ean h\u1ec7 ngay h\u1ecdc vi\u1ec7n c\u00f4ng ngh\u1ec7 s\u00e1ng t\u1ea1o TEKY \u0111\u1ec3 \u0111\u01b0\u1ee3c t\u01b0 v\u1ea5n kh\u00f3a h\u1ecdc:<\/b><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Cam k\u00eat 7 tu\u1ed5i c\u00f3 th\u1ec3 l\u1eadp tr\u00ecnh<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Top 10 d\u1ef1 \u00e1n gi\u00e1o d\u1ee5c c\u00f3 t\u1ea7m \u1ea3nh h\u01b0\u1edfng nh\u1ea5t \u0110\u00f4ng Nam \u00c1 2017 &amp; 2018<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Top 3 D\u1ef1 \u00e1n xu\u1ea5t s\u1eafc nh\u1ea5t, NextGen \u2013 Th\u1ee5y S\u0129<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u00a0Hotline H\u00e0 N\u1ed9i: 024-7109-6668 | 0975-241-015<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u00a0Hotline H\u1ed3 Ch\u00ed Minh: 028-7109 9948 | 097-900-8642<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">Website <\/span><a href=\"https:\/\/teky.edu.vn\/\"><span style=\"font-weight: 400;\">https:\/\/teky.edu.vn<\/span><\/a><span style=\"font-weight: 400;\"> | Email: support@teky.edu.vn |<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Khi nh\u1eafc \u0111\u1ebfn nh\u1eefng thu\u1eadt to\u00e1n \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng ph\u1ed5 bi\u1ebfn trong l\u1eadp tr\u00ecnh th\u00ec kh\u00f4ng th\u1ec3 n\u00e0o thi\u1ebfu Quick Sort. C\u0169ng gi\u1ed1ng nh\u01b0 c\u00e1c thu\u1eadt to\u00e1n kh\u00e1c, Quick Sort kh\u00f4ng h\u1ec1 d\u1ec5 \u201cx\u01a1i\u201d m\u00e0 c\u1ea7n c\u00f3 th\u1eddi gian nghi\u00ean c\u1ee9u k\u1ef9 l\u01b0\u1ee1ng \u0111\u1ec3 ho\u00e0n to\u00e0n n\u1eafm ch\u1eafc n\u00f3 trong b\u00e0n tay. Trong b\u00e0i vi\u1ebft &hellip;<\/p>\n","protected":false},"author":10,"featured_media":8016,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[28],"tags":[],"class_list":["post-8013","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-lap-trinh"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v20.9 (Yoast SEO v26.0) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Thu\u1eadt to\u00e1n Quick Sort l\u00e0 g\u00ec? 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