{"id":27427,"date":"2025-04-23T14:26:59","date_gmt":"2025-04-23T07:26:59","guid":{"rendered":"https:\/\/interdata.vn\/blog\/?p=27427"},"modified":"2025-04-23T14:26:59","modified_gmt":"2025-04-23T07:26:59","slug":"hash-table-la-gi","status":"publish","type":"post","link":"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/","title":{"rendered":"Hash Table (B\u1ea3ng B\u0103m) l\u00e0 g\u00ec? To\u00e0n t\u1eadp v\u1ec1 c\u1ea5u tr\u00fac &#038; ho\u1ea1t \u0111\u1ed9ng"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_84 counter-hierarchy ez-toc-counter ez-toc-white ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">N\u1ed8I 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 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Hash-table-bang-bam-la-gi\" >Hash table (b\u1ea3ng b\u0103m) l\u00e0 g\u00ec?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Tai-sao-Hash-Table-lai-quan-trong-trong-lap-trinh\" >T\u1ea1i sao Hash Table l\u1ea1i quan tr\u1ecdng trong l\u1eadp tr\u00ecnh?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Cac-thanh-phan-cot-loi-cau-tao-nen-Hash-Table\" >C\u00e1c th\u00e0nh ph\u1ea7n c\u1ed1t l\u00f5i c\u1ea5u t\u1ea1o n\u00ean Hash Table<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Khoa-Key\" >Kh\u00f3a (Key)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Gia-tri-Value\" >Gi\u00e1 tr\u1ecb (Value)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Ham-bam-Hash-Function\" >H\u00e0m b\u0103m (Hash Function)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Bucket-Ngan-chua-Slot\" >Bucket (Ng\u0103n ch\u1ee9a \/ Slot)<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Hash-Table-hoat-dong-nhu-the-nao\" >Hash Table ho\u1ea1t \u0111\u1ed9ng nh\u01b0 th\u1ebf n\u00e0o?<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Thao-tac-Them-Insert-Put\" >Thao t\u00e1c Th\u00eam (Insert \/ Put)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Thao-tac-Tim-kiem-Search-Get\" >Thao t\u00e1c T\u00ecm ki\u1ebfm (Search \/ Get)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Thao-tac-Xoa-Delete-Remove\" >Thao t\u00e1c X\u00f3a (Delete \/ Remove)<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Van-de-nan-giai-Xung-dot-trong-Hash-Table-Hash-Collision\" >V\u1ea5n \u0111\u1ec1 nan gi\u1ea3i: Xung \u0111\u1ed9t trong Hash Table (Hash Collision)<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Xung-dot-Hash-Hash-Collision-la-gi\" >Xung \u0111\u1ed9t Hash (Hash Collision) l\u00e0 g\u00ec?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Cac-ky-thuat-xu-ly-xung-dot-Collision-Resolution-Techniques-pho-bien\" >C\u00e1c k\u1ef9 thu\u1eadt x\u1eed l\u00fd xung \u0111\u1ed9t (Collision Resolution Techniques) ph\u1ed5 bi\u1ebfn<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Phan-tich-hieu-nang-Do-phuc-tap-thoi-gian-Time-Complexity\" >Ph\u00e2n t\u00edch hi\u1ec7u n\u0103ng: \u0110\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian (Time Complexity)<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Truong-hop-trung-binh\" >Tr\u01b0\u1eddng h\u1ee3p trung b\u00ecnh<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Truong-hop-xau-nhat\" >Tr\u01b0\u1eddng h\u1ee3p x\u1ea5u nh\u1ea5t<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#He-so-tai-Load-Factor-va-anh-huong-den-hieu-suat\" >H\u1ec7 s\u1ed1 t\u1ea3i (Load Factor) v\u00e0 \u1ea3nh h\u01b0\u1edfng \u0111\u1ebfn hi\u1ec7u su\u1ea5t<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Uu-diem-va-Nhuoc-diem-cua-Hash-Table\" >\u01afu \u0111i\u1ec3m v\u00e0 Nh\u01b0\u1ee3c \u0111i\u1ec3m c\u1ee7a Hash Table<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Uu-diem\" >\u01afu \u0111i\u1ec3m<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Nhuoc-diem\" >Nh\u01b0\u1ee3c \u0111i\u1ec3m<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Ung-dung-thuc-te-cua-Hash-Table-Bang-Bam\" >\u1ee8ng d\u1ee5ng th\u1ef1c t\u1ebf c\u1ee7a Hash Table (B\u1ea3ng B\u0103m)<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Implementations-trong-Ngon-ngu-Lap-trinh-Dictionary-HashMap-Set\" >Implementations trong Ng\u00f4n ng\u1eef L\u1eadp tr\u00ecnh (Dictionary, HashMap, Set)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-24\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Bo-nho-dem-Caching\" >B\u1ed9 nh\u1edb \u0111\u1ec7m (Caching)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-25\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Chi-muc-co-so-du-lieu-Database-Indexing\" >Ch\u1ec9 m\u1ee5c c\u01a1 s\u1edf d\u1eef li\u1ec7u (Database Indexing)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-26\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Cac-ung-dung-khac\" >C\u00e1c \u1ee9ng d\u1ee5ng kh\u00e1c<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-27\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#So-sanh-nhanh-Hash-Table-voi-cac-cau-truc-du-lieu-khac\" >So s\u00e1nh nhanh: Hash Table v\u1edbi c\u00e1c c\u1ea5u tr\u00fac d\u1eef li\u1ec7u kh\u00e1c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-28\" href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/#Tong-ket-Khi-nao-nen-su-dung-Hash-Table\" >T\u1ed5ng k\u1ebft: Khi n\u00e0o n\u00ean s\u1eed d\u1ee5ng Hash Table?<\/a><\/li><\/ul><\/nav><\/div>\n\n<p>B\u1ea1n \u0111\u00e3 bao gi\u1edd t\u1ef1 h\u1ecfi l\u00e0m th\u1ebf n\u00e0o c\u00e1c \u1ee9ng d\u1ee5ng c\u00f3 th\u1ec3 t\u00ecm ki\u1ebfm th\u00f4ng tin nhanh nh\u01b0 ch\u1edbp trong h\u00e0ng tri\u1ec7u d\u1eef li\u1ec7u ch\u01b0a? Hay l\u00e0m sao c\u00e1c ng\u00f4n ng\u1eef <a href=\"https:\/\/interdata.vn\/blog\/lap-trinh-la-gi\/\">l\u1eadp tr\u00ecnh<\/a> qu\u1ea3n l\u00fd c\u00e1c \u0111\u1ed1i t\u01b0\u1ee3ng ph\u1ee9c t\u1ea1p m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3? B\u00ed m\u1eadt th\u01b0\u1eddng n\u1eb1m \u1edf m\u1ed9t c\u1ea5u tr\u00fac d\u1eef li\u1ec7u m\u1ea1nh m\u1ebd v\u00e0 linh ho\u1ea1t: <strong>Hash Table<\/strong>, hay c\u00f2n g\u1ecdi l\u00e0 <strong>B\u1ea3ng B\u0103m<\/strong>.<\/p>\n<p>B\u00e0i vi\u1ebft n\u00e0y s\u1ebd l\u00e0 c\u1ea9m nang to\u00e0n di\u1ec7n, gi\u00fap b\u1ea1n, \u0111\u1eb7c bi\u1ec7t l\u00e0 nh\u1eefng ng\u01b0\u1eddi m\u1edbi b\u1eaft \u0111\u1ea7u, hi\u1ec3u r\u00f5 <strong>Hash Table l\u00e0 g\u00ec<\/strong>, c\u1ea5u tr\u00fac b\u00ean trong, c\u00e1ch n\u00f3 ho\u1ea1t \u0111\u1ed9ng, nh\u1eefng th\u00e1ch th\u1ee9c g\u1eb7p ph\u1ea3i v\u00e0 v\u00f4 s\u1ed1 \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf c\u1ee7a n\u00f3 trong th\u1ebf gi\u1edbi c\u00f4ng ngh\u1ec7.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Hash-table-bang-bam-la-gi\"><\/span>Hash table (b\u1ea3ng b\u0103m) l\u00e0 g\u00ec?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong><a href=\"https:\/\/interdata.vn\/blog\/hash-table-la-gi\/\">Hash table (b\u1ea3ng b\u0103m)<\/a> l\u00e0 m\u1ed9t c\u1ea5u tr\u00fac d\u1eef li\u1ec7u<\/strong> \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf \u0111\u1ec3 l\u01b0u tr\u1eef th\u00f4ng tin d\u01b0\u1edbi d\u1ea1ng c\u00e1c c\u1eb7p <strong>kh\u00f3a-gi\u00e1 tr\u1ecb (key-value)<\/strong>. \u0110i\u1ec3m \u0111\u1eb7c bi\u1ec7t c\u1ee7a n\u00f3 l\u00e0 s\u1eed d\u1ee5ng m\u1ed9t <strong>h\u00e0m b\u0103m (hash function)<\/strong> \u0111\u1ec3 t\u00ednh to\u00e1n ra m\u1ed9t v\u1ecb tr\u00ed (ch\u1ec9 s\u1ed1 &#8211; index) g\u1ea7n nh\u01b0 duy nh\u1ea5t trong b\u1ed9 nh\u1edb cho m\u1ed7i kh\u00f3a, cho ph\u00e9p vi\u1ec7c th\u00eam, x\u00f3a v\u00e0 \u0111\u1eb7c bi\u1ec7t l\u00e0 t\u00ecm ki\u1ebfm d\u1eef li\u1ec7u di\u1ec5n ra c\u1ef1c k\u1ef3 nhanh ch\u00f3ng.<\/p>\n<p>H\u00e3y t\u01b0\u1edfng t\u01b0\u1ee3ng hash table gi\u1ed1ng nh\u01b0 m\u1ed9t cu\u1ed1n t\u1eeb \u0111i\u1ec3n ho\u1eb7c danh b\u1ea1 \u0111i\u1ec7n tho\u1ea1i si\u00eau t\u1ed1c. Thay v\u00ec ph\u1ea3i l\u1eadt t\u1eebng trang theo th\u1ee9 t\u1ef1 A-Z (nh\u01b0 trong m\u1ed9t danh s\u00e1ch th\u00f4ng th\u01b0\u1eddng), b\u1ea1n c\u00f3 m\u1ed9t &#8220;c\u00f4ng th\u1ee9c th\u1ea7n k\u1ef3&#8221; (ch\u00ednh l\u00e0 h\u00e0m b\u0103m). B\u1ea1n \u0111\u01b0a t\u00ean ng\u01b0\u1eddi (kh\u00f3a) v\u00e0o c\u00f4ng th\u1ee9c, n\u00f3 l\u1eadp t\u1ee9c ch\u1ec9 cho b\u1ea1n s\u1ed1 trang (ch\u1ec9 s\u1ed1) ch\u1ee9a s\u1ed1 \u0111i\u1ec7n tho\u1ea1i (gi\u00e1 tr\u1ecb) c\u1ee7a ng\u01b0\u1eddi \u0111\u00f3. Vi\u1ec7c tra c\u1ee9u g\u1ea7n nh\u01b0 t\u1ee9c th\u00ec!<\/p>\n<p>\u0110\u1ec3 hi\u1ec3u r\u00f5 h\u01a1n, ch\u00fang ta c\u1ea7n bi\u1ebft c\u00e1c th\u00e0nh ph\u1ea7n ch\u00ednh t\u1ea1o n\u00ean n\u00f3. \u0110\u00f3 l\u00e0 <strong>Kh\u00f3a (Key)<\/strong> &#8211; d\u00f9ng \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh d\u1eef li\u1ec7u, <strong>Gi\u00e1 tr\u1ecb (Value)<\/strong> &#8211; l\u00e0 d\u1eef li\u1ec7u th\u1ef1c t\u1ebf b\u1ea1n mu\u1ed1n l\u01b0u, v\u00e0 <strong>H\u00e0m b\u0103m (Hash Function)<\/strong> &#8211; b\u1ed9 n\u00e3o x\u1eed l\u00fd vi\u1ec7c \u00e1nh x\u1ea1 Kh\u00f3a th\u00e0nh v\u1ecb tr\u00ed l\u01b0u tr\u1eef. C\u00e1c v\u1ecb tr\u00ed n\u00e0y th\u01b0\u1eddng n\u1eb1m trong m\u1ed9t c\u1ea5u tr\u00fac gi\u1ed1ng nh\u01b0 m\u1ea3ng, g\u1ecdi l\u00e0 c\u00e1c <strong>ng\u0103n ch\u1ee9a (buckets)<\/strong>.<\/p>\n<p>M\u1ee5c ti\u00eau t\u1ed1i th\u01b0\u1ee3ng khi thi\u1ebft k\u1ebf v\u00e0 s\u1eed d\u1ee5ng hash table ch\u00ednh l\u00e0 t\u1ed1c \u0111\u1ed9. Nh\u1edd c\u01a1 ch\u1ebf \u00e1nh x\u1ea1 tr\u1ef1c ti\u1ebfp t\u1eeb kh\u00f3a \u0111\u1ebfn v\u1ecb tr\u00ed, th\u1eddi gian trung b\u00ecnh \u0111\u1ec3 th\u1ef1c hi\u1ec7n c\u00e1c thao t\u00e1c c\u01a1 b\u1ea3n nh\u01b0 t\u00ecm ki\u1ebfm, th\u00eam m\u1edbi hay x\u00f3a m\u1ed9t ph\u1ea7n t\u1eed l\u00e0 kh\u00f4ng \u0111\u1ed5i, kh\u00f4ng ph\u1ee5 thu\u1ed9c v\u00e0o s\u1ed1 l\u01b0\u1ee3ng ph\u1ea7n t\u1eed \u0111ang c\u00f3. Trong khoa h\u1ecdc m\u00e1y t\u00ednh, \u0111i\u1ec1u n\u00e0y \u0111\u01b0\u1ee3c bi\u1ec3u th\u1ecb b\u1eb1ng k\u00fd hi\u1ec7u <strong>O(1)<\/strong> &#8211; t\u1ee9c l\u00e0 <strong>\u0111\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian trung b\u00ecnh kh\u00f4ng \u0111\u1ed5i<\/strong>.<\/p>\n<p>Ch\u00ednh v\u00ec t\u1ed1c \u0111\u1ed9 truy xu\u1ea5t d\u1eef li\u1ec7u \u0111\u00e1ng kinh ng\u1ea1c n\u00e0y, hash table tr\u1edf th\u00e0nh n\u1ec1n t\u1ea3ng cho r\u1ea5t nhi\u1ec1u \u1ee9ng d\u1ee5ng quan tr\u1ecdng. B\u1ea1n c\u00f3 th\u1ec3 th\u1ea5y n\u00f3 trong c\u00e1ch Python tri\u1ec3n khai ki\u1ec3u d\u1eef li\u1ec7u <code>dict<\/code>, <a href=\"https:\/\/interdata.vn\/blog\/ngon-ngu-lap-trinh-java\/\">Java<\/a> d\u00f9ng <code>HashMap<\/code>, hay trong c\u00e1c h\u1ec7 th\u1ed1ng y\u00eau c\u1ea7u tra c\u1ee9u nhanh nh\u01b0 b\u1ed9 nh\u1edb \u0111\u1ec7m (<a href=\"https:\/\/interdata.vn\/blog\/cache-la-gi\/\">cache<\/a>) v\u00e0 c\u00e1c h\u1ec7 th\u1ed1ng ch\u1ec9 m\u1ee5c c\u01a1 s\u1edf d\u1eef li\u1ec7u (<a href=\"https:\/\/interdata.vn\/blog\/index-trong-database-la-gi\/\">database index<\/a>).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/interdata.vn\/blog\/wp-content\/uploads\/2025\/04\/Hash-table.jpg\" alt=\"Hash table\" width=\"750\" height=\"500\" class=\"aligncenter size-full wp-image-27430\" title=\"\" srcset=\"https:\/\/interdata.vn\/blog\/wp-content\/uploads\/2025\/04\/Hash-table.jpg 750w, https:\/\/interdata.vn\/blog\/wp-content\/uploads\/2025\/04\/Hash-table-300x200.jpg 300w\" sizes=\"auto, (max-width: 750px) 100vw, 750px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Tai-sao-Hash-Table-lai-quan-trong-trong-lap-trinh\"><\/span>T\u1ea1i sao Hash Table l\u1ea1i quan tr\u1ecdng trong l\u1eadp tr\u00ecnh?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>T\u1ed1c \u0111\u1ed9 l\u00e0 y\u1ebfu t\u1ed1 then ch\u1ed1t trong nhi\u1ec1u \u1ee9ng d\u1ee5ng ph\u1ea7n m\u1ec1m. Hash table cung c\u1ea5p hi\u1ec7u su\u1ea5t truy xu\u1ea5t d\u1eef li\u1ec7u v\u01b0\u1ee3t tr\u1ed9i, th\u01b0\u1eddng l\u00e0 <strong>O(1) \u1edf tr\u01b0\u1eddng h\u1ee3p trung b\u00ecnh<\/strong>. \u0110i\u1ec1u n\u00e0y c\u00f3 ngh\u0129a l\u00e0 d\u00f9 b\u1ea1n c\u00f3 l\u01b0u tr\u1eef h\u00e0ng ng\u00e0n hay h\u00e0ng tri\u1ec7u c\u1eb7p key-value, th\u1eddi gian \u0111\u1ec3 t\u00ecm m\u1ed9t gi\u00e1 tr\u1ecb d\u1ef1a tr\u00ean kh\u00f3a c\u1ee7a n\u00f3 g\u1ea7n nh\u01b0 kh\u00f4ng thay \u0111\u1ed5i.<\/p>\n<p>H\u00e3y so s\u00e1nh v\u1edbi c\u00e1c c\u1ea5u tr\u00fac d\u1eef li\u1ec7u kh\u00e1c. N\u1ebfu b\u1ea1n l\u01b0u d\u1eef li\u1ec7u trong m\u1ed9t danh s\u00e1ch (<a href=\"https:\/\/interdata.vn\/blog\/array-la-gi\/\">array<\/a> ho\u1eb7c linked <a href=\"https:\/\/interdata.vn\/blog\/list-trong-python\/\">list<\/a>) v\u00e0 mu\u1ed1n t\u00ecm m\u1ed9t ph\u1ea7n t\u1eed, b\u1ea1n c\u00f3 th\u1ec3 ph\u1ea3i duy\u1ec7t qua t\u1eebng ph\u1ea7n t\u1eed m\u1ed9t. Trong tr\u01b0\u1eddng h\u1ee3p x\u1ea5u nh\u1ea5t, b\u1ea1n ph\u1ea3i xem h\u1ebft c\u1ea3 danh s\u00e1ch, d\u1eabn \u0111\u1ebfn \u0111\u1ed9 ph\u1ee9c t\u1ea1p <strong>O(n)<\/strong>, ngh\u0129a l\u00e0 th\u1eddi gian t\u00ecm ki\u1ebfm t\u0103ng tuy\u1ebfn t\u00ednh theo s\u1ed1 l\u01b0\u1ee3ng ph\u1ea7n t\u1eed (n).<\/p>\n<p>V\u1edbi c\u00e1c <a href=\"https:\/\/interdata.vn\/blog\/cau-truc-du-lieu-tree-cay\/\">c\u1ea5u tr\u00fac d\u1eef li\u1ec7u c\u00e2y<\/a> c\u00e2n b\u1eb1ng (nh\u01b0 C\u00e2y t\u00ecm ki\u1ebfm nh\u1ecb ph\u00e2n &#8211; Binary Search Tree), t\u1ed1c \u0111\u1ed9 t\u00ecm ki\u1ebfm t\u1ed1t h\u01a1n, th\u01b0\u1eddng l\u00e0 <strong>O(log n)<\/strong>. Tuy nhi\u00ean, O(1) c\u1ee7a hash table v\u1eabn nhanh h\u01a1n \u0111\u00e1ng k\u1ec3, \u0111\u1eb7c bi\u1ec7t khi t\u1eadp <a href=\"https:\/\/interdata.vn\/blog\/big-data-la-gi\/\">d\u1eef li\u1ec7u l\u1edbn<\/a>. S\u1ef1 kh\u00e1c bi\u1ec7t gi\u1eefa mili gi\u00e2y v\u00e0 nano gi\u00e2y c\u00f3 th\u1ec3 quy\u1ebft \u0111\u1ecbnh th\u00e0nh b\u1ea1i c\u1ee7a m\u1ed9t h\u1ec7 th\u1ed1ng hi\u1ec7u n\u0103ng cao nh\u01b0 <a href=\"https:\/\/interdata.vn\/blog\/web-server\/\">m\u00e1y ch\u1ee7 web<\/a>, c\u01a1 s\u1edf d\u1eef li\u1ec7u th\u1eddi gian th\u1ef1c, hay c\u00e1c <a href=\"https:\/\/interdata.vn\/blog\/thuat-toan-algorithm\/\">thu\u1eadt to\u00e1n<\/a> ph\u1ee9c t\u1ea1p.<\/p>\n<p>V\u00ec v\u1eady, s\u1ef1 t\u1ed3n t\u1ea1i c\u1ee7a hash table cho ph\u00e9p c\u00e1c l\u1eadp tr\u00ecnh vi\u00ean x\u00e2y d\u1ef1ng nh\u1eefng \u1ee9ng d\u1ee5ng nhanh h\u01a1n, hi\u1ec7u qu\u1ea3 h\u01a1n v\u00e0 c\u00f3 kh\u1ea3 n\u0103ng m\u1edf r\u1ed9ng t\u1ed1t h\u01a1n. N\u00f3 l\u00e0 c\u00f4ng c\u1ee5 kh\u00f4ng th\u1ec3 thi\u1ebfu trong b\u1ed9 k\u1ef9 n\u0103ng c\u1ee7a b\u1ea5t k\u1ef3 nh\u00e0 ph\u00e1t tri\u1ec3n ph\u1ea7n m\u1ec1m n\u00e0o mu\u1ed1n t\u1ed1i \u01b0u h\u00f3a hi\u1ec7u su\u1ea5t x\u1eed l\u00fd d\u1eef li\u1ec7u.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Cac-thanh-phan-cot-loi-cau-tao-nen-Hash-Table\"><\/span>C\u00e1c th\u00e0nh ph\u1ea7n c\u1ed1t l\u00f5i c\u1ea5u t\u1ea1o n\u00ean Hash Table<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0110\u1ec3 th\u1ef1c s\u1ef1 l\u00e0m ch\u1ee7 hash table, ch\u00fang ta c\u1ea7n hi\u1ec3u r\u00f5 t\u1eebng vi\u00ean g\u1ea1ch x\u00e2y d\u1ef1ng n\u00ean n\u00f3. M\u1ed7i th\u00e0nh ph\u1ea7n \u0111\u00f3ng m\u1ed9t vai tr\u00f2 quan tr\u1ecdng trong vi\u1ec7c \u0111\u1ea3m b\u1ea3o c\u1ea5u tr\u00fac n\u00e0y ho\u1ea1t \u0111\u1ed9ng hi\u1ec7u qu\u1ea3.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/interdata.vn\/blog\/wp-content\/uploads\/2025\/04\/Hash-table-01.jpg\" alt=\"Hash table 01\" width=\"750\" height=\"425\" class=\"aligncenter size-full wp-image-27428\" title=\"\" srcset=\"https:\/\/interdata.vn\/blog\/wp-content\/uploads\/2025\/04\/Hash-table-01.jpg 750w, https:\/\/interdata.vn\/blog\/wp-content\/uploads\/2025\/04\/Hash-table-01-300x170.jpg 300w\" sizes=\"auto, (max-width: 750px) 100vw, 750px\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Khoa-Key\"><\/span>Kh\u00f3a (Key)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Kh\u00f3a (Key)<\/strong> l\u00e0 tr\u00e1i tim c\u1ee7a vi\u1ec7c \u0111\u1ecbnh v\u1ecb d\u1eef li\u1ec7u trong hash table. M\u1ed7i gi\u00e1 tr\u1ecb (Value) b\u1ea1n l\u01b0u tr\u1eef s\u1ebd \u0111\u01b0\u1ee3c li\u00ean k\u1ebft v\u1edbi m\u1ed9t kh\u00f3a duy nh\u1ea5t. Khi b\u1ea1n mu\u1ed1n truy xu\u1ea5t, c\u1eadp nh\u1eadt hay x\u00f3a d\u1eef li\u1ec7u, b\u1ea1n s\u1ebd s\u1eed d\u1ee5ng ch\u00ednh kh\u00f3a n\u00e0y.<\/p>\n<p>M\u1ed9t y\u00eau c\u1ea7u quan tr\u1ecdng \u0111\u1ed1i v\u1edbi kh\u00f3a l\u00e0 n\u00f3 ph\u1ea3i <strong>&#8220;hashable&#8221;<\/strong>, ngh\u0129a l\u00e0 h\u00e0m b\u0103m c\u00f3 th\u1ec3 x\u1eed l\u00fd n\u00f3 \u0111\u1ec3 t\u1ea1o ra m\u1ed9t ch\u1ec9 s\u1ed1. Th\u00f4ng th\u01b0\u1eddng, c\u00e1c kh\u00f3a c\u1ea7n ph\u1ea3i l\u00e0 b\u1ea5t bi\u1ebfn (immutable). V\u00ed d\u1ee5, trong Python, c\u00e1c ki\u1ec3u d\u1eef li\u1ec7u nh\u01b0 s\u1ed1 (integer, float), chu\u1ed7i (<a href=\"https:\/\/interdata.vn\/blog\/string-la-gi\/\">string<\/a>), v\u00e0 tuple c\u00f3 th\u1ec3 l\u00e0m kh\u00f3a, nh\u01b0ng danh s\u00e1ch (list) th\u00ec kh\u00f4ng v\u00ec n\u00f3 c\u00f3 th\u1ec3 thay \u0111\u1ed5i \u0111\u01b0\u1ee3c.<\/p>\n<p>V\u00ed d\u1ee5 v\u1ec1 kh\u00f3a c\u00f3 th\u1ec3 l\u00e0 m\u00e3 s\u1ed1 sinh vi\u00ean, s\u1ed1 ch\u1ee9ng minh nh\u00e2n d\u00e2n, t\u00ean \u0111\u0103ng nh\u1eadp ng\u01b0\u1eddi d\u00f9ng, m\u00e3 s\u1ea3n ph\u1ea9m (SKU), ho\u1eb7c b\u1ea5t k\u1ef3 \u0111\u1ecbnh danh duy nh\u1ea5t n\u00e0o kh\u00e1c ph\u00f9 h\u1ee3p v\u1edbi b\u00e0i to\u00e1n c\u1ee7a b\u1ea1n. Vi\u1ec7c ch\u1ecdn kh\u00f3a ph\u00f9 h\u1ee3p v\u00e0 \u0111\u1ea3m b\u1ea3o t\u00ednh duy nh\u1ea5t l\u00e0 r\u1ea5t quan tr\u1ecdng.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Gia-tri-Value\"><\/span>Gi\u00e1 tr\u1ecb (Value)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Gi\u00e1 tr\u1ecb (Value)<\/strong> l\u00e0 d\u1eef li\u1ec7u th\u1ef1c t\u1ebf m\u00e0 b\u1ea1n mu\u1ed1n l\u01b0u tr\u1eef v\u00e0 li\u00ean k\u1ebft v\u1edbi m\u1ed9t kh\u00f3a c\u1ee5 th\u1ec3. Gi\u00e1 tr\u1ecb c\u00f3 th\u1ec3 l\u00e0 b\u1ea5t c\u1ee9 th\u1ee9 g\u00ec: m\u1ed9t con s\u1ed1, m\u1ed9t chu\u1ed7i v\u0103n b\u1ea3n, m\u1ed9t \u0111\u1ed1i t\u01b0\u1ee3ng ph\u1ee9c t\u1ea1p (nh\u01b0 th\u00f4ng tin chi ti\u1ebft c\u1ee7a m\u1ed9t ng\u01b0\u1eddi d\u00f9ng bao g\u1ed3m t\u00ean, tu\u1ed5i, \u0111\u1ecba ch\u1ec9), ho\u1eb7c th\u1eadm ch\u00ed l\u00e0 m\u1ed9t c\u1ea5u tr\u00fac d\u1eef li\u1ec7u kh\u00e1c.<\/p>\n<p>S\u1ef1 linh ho\u1ea1t n\u00e0y l\u00e0m cho hash table tr\u1edf n\u00ean c\u1ef1c k\u1ef3 h\u1eefu d\u1ee5ng. B\u1ea1n c\u00f3 th\u1ec3 l\u01b0u tr\u1eef h\u1ed3 s\u01a1 nh\u00e2n vi\u00ean v\u1edbi kh\u00f3a l\u00e0 m\u00e3 nh\u00e2n vi\u00ean, th\u00f4ng tin s\u1ea3n ph\u1ea9m v\u1edbi kh\u00f3a l\u00e0 m\u00e3 s\u1ea3n ph\u1ea9m, ho\u1eb7c tr\u1ea1ng th\u00e1i c\u1ee7a m\u1ed9t phi\u00ean l\u00e0m vi\u1ec7c web v\u1edbi kh\u00f3a l\u00e0 ID phi\u00ean. Gi\u00e1 tr\u1ecb l\u00e0 n\u01a1i ch\u1ee9a \u0111\u1ef1ng &#8220;n\u1ed9i dung&#8221; m\u00e0 b\u1ea1n quan t\u00e2m.<\/p>\n<p>Khi b\u1ea1n <a href=\"https:\/\/interdata.vn\/blog\/query-la-gi\/\">truy v\u1ea5n<\/a> hash table b\u1eb1ng m\u1ed9t kh\u00f3a, m\u1ee5c ti\u00eau l\u00e0 l\u1ea5y l\u1ea1i \u0111\u01b0\u1ee3c gi\u00e1 tr\u1ecb t\u01b0\u01a1ng \u1ee9ng \u0111\u00e3 l\u01b0u tr\u1eef tr\u01b0\u1edbc \u0111\u00f3. M\u1ed1i li\u00ean k\u1ebft ch\u1eb7t ch\u1ebd gi\u1eefa kh\u00f3a v\u00e0 gi\u00e1 tr\u1ecb l\u00e0 n\u1ec1n t\u1ea3ng c\u01a1 b\u1ea3n c\u1ee7a c\u1ea5u tr\u00fac d\u1eef li\u1ec7u n\u00e0y.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Ham-bam-Hash-Function\"><\/span>H\u00e0m b\u0103m (Hash Function)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>H\u00e0m b\u0103m (Hash Function)<\/strong> c\u00f3 th\u1ec3 coi l\u00e0 &#8220;b\u1ed9 n\u00e3o&#8221; hay &#8220;ph\u00e9p thu\u1eadt&#8221; \u0111\u1eb1ng sau hash table. \u0110\u00e2y l\u00e0 m\u1ed9t thu\u1eadt to\u00e1n nh\u1eadn \u0111\u1ea7u v\u00e0o l\u00e0 <strong>Kh\u00f3a (Key)<\/strong> v\u00e0 t\u1ea1o ra m\u1ed9t <a href=\"https:\/\/interdata.vn\/blog\/so-nguyen-integer\/\">s\u1ed1 nguy\u00ean<\/a>, g\u1ecdi l\u00e0 <strong>m\u00e3 b\u0103m (hash code)<\/strong>. M\u00e3 b\u0103m n\u00e0y sau \u0111\u00f3 th\u01b0\u1eddng \u0111\u01b0\u1ee3c chuy\u1ec3n \u0111\u1ed5i th\u00e0nh m\u1ed9t <strong>ch\u1ec9 s\u1ed1 (index)<\/strong> h\u1ee3p l\u1ec7 trong m\u1ea3ng c\u00e1c bucket c\u1ee7a hash table.<\/p>\n<p>M\u1ee5c ti\u00eau c\u1ee7a h\u00e0m b\u0103m l\u00e0 ph\u00e2n ph\u1ed1i c\u00e1c kh\u00f3a m\u1ed9t c\u00e1ch <strong>\u0111\u1ed3ng \u0111\u1ec1u<\/strong> v\u00e0o c\u00e1c bucket kh\u00e1c nhau. M\u1ed9t h\u00e0m b\u0103m t\u1ed1t c\u1ea7n c\u00f3 c\u00e1c \u0111\u1eb7c t\u00ednh sau:<\/p>\n<ul>\n<li><strong>T\u00ednh x\u00e1c \u0111\u1ecbnh (Deterministic):<\/strong> C\u00f9ng m\u1ed9t kh\u00f3a lu\u00f4n t\u1ea1o ra c\u00f9ng m\u1ed9t m\u00e3 b\u0103m.<\/li>\n<li><strong>Ph\u00e2n b\u1ed1 \u0111\u1ec1u (Uniform Distribution):<\/strong> C\u00e1c kh\u00f3a kh\u00e1c nhau n\u00ean \u0111\u01b0\u1ee3c \u00e1nh x\u1ea1 v\u00e0o c\u00e1c bucket kh\u00e1c nhau c\u00e0ng nhi\u1ec1u c\u00e0ng t\u1ed1t \u0111\u1ec3 gi\u1ea3m thi\u1ec3u xung \u0111\u1ed9t.<\/li>\n<li><strong>Nhanh ch\u00f3ng (Fast Computation):<\/strong> T\u00ednh to\u00e1n m\u00e3 b\u0103m ph\u1ea3i nhanh, v\u00ec n\u00f3 \u0111\u01b0\u1ee3c th\u1ef1c hi\u1ec7n m\u1ed7i khi c\u00f3 thao t\u00e1c tr\u00ean hash table.<\/li>\n<li><strong>Hi\u1ec7u \u1ee9ng th\u00e1c \u0111\u1ed5 (Avalanche Effect):<\/strong> M\u1ed9t thay \u0111\u1ed5i nh\u1ecf trong kh\u00f3a n\u00ean t\u1ea1o ra s\u1ef1 thay \u0111\u1ed5i l\u1edbn trong m\u00e3 b\u0103m, gi\u00fap ph\u00e2n t\u00e1n c\u00e1c kh\u00f3a t\u01b0\u01a1ng t\u1ef1 nhau.<\/li>\n<\/ul>\n<p>V\u00ed d\u1ee5 \u0111\u01a1n gi\u1ea3n v\u1ec1 h\u00e0m b\u0103m cho s\u1ed1 nguy\u00ean l\u00e0 s\u1eed d\u1ee5ng ph\u00e9p to\u00e1n modulo (<code>%<\/code>). N\u1ebfu b\u1ea3ng b\u0103m c\u00f3 <code>m<\/code> buckets, ch\u1ec9 s\u1ed1 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng <code>index = key % m<\/code>. \u0110\u1ed1i v\u1edbi chu\u1ed7i, c\u00e1c thu\u1eadt to\u00e1n ph\u1ee9c t\u1ea1p h\u01a1n nh\u01b0 b\u0103m \u0111a th\u1ee9c (polynomial hashing) th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng.<\/p>\n<p>Ch\u1ea5t l\u01b0\u1ee3ng c\u1ee7a h\u00e0m b\u0103m \u1ea3nh h\u01b0\u1edfng tr\u1ef1c ti\u1ebfp \u0111\u1ebfn hi\u1ec7u su\u1ea5t c\u1ee7a hash table. M\u1ed9t h\u00e0m b\u0103m t\u1ed3i c\u00f3 th\u1ec3 d\u1eabn \u0111\u1ebfn nhi\u1ec1u xung \u0111\u1ed9t, l\u00e0m gi\u1ea3m t\u1ed1c \u0111\u1ed9 truy xu\u1ea5t.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Bucket-Ngan-chua-Slot\"><\/span>Bucket (Ng\u0103n ch\u1ee9a \/ Slot)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Bucket (Ng\u0103n ch\u1ee9a)<\/strong> hay <strong>Slot<\/strong> l\u00e0 c\u00e1c v\u1ecb tr\u00ed th\u1ef1c t\u1ebf trong b\u1ed9 nh\u1edb n\u01a1i d\u1eef li\u1ec7u (ho\u1eb7c tham chi\u1ebfu \u0111\u1ebfn d\u1eef li\u1ec7u) \u0111\u01b0\u1ee3c l\u01b0u tr\u1eef. Th\u00f4ng th\u01b0\u1eddng, c\u1ea5u tr\u00fac n\u1ec1n t\u1ea3ng c\u1ee7a hash table l\u00e0 m\u1ed9t <strong>m\u1ea3ng (array)<\/strong>, v\u00e0 m\u1ed7i ph\u1ea7n t\u1eed c\u1ee7a m\u1ea3ng n\u00e0y ch\u00ednh l\u00e0 m\u1ed9t bucket.<\/p>\n<p>S\u1ed1 l\u01b0\u1ee3ng bucket trong b\u1ea3ng b\u0103m th\u01b0\u1eddng \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh tr\u01b0\u1edbc khi t\u1ea1o b\u1ea3ng. H\u00e0m b\u0103m s\u1ebd \u00e1nh x\u1ea1 m\u1ed7i kh\u00f3a v\u00e0o ch\u1ec9 s\u1ed1 c\u1ee7a m\u1ed9t trong c\u00e1c bucket n\u00e0y. V\u00ed d\u1ee5, n\u1ebfu h\u00e0m b\u0103m tr\u1ea3 v\u1ec1 ch\u1ec9 s\u1ed1 5 cho m\u1ed9t kh\u00f3a, c\u1eb7p key-value t\u01b0\u01a1ng \u1ee9ng s\u1ebd \u0111\u01b0\u1ee3c l\u01b0u tr\u1eef t\u1ea1i bucket th\u1ee9 5 c\u1ee7a m\u1ea3ng.<\/p>\n<p>Trong tr\u01b0\u1eddng h\u1ee3p x\u1ea3y ra <strong>xung \u0111\u1ed9t<\/strong> (nhi\u1ec1u kh\u00f3a c\u00f9ng \u0111\u01b0\u1ee3c b\u0103m v\u00e0o m\u1ed9t bucket), c\u00e1ch t\u1ed5 ch\u1ee9c b\u00ean trong bucket s\u1ebd ph\u1ee5 thu\u1ed9c v\u00e0o k\u1ef9 thu\u1eadt x\u1eed l\u00fd xung \u0111\u1ed9t \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng. V\u00ed d\u1ee5, v\u1edbi Separate Chaining, m\u1ed7i bucket c\u00f3 th\u1ec3 l\u00e0 m\u1ed9t danh s\u00e1ch li\u00ean k\u1ebft (linked list) ch\u1ee9a t\u1ea5t c\u1ea3 c\u00e1c c\u1eb7p key-value b\u1ecb tr\u00f9ng ch\u1ec9 s\u1ed1.<\/p>\n<p>Vi\u1ec7c qu\u1ea3n l\u00fd s\u1ed1 l\u01b0\u1ee3ng v\u00e0 c\u1ea5u tr\u00fac c\u1ee7a c\u00e1c bucket l\u00e0 r\u1ea5t quan tr\u1ecdng \u0111\u1ec3 c\u00e2n b\u1eb1ng gi\u1eefa vi\u1ec7c s\u1eed d\u1ee5ng b\u1ed9 nh\u1edb v\u00e0 hi\u1ec7u su\u1ea5t truy xu\u1ea5t.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Hash-Table-hoat-dong-nhu-the-nao\"><\/span>Hash Table ho\u1ea1t \u0111\u1ed9ng nh\u01b0 th\u1ebf n\u00e0o?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Hi\u1ec3u \u0111\u01b0\u1ee3c c\u00e1c th\u00e0nh ph\u1ea7n r\u1ed3i, gi\u1edd ch\u00fang ta h\u00e3y xem c\u00e1ch ch\u00fang ph\u1ed1i h\u1ee3p v\u1edbi nhau qua c\u00e1c thao t\u00e1c c\u01a1 b\u1ea3n: Th\u00eam, T\u00ecm ki\u1ebfm v\u00e0 X\u00f3a d\u1eef li\u1ec7u.<\/p>\n<p>Gi\u1ea3 s\u1eed ch\u00fang ta c\u00f3 m\u1ed9t hash table \u0111\u01a1n gi\u1ea3n v\u1edbi 10 buckets (ch\u1ec9 s\u1ed1 t\u1eeb 0 \u0111\u1ebfn 9) v\u00e0 mu\u1ed1n l\u01b0u danh b\u1ea1 \u0111i\u1ec7n tho\u1ea1i (T\u00ean l\u00e0 Key, S\u1ed1 \u0111i\u1ec7n tho\u1ea1i l\u00e0 Value). H\u00e0m b\u0103m c\u1ee7a ch\u00fang ta l\u00e0 l\u1ea5y m\u00e3 ASCII c\u1ee7a ch\u1eef c\u00e1i \u0111\u1ea7u ti\u00ean trong t\u00ean v\u00e0 l\u1ea5y ph\u1ea7n d\u01b0 khi chia cho 10 (<code>index = ascii(T\u00ean[0]) % 10<\/code>).<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Thao-tac-Them-Insert-Put\"><\/span>Thao t\u00e1c Th\u00eam (Insert \/ Put)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0110\u1ec3 th\u00eam m\u1ed9t c\u1eb7p <code>(\"An\", \"090123456\")<\/code>:<\/p>\n<ol>\n<li><strong>B\u0103m Kh\u00f3a:<\/strong> L\u1ea5y kh\u00f3a l\u00e0 &#8220;An&#8221;. Ch\u1eef c\u00e1i \u0111\u1ea7u l\u00e0 &#8216;A&#8217;. Gi\u1ea3 s\u1eed m\u00e3 ASCII c\u1ee7a &#8216;A&#8217; l\u00e0 65.<\/li>\n<li><strong>T\u00ednh Ch\u1ec9 s\u1ed1:<\/strong> \u00c1p d\u1ee5ng h\u00e0m b\u0103m: <code>index = 65 % 10 = 5<\/code>.<\/li>\n<li><strong>L\u01b0u tr\u1eef:<\/strong> \u0110\u1eb7t c\u1eb7p <code>(\"An\", \"090123456\")<\/code> v\u00e0o bucket c\u00f3 ch\u1ec9 s\u1ed1 5.<\/li>\n<\/ol>\n<p>N\u1ebfu sau \u0111\u00f3 th\u00eam <code>(\"Anh\", \"098765432\")<\/code>:<\/p>\n<ol>\n<li><strong>B\u0103m Kh\u00f3a:<\/strong> L\u1ea5y kh\u00f3a l\u00e0 &#8220;Anh&#8221;. Ch\u1eef c\u00e1i \u0111\u1ea7u l\u00e0 &#8216;A&#8217;. M\u00e3 ASCII l\u00e0 65.<\/li>\n<li><strong>T\u00ednh Ch\u1ec9 s\u1ed1:<\/strong> <code>index = 65 % 10 = 5<\/code>.<\/li>\n<li><strong>X\u1eed l\u00fd Xung \u0111\u1ed9t:<\/strong> Bucket 5 \u0111\u00e3 c\u00f3 &#8220;An&#8221;. L\u00fac n\u00e0y, k\u1ef9 thu\u1eadt x\u1eed l\u00fd xung \u0111\u1ed9t s\u1ebd ph\u00e1t huy t\u00e1c d\u1ee5ng (ch\u00fang ta s\u1ebd t\u00ecm hi\u1ec3u k\u1ef9 h\u01a1n \u1edf ph\u1ea7n sau). V\u00ed d\u1ee5, n\u1ebfu d\u00f9ng Separate Chaining, &#8220;Anh&#8221; s\u1ebd \u0111\u01b0\u1ee3c th\u00eam v\u00e0o danh s\u00e1ch li\u00ean k\u1ebft t\u1ea1i bucket 5.<\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"Thao-tac-Tim-kiem-Search-Get\"><\/span>Thao t\u00e1c T\u00ecm ki\u1ebfm (Search \/ Get)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0110\u1ec3 t\u00ecm s\u1ed1 \u0111i\u1ec7n tho\u1ea1i c\u1ee7a &#8220;An&#8221;:<\/p>\n<ol>\n<li><strong>B\u0103m Kh\u00f3a:<\/strong> L\u1ea5y kh\u00f3a l\u00e0 &#8220;An&#8221;. Ch\u1eef c\u00e1i \u0111\u1ea7u &#8216;A&#8217;, m\u00e3 ASCII 65.<\/li>\n<li><strong>T\u00ednh Ch\u1ec9 s\u1ed1:<\/strong> <code>index = 65 % 10 = 5<\/code>.<\/li>\n<li><strong>Truy c\u1eadp Bucket:<\/strong> \u0110\u1ebfn bucket c\u00f3 ch\u1ec9 s\u1ed1 5.<\/li>\n<li><strong>T\u00ecm ch\u00ednh x\u00e1c Key:<\/strong> Ki\u1ec3m tra c\u00e1c ph\u1ea7n t\u1eed trong bucket 5. N\u1ebfu d\u00f9ng Separate Chaining, duy\u1ec7t qua danh s\u00e1ch t\u1ea1i bucket 5. Khi t\u00ecm th\u1ea5y ph\u1ea7n t\u1eed c\u00f3 <a href=\"https:\/\/interdata.vn\/blog\/khoa-chinh-la-gi\/\">kh\u00f3a ch\u00ednh<\/a> x\u00e1c l\u00e0 &#8220;An&#8221;, tr\u1ea3 v\u1ec1 gi\u00e1 tr\u1ecb t\u01b0\u01a1ng \u1ee9ng l\u00e0 &#8220;090123456&#8221;. N\u1ebfu kh\u00f4ng t\u00ecm th\u1ea5y kh\u00f3a, tr\u1ea3 v\u1ec1 null ho\u1eb7c b\u00e1o l\u1ed7i.<\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"Thao-tac-Xoa-Delete-Remove\"><\/span>Thao t\u00e1c X\u00f3a (Delete \/ Remove)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0110\u1ec3 x\u00f3a th\u00f4ng tin c\u1ee7a &#8220;An&#8221;:<\/p>\n<ol>\n<li><strong>B\u0103m Kh\u00f3a:<\/strong> L\u1ea5y kh\u00f3a l\u00e0 &#8220;An&#8221;. Ch\u1eef c\u00e1i \u0111\u1ea7u &#8216;A&#8217;, m\u00e3 ASCII 65.<\/li>\n<li><strong>T\u00ednh Ch\u1ec9 s\u1ed1:<\/strong> <code>index = 65 % 10 = 5<\/code>.<\/li>\n<li><strong>Truy c\u1eadp Bucket:<\/strong> \u0110\u1ebfn bucket c\u00f3 ch\u1ec9 s\u1ed1 5.<\/li>\n<li><strong>T\u00ecm v\u00e0 X\u00f3a:<\/strong> T\u00ecm ph\u1ea7n t\u1eed c\u00f3 kh\u00f3a ch\u00ednh x\u00e1c l\u00e0 &#8220;An&#8221; trong bucket 5 (v\u00ed d\u1ee5, trong danh s\u00e1ch li\u00ean k\u1ebft n\u1ebfu d\u00f9ng Separate Chaining). Khi t\u00ecm th\u1ea5y, x\u00f3a ph\u1ea7n t\u1eed \u0111\u00f3 kh\u1ecfi bucket.<\/li>\n<\/ol>\n<p>Nh\u01b0 b\u1ea1n th\u1ea5y, m\u1ea5u ch\u1ed1t c\u1ee7a t\u1ed1c \u0111\u1ed9 l\u00e0 h\u00e0m b\u0103m nhanh ch\u00f3ng ch\u1ec9 ra \u0111\u00fang bucket c\u1ea7n thao t\u00e1c, gi\u00fap thu h\u1eb9p \u0111\u00e1ng k\u1ec3 ph\u1ea1m vi t\u00ecm ki\u1ebfm so v\u1edbi vi\u1ec7c duy\u1ec7t to\u00e0n b\u1ed9 d\u1eef li\u1ec7u.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Van-de-nan-giai-Xung-dot-trong-Hash-Table-Hash-Collision\"><\/span>V\u1ea5n \u0111\u1ec1 nan gi\u1ea3i: Xung \u0111\u1ed9t trong Hash Table (Hash Collision)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>D\u00f9 h\u00e0m b\u0103m c\u00f3 t\u1ed1t \u0111\u1ebfn \u0111\u00e2u, vi\u1ec7c hai ho\u1eb7c nhi\u1ec1u kh\u00f3a kh\u00e1c nhau sau khi b\u0103m l\u1ea1i cho ra c\u00f9ng m\u1ed9t ch\u1ec9 s\u1ed1 (index) l\u00e0 \u0111i\u1ec1u kh\u00f3 tr\u00e1nh kh\u1ecfi, \u0111\u1eb7c bi\u1ec7t khi s\u1ed1 l\u01b0\u1ee3ng kh\u00f3a l\u1edbn h\u01a1n s\u1ed1 l\u01b0\u1ee3ng bucket. Hi\u1ec7n t\u01b0\u1ee3ng n\u00e0y \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 <strong>xung \u0111\u1ed9t hash (hash collision)<\/strong>.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/interdata.vn\/blog\/wp-content\/uploads\/2025\/04\/Hash-table-02.jpg\" alt=\"Hash table 02\" width=\"750\" height=\"422\" class=\"aligncenter size-full wp-image-27429\" title=\"\" srcset=\"https:\/\/interdata.vn\/blog\/wp-content\/uploads\/2025\/04\/Hash-table-02.jpg 750w, https:\/\/interdata.vn\/blog\/wp-content\/uploads\/2025\/04\/Hash-table-02-300x169.jpg 300w\" sizes=\"auto, (max-width: 750px) 100vw, 750px\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Xung-dot-Hash-Hash-Collision-la-gi\"><\/span>Xung \u0111\u1ed9t Hash (Hash Collision) l\u00e0 g\u00ec?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Xung \u0111\u1ed9t hash (Hash Collision)<\/strong> x\u1ea3y ra khi h\u00e0m b\u0103m t\u1ea1o ra c\u00f9ng m\u1ed9t ch\u1ec9 s\u1ed1 cho hai ho\u1eb7c nhi\u1ec1u kh\u00f3a kh\u00e1c nhau. V\u00ed d\u1ee5, v\u1edbi h\u00e0m b\u0103m <code>index = ascii(T\u00ean[0]) % 10<\/code>, c\u1ea3 &#8220;An&#8221; v\u00e0 &#8220;Anh&#8221; \u0111\u1ec1u \u0111\u01b0\u1ee3c b\u0103m v\u00e0o ch\u1ec9 s\u1ed1 5, g\u00e2y ra xung \u0111\u1ed9t.<\/p>\n<p>Nguy\u00ean nh\u00e2n g\u1ed1c r\u1ec5 l\u00e0 do <strong>Nguy\u00ean l\u00fd chu\u1ed3ng b\u1ed3 c\u00e2u (Pigeonhole Principle)<\/strong>: n\u1ebfu b\u1ea1n c\u00f3 nhi\u1ec1u b\u1ed3 c\u00e2u (keys) h\u01a1n s\u1ed1 chu\u1ed3ng (buckets), th\u00ec \u00edt nh\u1ea5t m\u1ed9t chu\u1ed3ng ph\u1ea3i ch\u1ee9a nhi\u1ec1u h\u01a1n m\u1ed9t con b\u1ed3 c\u00e2u. Hash collision l\u00e0 kh\u00f4ng th\u1ec3 tr\u00e1nh kh\u1ecfi ho\u00e0n to\u00e0n trong th\u1ef1c t\u1ebf.<\/p>\n<p>Xung \u0111\u1ed9t l\u00e0m gi\u1ea3m hi\u1ec7u su\u1ea5t c\u1ee7a hash table. N\u1ebfu kh\u00f4ng \u0111\u01b0\u1ee3c x\u1eed l\u00fd \u0111\u00fang c\u00e1ch, thay v\u00ec truy c\u1eadp tr\u1ef1c ti\u1ebfp O(1), b\u1ea1n c\u00f3 th\u1ec3 ph\u1ea3i duy\u1ec7t qua nhi\u1ec1u ph\u1ea7n t\u1eed t\u1ea1i c\u00f9ng m\u1ed9t bucket, l\u00e0m t\u0103ng th\u1eddi gian t\u00ecm ki\u1ebfm, th\u1eadm ch\u00ed ti\u1ebfn t\u1edbi O(n) trong tr\u01b0\u1eddng h\u1ee3p x\u1ea5u nh\u1ea5t (t\u1ea5t c\u1ea3 kh\u00f3a b\u0103m v\u00e0o c\u00f9ng m\u1ed9t ch\u1ed7).<\/p>\n<p>Do \u0111\u00f3, vi\u1ec7c hi\u1ec3u v\u00e0 l\u1ef1a ch\u1ecdn <strong>k\u1ef9 thu\u1eadt x\u1eed l\u00fd xung \u0111\u1ed9t (collision resolution techniques)<\/strong> ph\u00f9 h\u1ee3p l\u00e0 c\u1ef1c k\u1ef3 quan tr\u1ecdng \u0111\u1ec3 duy tr\u00ec hi\u1ec7u su\u1ea5t cao c\u1ee7a hash table.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Cac-ky-thuat-xu-ly-xung-dot-Collision-Resolution-Techniques-pho-bien\"><\/span>C\u00e1c k\u1ef9 thu\u1eadt x\u1eed l\u00fd xung \u0111\u1ed9t (Collision Resolution Techniques) ph\u1ed5 bi\u1ebfn<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>C\u00f3 hai nh\u00f3m ph\u01b0\u01a1ng ph\u00e1p ch\u00ednh \u0111\u1ec3 gi\u1ea3i quy\u1ebft xung \u0111\u1ed9t trong hash table: <strong>K\u1ebft n\u1ed1i ri\u00eang (Separate Chaining)<\/strong> v\u00e0 <strong>\u0110\u1ecba ch\u1ec9 m\u1edf (Open Addressing)<\/strong>.<\/p>\n<h4>K\u1ebft n\u1ed1i ri\u00eang (Separate Chaining)<\/h4>\n<p>\u0110\u00e2y l\u00e0 ph\u01b0\u01a1ng ph\u00e1p ph\u1ed5 bi\u1ebfn v\u00e0 t\u01b0\u01a1ng \u0111\u1ed1i d\u1ec5 hi\u1ec3u. \u00dd t\u01b0\u1edfng l\u00e0 m\u1ed7i bucket trong b\u1ea3ng b\u0103m kh\u00f4ng ch\u1ec9 l\u01b0u m\u1ed9t gi\u00e1 tr\u1ecb duy nh\u1ea5t, m\u00e0 s\u1ebd tr\u1ecf \u0111\u1ebfn m\u1ed9t <strong>c\u1ea5u tr\u00fac d\u1eef li\u1ec7u ph\u1ee5<\/strong> (th\u01b0\u1eddng l\u00e0 danh s\u00e1ch li\u00ean k\u1ebft &#8211; linked list) ch\u1ee9a t\u1ea5t c\u1ea3 c\u00e1c c\u1eb7p key-value \u0111\u01b0\u1ee3c b\u0103m v\u00e0o c\u00f9ng bucket \u0111\u00f3.<\/p>\n<p>Khi th\u00eam m\u1ed9t ph\u1ea7n t\u1eed v\u00e0 x\u1ea3y ra xung \u0111\u1ed9t t\u1ea1i bucket <code>i<\/code>, ph\u1ea7n t\u1eed m\u1edbi ch\u1ec9 \u0111\u01a1n gi\u1ea3n \u0111\u01b0\u1ee3c th\u00eam v\u00e0o cu\u1ed1i (ho\u1eb7c \u0111\u1ea7u) danh s\u00e1ch li\u00ean k\u1ebft t\u1ea1i bucket <code>i<\/code>. Khi t\u00ecm ki\u1ebfm, ta b\u0103m kh\u00f3a ra index <code>i<\/code>, sau \u0111\u00f3 duy\u1ec7t qua danh s\u00e1ch li\u00ean k\u1ebft t\u1ea1i bucket <code>i<\/code> \u0111\u1ec3 t\u00ecm \u0111\u00fang kh\u00f3a c\u1ea7n t\u00ecm.<\/p>\n<ul>\n<li><strong>\u01afu \u0111i\u1ec3m:<\/strong> \u0110\u01a1n gi\u1ea3n \u0111\u1ec3 tri\u1ec3n khai. Hi\u1ec7u su\u1ea5t kh\u00f4ng gi\u1ea3m qu\u00e1 nhanh khi b\u1ea3ng b\u0103m \u0111\u1ea7y (load factor c\u00f3 th\u1ec3 l\u1edbn h\u01a1n 1). Thao t\u00e1c x\u00f3a \u0111\u01a1n gi\u1ea3n.<\/li>\n<li><strong>Nh\u01b0\u1ee3c \u0111i\u1ec3m:<\/strong> T\u1ed1n th\u00eam b\u1ed9 nh\u1edb cho c\u00e1c con tr\u1ecf c\u1ee7a danh s\u00e1ch li\u00ean k\u1ebft. C\u00f3 th\u1ec3 l\u00e0m gi\u1ea3m hi\u1ec7u qu\u1ea3 c\u1ee7a b\u1ed9 nh\u1edb \u0111\u1ec7m (cache) do c\u00e1c n\u00fat trong danh s\u00e1ch li\u00ean k\u1ebft c\u00f3 th\u1ec3 n\u1eb1m r\u1ea3i r\u00e1c trong b\u1ed9 nh\u1edb. Trong tr\u01b0\u1eddng h\u1ee3p x\u1ea5u nh\u1ea5t (t\u1ea5t c\u1ea3 kh\u00f3a v\u00e0o c\u00f9ng m\u1ed9t bucket), hi\u1ec7u su\u1ea5t tr\u1edf th\u00e0nh O(n).<\/li>\n<\/ul>\n<h4>\u0110\u1ecba ch\u1ec9 m\u1edf (Open Addressing)<\/h4>\n<p>Kh\u00e1c v\u1edbi Separate Chaining, trong Open Addressing, t\u1ea5t c\u1ea3 c\u00e1c c\u1eb7p key-value \u0111\u1ec1u \u0111\u01b0\u1ee3c l\u01b0u tr\u1eef <strong>ngay trong ch\u00ednh m\u1ea3ng c\u00e1c bucket<\/strong>. Khi x\u1ea3y ra xung \u0111\u1ed9t t\u1ea1i bucket <code>i<\/code>, thay v\u00ec d\u00f9ng c\u1ea5u tr\u00fac d\u1eef li\u1ec7u ph\u1ee5, thu\u1eadt to\u00e1n s\u1ebd <strong>d\u00f2 t\u00ecm (probe)<\/strong> m\u1ed9t bucket tr\u1ed1ng kh\u00e1c trong b\u1ea3ng \u0111\u1ec3 \u0111\u1eb7t ph\u1ea7n t\u1eed b\u1ecb xung \u0111\u1ed9t v\u00e0o \u0111\u00f3.<\/p>\n<p>Qu\u00e1 tr\u00ecnh d\u00f2 t\u00ecm n\u00e0y \u0111\u01b0\u1ee3c th\u1ef1c hi\u1ec7n theo m\u1ed9t quy t\u1eafc nh\u1ea5t \u0111\u1ecbnh. C\u00f3 ba k\u1ef9 thu\u1eadt d\u00f2 t\u00ecm ph\u1ed5 bi\u1ebfn:<\/p>\n<h5>D\u00f2 tuy\u1ebfn t\u00ednh (Linear Probing)<\/h5>\n<p>\u0110\u00e2y l\u00e0 k\u1ef9 thu\u1eadt \u0111\u01a1n gi\u1ea3n nh\u1ea5t c\u1ee7a Open Addressing. N\u1ebfu bucket <code>i<\/code> (k\u1ebft qu\u1ea3 t\u1eeb h\u00e0m b\u0103m) \u0111\u00e3 b\u1ecb chi\u1ebfm, thu\u1eadt to\u00e1n s\u1ebd ki\u1ec3m tra tu\u1ea7n t\u1ef1 c\u00e1c bucket k\u1ebf ti\u1ebfp: <code>i+1<\/code>, <code>i+2<\/code>, <code>i+3<\/code>,&#8230; (c\u00f3 th\u1ec3 v\u00f2ng l\u1ea1i t\u1eeb \u0111\u1ea7u b\u1ea3ng n\u1ebfu \u0111\u1ebfn cu\u1ed1i) cho \u0111\u1ebfn khi t\u00ecm th\u1ea5y m\u1ed9t bucket tr\u1ed1ng.<\/p>\n<ul>\n<li><strong>\u01afu \u0111i\u1ec3m:<\/strong> D\u1ec5 c\u00e0i \u0111\u1eb7t. Khai th\u00e1c t\u1ed1t t\u00ednh ch\u1ea5t c\u1ee7a b\u1ed9 nh\u1edb \u0111\u1ec7m (cache locality) v\u00ec c\u00e1c ph\u1ea7n t\u1eed d\u00f2 t\u00ecm th\u01b0\u1eddng n\u1eb1m g\u1ea7n nhau.<\/li>\n<li><strong>Nh\u01b0\u1ee3c \u0111i\u1ec3m:<\/strong> G\u00e2y ra hi\u1ec7n t\u01b0\u1ee3ng <strong>ph\u00e2n c\u1ee5m s\u01a1 c\u1ea5p (primary <a href=\"https:\/\/interdata.vn\/blog\/clustering-la-gi\/\">clustering<\/a>)<\/strong>. C\u00e1c nh\u00f3m bucket b\u1ecb chi\u1ebfm li\u00ean ti\u1ebfp c\u00f3 xu h\u01b0\u1edbng ng\u00e0y c\u00e0ng d\u00e0i ra, l\u00e0m t\u0103ng \u0111\u00e1ng k\u1ec3 th\u1eddi gian t\u00ecm ki\u1ebfm v\u00e0 th\u00eam m\u1edbi khi b\u1ea3ng \u0111\u1ea7y. Thao t\u00e1c x\u00f3a ph\u1ee9c t\u1ea1p h\u01a1n (c\u1ea7n \u0111\u00e1nh d\u1ea5u v\u1ecb tr\u00ed \u0111\u00e3 x\u00f3a thay v\u00ec x\u00f3a h\u1eb3n \u0111\u1ec3 kh\u00f4ng l\u00e0m gi\u00e1n \u0111o\u1ea1n chu\u1ed7i d\u00f2 t\u00ecm).<\/li>\n<\/ul>\n<h5>D\u00f2 b\u1eadc hai (Quadratic Probing)<\/h5>\n<p>\u0110\u1ec3 gi\u1ea3m b\u1edbt v\u1ea5n \u0111\u1ec1 primary clustering, Quadratic Probing s\u1eed d\u1ee5ng m\u1ed9t b\u01b0\u1edbc nh\u1ea3y b\u1eadc hai \u0111\u1ec3 d\u00f2 t\u00ecm. N\u1ebfu bucket <code>i<\/code> b\u1ecb chi\u1ebfm, n\u00f3 s\u1ebd ki\u1ec3m tra c\u00e1c v\u1ecb tr\u00ed <code>i + 1^2<\/code>, <code>i + 2^2<\/code>, <code>i + 3^2<\/code>,&#8230; (modulo k\u00edch th\u01b0\u1edbc b\u1ea3ng). B\u01b0\u1edbc nh\u1ea3y t\u0103ng d\u1ea7n gi\u00fap &#8220;nh\u1ea3y&#8221; qua c\u00e1c c\u1ee5m ph\u1ea7n t\u1eed \u0111\u00e3 b\u1ecb chi\u1ebfm.<\/p>\n<ul>\n<li><strong>\u01afu \u0111i\u1ec3m:<\/strong> Gi\u1ea3m thi\u1ec3u primary clustering hi\u1ec7u qu\u1ea3 h\u01a1n Linear Probing.<\/li>\n<li><strong>Nh\u01b0\u1ee3c \u0111i\u1ec3m:<\/strong> C\u00f3 th\u1ec3 g\u00e2y ra <strong>ph\u00e2n c\u1ee5m th\u1ee9 c\u1ea5p (secondary clustering)<\/strong> &#8211; c\u00e1c kh\u00f3a b\u0103m v\u00e0o c\u00f9ng m\u1ed9t v\u1ecb tr\u00ed ban \u0111\u1ea7u s\u1ebd \u0111i theo c\u00f9ng m\u1ed9t chu\u1ed7i d\u00f2 t\u00ecm. C\u00f3 th\u1ec3 kh\u00f4ng t\u00ecm \u0111\u01b0\u1ee3c ch\u1ed7 tr\u1ed1ng ngay c\u1ea3 khi b\u1ea3ng ch\u01b0a \u0111\u1ea7y n\u1ebfu k\u00edch th\u01b0\u1edbc b\u1ea3ng kh\u00f4ng \u0111\u01b0\u1ee3c ch\u1ecdn c\u1ea9n th\u1eadn (v\u00ed d\u1ee5, kh\u00f4ng ph\u1ea3i s\u1ed1 nguy\u00ean t\u1ed1). Thao t\u00e1c x\u00f3a v\u1eabn ph\u1ee9c t\u1ea1p.<\/li>\n<\/ul>\n<h5>B\u0103m k\u00e9p (Double Hashing)<\/h5>\n<p>K\u1ef9 thu\u1eadt n\u00e0y \u0111\u01b0\u1ee3c xem l\u00e0 m\u1ed9t trong nh\u1eefng ph\u01b0\u01a1ng ph\u00e1p hi\u1ec7u qu\u1ea3 nh\u1ea5t c\u1ee7a Open Addressing. N\u00f3 s\u1eed d\u1ee5ng <strong>hai h\u00e0m b\u0103m<\/strong>: h\u00e0m th\u1ee9 nh\u1ea5t <code>h1(key)<\/code> \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh v\u1ecb tr\u00ed ban \u0111\u1ea7u, v\u00e0 h\u00e0m th\u1ee9 hai <code>h2(key)<\/code> \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh <strong>b\u01b0\u1edbc nh\u1ea3y<\/strong> khi d\u00f2 t\u00ecm. Chu\u1ed7i d\u00f2 t\u00ecm s\u1ebd l\u00e0 <code>(h1(key) + j * h2(key)) % m<\/code>, v\u1edbi <code>j = 0, 1, 2,...<\/code>.<\/p>\n<p>V\u00ec b\u01b0\u1edbc nh\u1ea3y ph\u1ee5 thu\u1ed9c v\u00e0o ch\u00ednh kh\u00f3a (th\u00f4ng qua <code>h2<\/code>), c\u00e1c kh\u00f3a kh\u00e1c nhau b\u0103m v\u00e0o c\u00f9ng v\u1ecb tr\u00ed ban \u0111\u1ea7u c\u00f3 kh\u1ea3 n\u0103ng cao s\u1ebd c\u00f3 chu\u1ed7i d\u00f2 t\u00ecm kh\u00e1c nhau, gi\u00fap gi\u1ea3m thi\u1ec3u c\u1ea3 primary v\u00e0 secondary clustering.<\/p>\n<ul>\n<li><strong>\u01afu \u0111i\u1ec3m:<\/strong> Ph\u00e2n b\u1ed1 c\u00e1c ph\u1ea7n t\u1eed \u0111\u1ec1u h\u01a1n, gi\u1ea3m clustering hi\u1ec7u qu\u1ea3.<\/li>\n<li><strong>Nh\u01b0\u1ee3c \u0111i\u1ec3m:<\/strong> Y\u00eau c\u1ea7u th\u00eam m\u1ed9t h\u00e0m b\u0103m t\u1ed1t th\u1ee9 hai (v\u00e0 <code>h2(key)<\/code> kh\u00f4ng bao gi\u1edd \u0111\u01b0\u1ee3c tr\u1ea3 v\u1ec1 0). T\u00ednh to\u00e1n t\u1ed1n k\u00e9m h\u01a1n m\u1ed9t ch\u00fat do ph\u1ea3i g\u1ecdi hai h\u00e0m b\u0103m. Thao t\u00e1c x\u00f3a v\u1eabn ph\u1ee9c t\u1ea1p.<\/li>\n<\/ul>\n<p>Vi\u1ec7c l\u1ef1a ch\u1ecdn k\u1ef9 thu\u1eadt x\u1eed l\u00fd xung \u0111\u1ed9t ph\u1ee5 thu\u1ed9c v\u00e0o nhi\u1ec1u y\u1ebfu t\u1ed1 nh\u01b0 y\u00eau c\u1ea7u v\u1ec1 b\u1ed9 nh\u1edb, t\u1ea7n su\u1ea5t thao t\u00e1c th\u00eam\/x\u00f3a, v\u00e0 m\u1ee9c \u0111\u1ed9 ch\u1ea5p nh\u1eadn v\u1ec1 hi\u1ec7u su\u1ea5t trong tr\u01b0\u1eddng h\u1ee3p x\u1ea5u.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Phan-tich-hieu-nang-Do-phuc-tap-thoi-gian-Time-Complexity\"><\/span>Ph\u00e2n t\u00edch hi\u1ec7u n\u0103ng: \u0110\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian (Time Complexity)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Hi\u1ec7u n\u0103ng l\u00e0 l\u00fd do ch\u00ednh khi\u1ebfn hash table \u0111\u01b0\u1ee3c \u01b0a chu\u1ed9ng. Ch\u00fang ta th\u01b0\u1eddng \u0111\u00e1nh gi\u00e1 hi\u1ec7u n\u0103ng qua <strong>\u0110\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian (Time Complexity)<\/strong>, s\u1eed d\u1ee5ng k\u00fd hi\u1ec7u <strong>Big O Notation<\/strong> \u0111\u1ec3 m\u00f4 t\u1ea3 m\u1ed1i quan h\u1ec7 gi\u1eefa th\u1eddi gian th\u1ef1c thi v\u00e0 k\u00edch th\u01b0\u1edbc d\u1eef li\u1ec7u \u0111\u1ea7u v\u00e0o (s\u1ed1 l\u01b0\u1ee3ng ph\u1ea7n t\u1eed <code>n<\/code>).<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Truong-hop-trung-binh\"><\/span>Tr\u01b0\u1eddng h\u1ee3p trung b\u00ecnh<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Trong \u0111i\u1ec1u ki\u1ec7n l\u00fd t\u01b0\u1edfng \u2013 h\u00e0m b\u0103m ph\u00e2n b\u1ed1 \u0111\u1ec1u v\u00e0 k\u1ef9 thu\u1eadt x\u1eed l\u00fd xung \u0111\u1ed9t hi\u1ec7u qu\u1ea3 \u2013 th\u1eddi gian trung b\u00ecnh cho c\u00e1c thao t\u00e1c <strong>Th\u00eam (Insert)<\/strong>, <strong>T\u00ecm ki\u1ebfm (Search)<\/strong>, v\u00e0 <strong>X\u00f3a (Delete)<\/strong> trong hash table l\u00e0 <strong>O(1)<\/strong>.<\/p>\n<p>\u0110i\u1ec1u n\u00e0y c\u00f3 ngh\u0129a l\u00e0, trung b\u00ecnh, th\u1eddi gian th\u1ef1c hi\u1ec7n c\u00e1c thao t\u00e1c n\u00e0y kh\u00f4ng ph\u1ee5 thu\u1ed9c v\u00e0o s\u1ed1 l\u01b0\u1ee3ng ph\u1ea7n t\u1eed <code>n<\/code> \u0111ang c\u00f3 trong b\u1ea3ng. D\u00f9 b\u1ea3ng c\u00f3 100 hay 1 tri\u1ec7u ph\u1ea7n t\u1eed, b\u1ea1n v\u1eabn c\u00f3 th\u1ec3 t\u00ecm th\u1ea5y th\u1ee9 m\u00ecnh c\u1ea7n trong m\u1ed9t kho\u1ea3ng th\u1eddi gian g\u1ea7n nh\u01b0 kh\u00f4ng \u0111\u1ed5i. \u0110\u00e2y ch\u00ednh l\u00e0 s\u1ee9c m\u1ea1nh c\u1ed1t l\u00f5i c\u1ee7a hash table.<\/p>\n<p>\u0110\u1ec3 \u0111\u1ea1t \u0111\u01b0\u1ee3c O(1) trung b\u00ecnh, \u0111i\u1ec1u quan tr\u1ecdng l\u00e0 gi\u1eef cho <strong>H\u1ec7 s\u1ed1 t\u1ea3i (Load Factor)<\/strong> \u1edf m\u1ee9c h\u1ee3p l\u00fd (s\u1ebd n\u00f3i r\u00f5 h\u01a1n \u1edf ph\u1ea7n sau) v\u00e0 ch\u1ecdn h\u00e0m b\u0103m t\u1ed1t.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Truong-hop-xau-nhat\"><\/span>Tr\u01b0\u1eddng h\u1ee3p x\u1ea5u nh\u1ea5t<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Tuy nhi\u00ean, hash table kh\u00f4ng ph\u1ea3i l\u00fac n\u00e0o c\u0169ng ho\u00e0n h\u1ea3o. Trong tr\u01b0\u1eddng h\u1ee3p x\u1ea5u nh\u1ea5t, \u0111\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian cho c\u00e1c thao t\u00e1c Th\u00eam, T\u00ecm ki\u1ebfm v\u00e0 X\u00f3a c\u00f3 th\u1ec3 l\u00ean t\u1edbi <strong>O(n)<\/strong>.<\/p>\n<p>Tr\u01b0\u1eddng h\u1ee3p x\u1ea5u nh\u1ea5t x\u1ea3y ra khi <strong>t\u1ea5t c\u1ea3 (ho\u1eb7c ph\u1ea7n l\u1edbn) c\u00e1c kh\u00f3a \u0111\u1ec1u b\u1ecb b\u0103m v\u00e0o c\u00f9ng m\u1ed9t bucket<\/strong>. \u0110i\u1ec1u n\u00e0y c\u00f3 th\u1ec3 do h\u00e0m b\u0103m r\u1ea5t t\u1ed3i ho\u1eb7c do d\u1eef li\u1ec7u \u0111\u1ea7u v\u00e0o c\u00f3 t\u00ednh ch\u1ea5t \u0111\u1eb7c bi\u1ec7t.<\/p>\n<ul>\n<li>V\u1edbi <strong>Separate Chaining<\/strong>: N\u1ebfu t\u1ea5t c\u1ea3 <code>n<\/code> ph\u1ea7n t\u1eed r\u01a1i v\u00e0o c\u00f9ng m\u1ed9t bucket, danh s\u00e1ch li\u00ean k\u1ebft t\u1ea1i bucket \u0111\u00f3 s\u1ebd c\u00f3 \u0111\u1ed9 d\u00e0i <code>n<\/code>. Vi\u1ec7c t\u00ecm ki\u1ebfm ho\u1eb7c x\u00f3a m\u1ed9t ph\u1ea7n t\u1eed s\u1ebd t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi vi\u1ec7c duy\u1ec7t qua to\u00e0n b\u1ed9 danh s\u00e1ch li\u00ean k\u1ebft, t\u1ee9c l\u00e0 O(n).<\/li>\n<li>V\u1edbi <strong>Open Addressing<\/strong>: N\u1ebfu x\u1ea3y ra clustering nghi\u00eam tr\u1ecdng, vi\u1ec7c d\u00f2 t\u00ecm m\u1ed9t ch\u1ed7 tr\u1ed1ng ho\u1eb7c t\u00ecm m\u1ed9t ph\u1ea7n t\u1eed c\u00f3 th\u1ec3 y\u00eau c\u1ea7u duy\u1ec7t qua g\u1ea7n nh\u01b0 to\u00e0n b\u1ed9 <code>n<\/code> ph\u1ea7n t\u1eed trong b\u1ea3ng, c\u0169ng d\u1eabn \u0111\u1ebfn O(n).<\/li>\n<\/ul>\n<p>M\u1eb7c d\u00f9 tr\u01b0\u1eddng h\u1ee3p x\u1ea5u nh\u1ea5t O(n) hi\u1ebfm khi x\u1ea3y ra trong th\u1ef1c t\u1ebf v\u1edbi c\u00e1c h\u00e0m b\u0103m v\u00e0 k\u1ef9 thu\u1eadt x\u1eed l\u00fd xung \u0111\u1ed9t t\u1ed1t, nh\u01b0ng vi\u1ec7c hi\u1ec3u r\u00f5 gi\u1edbi h\u1ea1n n\u00e0y l\u00e0 c\u1ea7n thi\u1ebft khi thi\u1ebft k\u1ebf h\u1ec7 th\u1ed1ng.<\/p>\n<p><strong>B\u1ea3ng t\u00f3m t\u1eaft \u0111\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian:<\/strong><\/p>\n<figure class=\"table\">\n<table>\n<thead>\n<tr>\n<th>Thao t\u00e1c<\/th>\n<th>Tr\u01b0\u1eddng h\u1ee3p Trung b\u00ecnh<\/th>\n<th>Tr\u01b0\u1eddng h\u1ee3p X\u1ea5u nh\u1ea5t<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Th\u00eam<\/td>\n<td>O(1)<\/td>\n<td>O(n)<\/td>\n<\/tr>\n<tr>\n<td>T\u00ecm ki\u1ebfm<\/td>\n<td>O(1)<\/td>\n<td>O(n)<\/td>\n<\/tr>\n<tr>\n<td>X\u00f3a<\/td>\n<td>O(1)<\/td>\n<td>O(n)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<h2><span class=\"ez-toc-section\" id=\"He-so-tai-Load-Factor-va-anh-huong-den-hieu-suat\"><\/span>H\u1ec7 s\u1ed1 t\u1ea3i (Load Factor) v\u00e0 \u1ea3nh h\u01b0\u1edfng \u0111\u1ebfn hi\u1ec7u su\u1ea5t<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>H\u1ec7 s\u1ed1 t\u1ea3i (Load Factor)<\/strong>, th\u01b0\u1eddng k\u00fd hi\u1ec7u l\u00e0 alpha (\u03b1), l\u00e0 m\u1ed9t ch\u1ec9 s\u1ed1 quan tr\u1ecdng \u0111o l\u01b0\u1eddng m\u1ee9c \u0111\u1ed9 &#8220;\u0111\u1ea7y&#8221; c\u1ee7a hash table. N\u00f3 \u0111\u01b0\u1ee3c \u0111\u1ecbnh ngh\u0129a l\u00e0 t\u1ef7 l\u1ec7 gi\u1eefa <strong>s\u1ed1 l\u01b0\u1ee3ng ph\u1ea7n t\u1eed (n)<\/strong> \u0111ang \u0111\u01b0\u1ee3c l\u01b0u tr\u1eef trong b\u1ea3ng v\u00e0 <strong>t\u1ed5ng s\u1ed1 bucket (m)<\/strong> c\u1ee7a b\u1ea3ng:<\/p>\n<p><code>\u03b1 = n \/ m<\/code><\/p>\n<p>H\u1ec7 s\u1ed1 t\u1ea3i \u1ea3nh h\u01b0\u1edfng tr\u1ef1c ti\u1ebfp \u0111\u1ebfn hi\u1ec7u su\u1ea5t v\u00e0 x\u00e1c su\u1ea5t x\u1ea3y ra xung \u0111\u1ed9t.<\/p>\n<ul>\n<li><strong>\u03b1 nh\u1ecf:<\/strong> B\u1ea3ng b\u0103m c\u00f2n nhi\u1ec1u ch\u1ed7 tr\u1ed1ng. X\u00e1c su\u1ea5t xung \u0111\u1ed9t th\u1ea5p, hi\u1ec7u su\u1ea5t truy c\u1eadp g\u1ea7n v\u1edbi O(1) l\u00fd t\u01b0\u1edfng. Tuy nhi\u00ean, l\u00e3ng ph\u00ed b\u1ed9 nh\u1edb v\u00ec nhi\u1ec1u bucket kh\u00f4ng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng.<\/li>\n<li><strong>\u03b1 l\u1edbn:<\/strong> B\u1ea3ng b\u0103m g\u1ea7n \u0111\u1ea7y (ho\u1eb7c th\u1eadm ch\u00ed v\u01b0\u1ee3t qu\u00e1 s\u1ee9c ch\u1ee9a n\u1ebfu d\u00f9ng Separate Chaining). X\u00e1c su\u1ea5t xung \u0111\u1ed9t t\u0103ng cao. Hi\u1ec7u su\u1ea5t b\u1eaft \u0111\u1ea7u gi\u1ea3m, ti\u1ebfn g\u1ea7n h\u01a1n \u0111\u1ebfn O(n) khi \u03b1 qu\u00e1 l\u1edbn, do ph\u1ea3i x\u1eed l\u00fd nhi\u1ec1u xung \u0111\u1ed9t h\u01a1n (duy\u1ec7t danh s\u00e1ch d\u00e0i h\u01a1n ho\u1eb7c d\u00f2 t\u00ecm l\u00e2u h\u01a1n).<\/li>\n<\/ul>\n<p>Do \u0111\u00f3, c\u1ea7n c\u00f3 s\u1ef1 c\u00e2n b\u1eb1ng. Th\u00f4ng th\u01b0\u1eddng, ng\u01b0\u1eddi ta s\u1ebd ch\u1ecdn m\u1ed9t ng\u01b0\u1ee1ng cho h\u1ec7 s\u1ed1 t\u1ea3i (v\u00ed d\u1ee5: 0.7 ho\u1eb7c 0.75 cho Open Addressing). Khi s\u1ed1 l\u01b0\u1ee3ng ph\u1ea7n t\u1eed <code>n<\/code> t\u0103ng l\u00ean khi\u1ebfn <code>\u03b1<\/code> v\u01b0\u1ee3t qua ng\u01b0\u1ee1ng n\u00e0y, hash table s\u1ebd \u0111\u01b0\u1ee3c <strong>thay \u0111\u1ed5i k\u00edch th\u01b0\u1edbc (resize)<\/strong>.<\/p>\n<p>Qu\u00e1 tr\u00ecnh resize th\u01b0\u1eddng bao g\u1ed3m vi\u1ec7c t\u1ea1o m\u1ed9t b\u1ea3ng b\u0103m m\u1edbi v\u1edbi s\u1ed1 l\u01b0\u1ee3ng bucket l\u1edbn h\u01a1n (th\u01b0\u1eddng l\u00e0 g\u1ea5p \u0111\u00f4i), sau \u0111\u00f3 <strong>b\u0103m l\u1ea1i (rehash)<\/strong> t\u1ea5t c\u1ea3 c\u00e1c ph\u1ea7n t\u1eed t\u1eeb b\u1ea3ng c\u0169 v\u00e0 ch\u00e8n ch\u00fang v\u00e0o b\u1ea3ng m\u1edbi. \u0110\u00e2y l\u00e0 m\u1ed9t thao t\u00e1c t\u1ed1n k\u00e9m (th\u01b0\u1eddng m\u1ea5t O(n) th\u1eddi gian) nh\u01b0ng c\u1ea7n thi\u1ebft \u0111\u1ec3 duy tr\u00ec hi\u1ec7u su\u1ea5t O(1) trung b\u00ecnh cho c\u00e1c thao t\u00e1c sau n\u00e0y.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Uu-diem-va-Nhuoc-diem-cua-Hash-Table\"><\/span>\u01afu \u0111i\u1ec3m v\u00e0 Nh\u01b0\u1ee3c \u0111i\u1ec3m c\u1ee7a Hash Table<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Nh\u01b0 m\u1ecdi c\u1ea5u tr\u00fac d\u1eef li\u1ec7u, hash table c\u0169ng c\u00f3 nh\u1eefng \u0111i\u1ec3m m\u1ea1nh v\u00e0 \u0111i\u1ec3m y\u1ebfu ri\u00eang. Hi\u1ec3u r\u00f5 ch\u00fang gi\u00fap b\u1ea1n quy\u1ebft \u0111\u1ecbnh khi n\u00e0o n\u00ean v\u00e0 kh\u00f4ng n\u00ean s\u1eed d\u1ee5ng n\u00f3.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Uu-diem\"><\/span>\u01afu \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li><strong>T\u1ed1c \u0111\u1ed9 truy c\u1eadp trung b\u00ecnh c\u1ef1c nhanh (O(1)):<\/strong> \u0110\u00e2y l\u00e0 \u01b0u \u0111i\u1ec3m l\u1edbn nh\u1ea5t, l\u00e0m cho hash table tr\u1edf th\u00e0nh l\u1ef1a ch\u1ecdn h\u00e0ng \u0111\u1ea7u cho c\u00e1c t\u00e1c v\u1ee5 t\u00ecm ki\u1ebfm, th\u00eam, x\u00f3a d\u1eef li\u1ec7u th\u01b0\u1eddng xuy\u00ean.<\/li>\n<li><strong>Hi\u1ec7u qu\u1ea3 v\u1edbi <a href=\"https:\/\/interdata.vn\/blog\/dataset-la-gi\/\">t\u1eadp d\u1eef li\u1ec7u<\/a> l\u1edbn:<\/strong> T\u1ed1c \u0111\u1ed9 O(1) trung b\u00ecnh kh\u00f4ng \u0111\u1ed5i ngay c\u1ea3 khi s\u1ed1 l\u01b0\u1ee3ng ph\u1ea7n t\u1eed t\u0103ng l\u00ean \u0111\u00e1ng k\u1ec3 (mi\u1ec5n l\u00e0 qu\u1ea3n l\u00fd t\u1ed1t load factor v\u00e0 collision).<\/li>\n<li><strong>Linh ho\u1ea1t:<\/strong> C\u00f3 th\u1ec3 l\u01b0u tr\u1eef nhi\u1ec1u lo\u1ea1i d\u1eef li\u1ec7u kh\u00e1c nhau trong ph\u1ea7n gi\u00e1 tr\u1ecb (Value).<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Nhuoc-diem\"><\/span>Nh\u01b0\u1ee3c \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li><strong>Hi\u1ec7u su\u1ea5t tr\u01b0\u1eddng h\u1ee3p x\u1ea5u nh\u1ea5t t\u1ec7 (O(n)):<\/strong> N\u1ebfu h\u00e0m b\u0103m t\u1ed3i ho\u1eb7c x\u1ea3y ra nhi\u1ec1u xung \u0111\u1ed9t, hi\u1ec7u su\u1ea5t c\u00f3 th\u1ec3 gi\u1ea3m \u0111\u00e1ng k\u1ec3.<\/li>\n<li><strong>Kh\u00f3 duy\u1ec7t c\u00e1c ph\u1ea7n t\u1eed theo th\u1ee9 t\u1ef1:<\/strong> C\u00e1c ph\u1ea7n t\u1eed \u0111\u01b0\u1ee3c l\u01b0u tr\u1eef d\u1ef1a tr\u00ean gi\u00e1 tr\u1ecb b\u0103m c\u1ee7a kh\u00f3a, kh\u00f4ng theo th\u1ee9 t\u1ef1 t\u1ef1 nhi\u00ean hay th\u1ee9 t\u1ef1 ch\u00e8n v\u00e0o. Vi\u1ec7c duy\u1ec7t to\u00e0n b\u1ed9 ph\u1ea7n t\u1eed theo m\u1ed9t th\u1ee9 t\u1ef1 c\u1ee5 th\u1ec3 (v\u00ed d\u1ee5: s\u1eafp x\u1ebfp theo kh\u00f3a) th\u01b0\u1eddng kh\u00f4ng hi\u1ec7u qu\u1ea3.<\/li>\n<li><strong>Chi ph\u00ed b\u1ed9 nh\u1edb:<\/strong> C\u00f3 th\u1ec3 l\u00e3ng ph\u00ed b\u1ed9 nh\u1edb n\u1ebfu load factor qu\u00e1 th\u1ea5p (nhi\u1ec1u bucket tr\u1ed1ng). Separate chaining t\u1ed1n th\u00eam b\u1ed9 nh\u1edb cho con tr\u1ecf.<\/li>\n<li><strong>Chi ph\u00ed thay \u0111\u1ed5i k\u00edch th\u01b0\u1edbc (Resizing):<\/strong> Khi b\u1ea3ng \u0111\u1ea7y v\u00e0 c\u1ea7n resize, thao t\u00e1c rehashing c\u00f3 th\u1ec3 t\u1ed1n k\u00e9m th\u1eddi gian v\u00e0 t\u00e0i nguy\u00ean.<\/li>\n<li><strong>Y\u00eau c\u1ea7u kh\u00f3a ph\u1ea3i hashable:<\/strong> Kh\u00f4ng ph\u1ea3i m\u1ecdi \u0111\u1ed1i t\u01b0\u1ee3ng \u0111\u1ec1u c\u00f3 th\u1ec3 d\u00f9ng l\u00e0m kh\u00f3a (v\u00ed d\u1ee5: c\u00e1c \u0111\u1ed1i t\u01b0\u1ee3ng c\u00f3 th\u1ec3 thay \u0111\u1ed5i).<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Ung-dung-thuc-te-cua-Hash-Table-Bang-Bam\"><\/span>\u1ee8ng d\u1ee5ng th\u1ef1c t\u1ebf c\u1ee7a Hash Table (B\u1ea3ng B\u0103m)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>S\u1ee9c m\u1ea1nh v\u00e0 hi\u1ec7u qu\u1ea3 c\u1ee7a hash table khi\u1ebfn n\u00f3 xu\u1ea5t hi\u1ec7n trong v\u00f4 s\u1ed1 \u1ee9ng d\u1ee5ng quen thu\u1ed9c trong ng\u00e0nh c\u00f4ng ngh\u1ec7 ph\u1ea7n m\u1ec1m:<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Implementations-trong-Ngon-ngu-Lap-trinh-Dictionary-HashMap-Set\"><\/span>Implementations trong Ng\u00f4n ng\u1eef L\u1eadp tr\u00ecnh (Dictionary, HashMap, Set)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0110\u00e2y l\u00e0 \u1ee9ng d\u1ee5ng ph\u1ed5 bi\u1ebfn nh\u1ea5t. H\u1ea7u h\u1ebft c\u00e1c <a href=\"https:\/\/interdata.vn\/blog\/ngon-ngu-lap-trinh-la-gi\/\">ng\u00f4n ng\u1eef l\u1eadp tr\u00ecnh<\/a> hi\u1ec7n \u0111\u1ea1i \u0111\u1ec1u cung c\u1ea5p s\u1eb5n c\u00e1c c\u1ea5u tr\u00fac d\u1eef li\u1ec7u d\u1ef1a tr\u00ean hash table:<\/p>\n<ul>\n<li><strong>Python:<\/strong> Ki\u1ec3u d\u1eef li\u1ec7u <code>dict<\/code> (dictionary) v\u00e0 <code>set<\/code>.<\/li>\n<li><strong>Java:<\/strong> C\u00e1c l\u1edbp <code>HashMap<\/code>, <code>HashSet<\/code>, <code>Hashtable<\/code>, <code>ConcurrentHashMap<\/code>.<\/li>\n<li><strong>C++:<\/strong> <code>std::unordered_map<\/code> v\u00e0 <code>std::unordered_set<\/code> trong th\u01b0 vi\u1ec7n chu\u1ea9n (STL).<\/li>\n<li><strong><a href=\"https:\/\/interdata.vn\/blog\/javascript-la-gi\/\">JavaScript<\/a>:<\/strong> \u0110\u1ed1i t\u01b0\u1ee3ng <code>Object<\/code> ho\u1ea1t \u0111\u1ed9ng t\u01b0\u01a1ng t\u1ef1 hash table cho kh\u00f3a chu\u1ed7i, v\u00e0 c\u1ea5u tr\u00fac <code>Map<\/code> v\u00e0 <code>Set<\/code> hi\u1ec7n \u0111\u1ea1i h\u01a1n. Ch\u00fang \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i \u0111\u1ec3 l\u01b0u tr\u1eef v\u00e0 truy xu\u1ea5t d\u1eef li\u1ec7u c\u00f3 c\u1ea5u tr\u00fac m\u1ed9t c\u00e1ch nhanh ch\u00f3ng.<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Bo-nho-dem-Caching\"><\/span>B\u1ed9 nh\u1edb \u0111\u1ec7m (Caching)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><a href=\"https:\/\/interdata.vn\/blog\/caching-la-gi\/\">Caching<\/a> l\u00e0 k\u1ef9 thu\u1eadt l\u01b0u tr\u1eef t\u1ea1m th\u1eddi c\u00e1c d\u1eef li\u1ec7u th\u01b0\u1eddng xuy\u00ean truy c\u1eadp \u0111\u1ec3 t\u0103ng t\u1ed1c \u0111\u1ed9 ph\u1ea3n h\u1ed3i. Hash table r\u1ea5t l\u00fd t\u01b0\u1edfng cho vi\u1ec7c n\u00e0y. Kh\u00f3a c\u00f3 th\u1ec3 l\u00e0 URL c\u1ee7a m\u1ed9t <a href=\"https:\/\/interdata.vn\/blog\/page-la-gi\/\">trang web<\/a>, ID c\u1ee7a m\u1ed9t \u0111\u1ed1i t\u01b0\u1ee3ng d\u1eef li\u1ec7u, c\u00f2n gi\u00e1 tr\u1ecb l\u00e0 n\u1ed9i dung trang web ho\u1eb7c d\u1eef li\u1ec7u \u0111\u00e3 \u0111\u01b0\u1ee3c x\u1eed l\u00fd. Khi c\u00f3 y\u00eau c\u1ea7u, h\u1ec7 th\u1ed1ng ki\u1ec3m tra cache b\u1eb1ng hash table (O(1)), n\u1ebfu c\u00f3 th\u00ec tr\u1ea3 v\u1ec1 ngay, ti\u1ebft ki\u1ec7m th\u1eddi gian t\u00ednh to\u00e1n ho\u1eb7c truy v\u1ea5n database.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Chi-muc-co-so-du-lieu-Database-Indexing\"><\/span>Ch\u1ec9 m\u1ee5c c\u01a1 s\u1edf d\u1eef li\u1ec7u (Database Indexing)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Trong c\u01a1 s\u1edf d\u1eef li\u1ec7u, ch\u1ec9 m\u1ee5c (index) gi\u00fap t\u0103ng t\u1ed1c \u0111\u1ed9 truy v\u1ea5n d\u1eef li\u1ec7u. Hash index l\u00e0 m\u1ed9t lo\u1ea1i ch\u1ec9 m\u1ee5c s\u1eed d\u1ee5ng hash table. N\u00f3 \u0111\u1eb7c bi\u1ec7t hi\u1ec7u qu\u1ea3 cho c\u00e1c truy v\u1ea5n t\u00ecm ki\u1ebfm ch\u00ednh x\u00e1c theo kh\u00f3a (equality queries, v\u00ed d\u1ee5: <code>SELECT * FROM users WHERE user_id = 123<\/code>). H\u1ec7 th\u1ed1ng b\u0103m gi\u00e1 tr\u1ecb <code>user_id<\/code> \u0111\u1ec3 t\u00ecm nhanh v\u1ecb tr\u00ed b\u1ea3n ghi tr\u00ean \u0111\u0129a.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Cac-ung-dung-khac\"><\/span>C\u00e1c \u1ee9ng d\u1ee5ng kh\u00e1c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Hash table c\u00f2n \u0111\u01b0\u1ee3c d\u00f9ng trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c:<\/p>\n<ul>\n<li><strong>B\u1ea3ng k\u00fd hi\u1ec7u (Symbol Tables) trong <a href=\"https:\/\/interdata.vn\/blog\/compiler-trinh-bien-dich-la-gi\/\">tr\u00ecnh bi\u00ean d\u1ecbch<\/a>:<\/strong> L\u01b0u tr\u1eef th\u00f4ng tin v\u1ec1 c\u00e1c bi\u1ebfn, h\u00e0m trong <a href=\"https:\/\/interdata.vn\/blog\/source-code-la-gi\/\">m\u00e3 ngu\u1ed3n<\/a>.<\/li>\n<li><strong>Ki\u1ec3m tra tr\u00f9ng l\u1eb7p:<\/strong> Nhanh ch\u00f3ng x\u00e1c \u0111\u1ecbnh xem m\u1ed9t ph\u1ea7n t\u1eed \u0111\u00e3 t\u1ed3n t\u1ea1i trong m\u1ed9t t\u1eadp h\u1ee3p l\u1edbn hay ch\u01b0a (v\u00ed d\u1ee5: ki\u1ec3m tra \u0111\u1ea1o v\u0103n, ph\u00e1t hi\u1ec7n g\u00f3i tin m\u1ea1ng tr\u00f9ng l\u1eb7p).<\/li>\n<li><strong>B\u1ed9 \u0111\u1ecbnh tuy\u1ebfn (Routers):<\/strong> L\u01b0u tr\u1eef b\u1ea3ng \u0111\u1ecbnh tuy\u1ebfn \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1eddng \u0111i nhanh nh\u1ea5t cho c\u00e1c g\u00f3i tin m\u1ea1ng d\u1ef1a tr\u00ean <a href=\"https:\/\/interdata.vn\/blog\/dia-chi-ip-la-gi\/\">\u0111\u1ecba ch\u1ec9 IP<\/a> \u0111\u00edch.<\/li>\n<li><strong>Thu\u1eadt to\u00e1n m\u1eadt m\u00e3:<\/strong> C\u00e1c h\u00e0m b\u0103m m\u1eadt m\u00e3 (cryptographic hash functions) l\u00e0 n\u1ec1n t\u1ea3ng c\u1ee7a nhi\u1ec1u \u1ee9ng d\u1ee5ng b\u1ea3o m\u1eadt, d\u00f9 ch\u00fang c\u00f3 c\u00e1c y\u00eau c\u1ea7u kh\u1eaft khe h\u01a1n h\u00e0m b\u0103m th\u00f4ng th\u01b0\u1eddng.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"So-sanh-nhanh-Hash-Table-voi-cac-cau-truc-du-lieu-khac\"><\/span>So s\u00e1nh nhanh: Hash Table v\u1edbi c\u00e1c c\u1ea5u tr\u00fac d\u1eef li\u1ec7u kh\u00e1c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0110\u1ec3 hi\u1ec3u r\u00f5 h\u01a1n v\u1ecb tr\u00ed c\u1ee7a hash table, h\u00e3y so s\u00e1nh nhanh v\u1edbi hai c\u1ea5u tr\u00fac d\u1eef li\u1ec7u c\u01a1 b\u1ea3n kh\u00e1c:<\/p>\n<ul>\n<li><strong>Hash Table vs. M\u1ea3ng (Array):<\/strong> M\u1ea3ng cho ph\u00e9p truy c\u1eadp ph\u1ea7n t\u1eed theo ch\u1ec9 s\u1ed1 (index) v\u1edbi t\u1ed1c \u0111\u1ed9 O(1), t\u01b0\u01a1ng t\u1ef1 hash table. Tuy nhi\u00ean, m\u1ea3ng y\u00eau c\u1ea7u ch\u1ec9 s\u1ed1 l\u00e0 s\u1ed1 nguy\u00ean li\u00ean t\u1ee5c, c\u00f2n hash table cho ph\u00e9p d\u00f9ng nhi\u1ec1u lo\u1ea1i kh\u00f3a (string, object&#8230;) v\u00e0 \u00e1nh x\u1ea1 ch\u00fang v\u00e0o ch\u1ec9 s\u1ed1. T\u00ecm ki\u1ebfm m\u1ed9t gi\u00e1 tr\u1ecb c\u1ee5 th\u1ec3 trong m\u1ea3ng (n\u1ebfu kh\u00f4ng bi\u1ebft ch\u1ec9 s\u1ed1) th\u01b0\u1eddng m\u1ea5t O(n), ch\u1eadm h\u01a1n O(1) trung b\u00ecnh c\u1ee7a hash table. M\u1ea3ng d\u1ec5 d\u00e0ng duy\u1ec7t theo th\u1ee9 t\u1ef1, hash table th\u00ec kh\u00f4ng.<\/li>\n<li><strong>Hash Table vs. Danh s\u00e1ch li\u00ean k\u1ebft (Linked List):<\/strong> Danh s\u00e1ch li\u00ean k\u1ebft linh ho\u1ea1t trong vi\u1ec7c th\u00eam\/x\u00f3a ph\u1ea7n t\u1eed \u1edf gi\u1eefa (O(1) n\u1ebfu \u0111\u00e3 c\u00f3 con tr\u1ecf \u0111\u1ebfn n\u00fat tr\u01b0\u1edbc \u0111\u00f3), nh\u01b0ng t\u00ecm ki\u1ebfm m\u1ed9t ph\u1ea7n t\u1eed c\u1ee5 th\u1ec3 lu\u00f4n m\u1ea5t O(n) v\u00ec ph\u1ea3i duy\u1ec7t tu\u1ea7n t\u1ef1. Hash table v\u01b0\u1ee3t tr\u1ed9i v\u1ec1 t\u1ed1c \u0111\u1ed9 t\u00ecm ki\u1ebfm (O(1) trung b\u00ecnh).<\/li>\n<\/ul>\n<p>T\u00f3m l\u1ea1i, hash table t\u1ed1i \u01b0u cho vi\u1ec7c <strong>truy xu\u1ea5t nhanh d\u1ef1a tr\u00ean kh\u00f3a<\/strong>, trong khi c\u00e1c c\u1ea5u tr\u00fac kh\u00e1c c\u00f3 th\u1ec3 m\u1ea1nh h\u01a1n \u1edf c\u00e1c kh\u00eda c\u1ea1nh nh\u01b0 <strong>duy\u1ec7t theo th\u1ee9 t\u1ef1<\/strong> (m\u1ea3ng, c\u00e2y) ho\u1eb7c <strong>th\u00eam\/x\u00f3a linh ho\u1ea1t \u1edf gi\u1eefa<\/strong> (danh s\u00e1ch li\u00ean k\u1ebft).<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Tong-ket-Khi-nao-nen-su-dung-Hash-Table\"><\/span>T\u1ed5ng k\u1ebft: Khi n\u00e0o n\u00ean s\u1eed d\u1ee5ng Hash Table?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Hash Table (B\u1ea3ng B\u0103m) l\u00e0 m\u1ed9t c\u00f4ng c\u1ee5 c\u1ef1c k\u1ef3 m\u1ea1nh m\u1ebd trong kho v\u0169 kh\u00ed c\u1ee7a l\u1eadp tr\u00ecnh vi\u00ean. N\u00f3 t\u1ecfa s\u00e1ng trong c\u00e1c t\u00ecnh hu\u1ed1ng m\u00e0 <strong>t\u1ed1c \u0111\u1ed9 truy xu\u1ea5t, th\u00eam, x\u00f3a d\u1eef li\u1ec7u d\u1ef1a tr\u00ean m\u1ed9t kh\u00f3a duy nh\u1ea5t l\u00e0 \u01b0u ti\u00ean h\u00e0ng \u0111\u1ea7u<\/strong>.<\/p>\n<p>H\u00e3y c\u00e2n nh\u1eafc s\u1eed d\u1ee5ng hash table khi:<\/p>\n<ul>\n<li>B\u1ea1n c\u1ea7n l\u01b0u tr\u1eef v\u00e0 truy v\u1ea5n d\u1eef li\u1ec7u d\u1ea1ng key-value.<\/li>\n<li>T\u1ea7n su\u1ea5t t\u00ecm ki\u1ebfm\/th\u00eam\/x\u00f3a d\u1eef li\u1ec7u cao.<\/li>\n<li>Hi\u1ec7u su\u1ea5t O(1) trung b\u00ecnh l\u00e0 y\u00eau c\u1ea7u quan tr\u1ecdng.<\/li>\n<li>Th\u1ee9 t\u1ef1 c\u1ee7a c\u00e1c ph\u1ea7n t\u1eed kh\u00f4ng quan tr\u1ecdng.<\/li>\n<li>B\u1ea1n c\u00f3 th\u1ec3 ch\u1ea5p nh\u1eadn hi\u1ec7u su\u1ea5t O(n) trong tr\u01b0\u1eddng h\u1ee3p x\u1ea5u nh\u1ea5t (hi\u1ebfm g\u1eb7p v\u1edbi thi\u1ebft k\u1ebf t\u1ed1t).<\/li>\n<\/ul>\n<p>Hy v\u1ecdng qua b\u00e0i vi\u1ebft chi ti\u1ebft n\u00e0y, b\u1ea1n \u0111\u00e3 c\u00f3 c\u00e1i nh\u00ecn s\u00e2u s\u1eafc v\u00e0 to\u00e0n di\u1ec7n v\u1ec1 hash table. Hi\u1ec3u r\u00f5 c\u00e1ch n\u00f3 ho\u1ea1t \u0111\u1ed9ng, \u01b0u nh\u01b0\u1ee3c \u0111i\u1ec3m v\u00e0 c\u00e1c k\u1ef9 thu\u1eadt li\u00ean quan s\u1ebd gi\u00fap b\u1ea1n \u0111\u01b0a ra quy\u1ebft \u0111\u1ecbnh \u0111\u00fang \u0111\u1eafn khi l\u1ef1a ch\u1ecdn c\u1ea5u tr\u00fac d\u1eef li\u1ec7u v\u00e0 t\u1ed1i \u01b0u h\u00f3a hi\u1ec7u n\u0103ng cho \u1ee9ng d\u1ee5ng c\u1ee7a m\u00ecnh. \u0110\u1eebng ng\u1ea7n ng\u1ea1i \u00e1p d\u1ee5ng ki\u1ebfn th\u1ee9c n\u00e0y v\u00e0o c\u00e1c d\u1ef1 \u00e1n l\u1eadp tr\u00ecnh ti\u1ebfp theo!<\/p>\n<div style=\"background-color: #e6f2ff; border-radius: 10px; padding: 20px; margin: 20px 0; border: 1px solid #b3d9ff;\">\n<p>Hi\u1ec3u r\u00f5 c\u00e1c c\u1ea5u tr\u00fac d\u1eef li\u1ec7u hi\u1ec7u n\u0103ng cao nh\u01b0 Hash Table l\u00e0 m\u1ed9t chuy\u1ec7n, v\u1eadn h\u00e0nh \u1ee9ng d\u1ee5ng ch\u1ee9a ch\u00fang m\u01b0\u1ee3t m\u00e0 l\u1ea1i c\u1ea7n n\u1ec1n t\u1ea3ng h\u1ea1 t\u1ea7ng \u1ed5n \u0111\u1ecbnh. V\u1edbi <a href=\"https:\/\/interdata.vn\/blog\/website-la-gi\/\">website<\/a> c\u01a1 b\u1ea3n, <a target=\"_blank\" rel=\"noopener noreferrer\" href=\"https:\/\/interdata.vn\/thue-hosting\/\">d\u1ecbch v\u1ee5 thu\u00ea Hosting<\/a> t\u1ea1i InterData gi\u00fap b\u1ea1n kh\u1edfi \u0111\u1ea7u tr\u00ean ph\u1ea7n c\u1ee9ng chuy\u00ean d\u1ee5ng th\u1ebf h\u1ec7 m\u1edbi, dung l\u01b0\u1ee3ng \u0111\u01b0\u1ee3c t\u1ed1i \u01b0u.<\/p>\n<p>Khi \u1ee9ng d\u1ee5ng \u0111\u00f2i h\u1ecfi nhi\u1ec1u t\u00e0i nguy\u00ean h\u01a1n, <a target=\"_blank\" rel=\"noopener noreferrer\" href=\"https:\/\/interdata.vn\/thue-vps\/\">d\u1ecbch v\u1ee5 thu\u00ea VPS<\/a> cung c\u1ea5p c\u1ea5u h\u00ecnh m\u1ea1nh m\u1ebd v\u1edbi b\u1ed9 x\u1eed l\u00fd <a href=\"https:\/\/interdata.vn\/blog\/cpu-amd-epyc\/\">AMD EPYC<\/a> Gen 3th v\u00e0 SSD NVMe U.2 t\u1ed1c \u0111\u1ed9 cao. N\u1ebfu c\u1ea7n s\u1ef1 linh ho\u1ea1t cao c\u1ea5p v\u00e0 <a href=\"https:\/\/interdata.vn\/blog\/bang-thong-la-gi\/\">b\u0103ng th\u00f4ng<\/a> cao, h\u00e3y xem x\u00e9t <a target=\"_blank\" rel=\"noopener noreferrer\" href=\"https:\/\/interdata.vn\/cloud-server\/\">d\u1ecbch v\u1ee5 thu\u00ea Cloud Server<\/a> s\u1eed d\u1ee5ng c\u00f4ng ngh\u1ec7 <a href=\"https:\/\/interdata.vn\/blog\/ao-hoa-la-gi\/\">\u1ea3o h\u00f3a<\/a> ti\u00ean ti\u1ebfn, l\u00e0 l\u1ef1a ch\u1ecdn ch\u1ea5t l\u01b0\u1ee3ng, uy t\u00edn t\u1eeb InterData.<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>B\u1ea1n \u0111\u00e3 bao gi\u1edd t\u1ef1 h\u1ecfi l\u00e0m th\u1ebf n\u00e0o c\u00e1c \u1ee9ng d\u1ee5ng c\u00f3 th\u1ec3 t\u00ecm ki\u1ebfm th\u00f4ng tin nhanh nh\u01b0 ch\u1edbp trong h\u00e0ng tri\u1ec7u d\u1eef li\u1ec7u ch\u01b0a? Hay l\u00e0m sao c\u00e1c ng\u00f4n ng\u1eef l\u1eadp tr\u00ecnh qu\u1ea3n l\u00fd c\u00e1c \u0111\u1ed1i t\u01b0\u1ee3ng ph\u1ee9c t\u1ea1p m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3? B\u00ed m\u1eadt th\u01b0\u1eddng n\u1eb1m \u1edf m\u1ed9t c\u1ea5u tr\u00fac d\u1eef<\/p>\n","protected":false},"author":2,"featured_media":27430,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[140],"tags":[],"class_list":["post-27427","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-lap-trinh"],"_links":{"self":[{"href":"https:\/\/interdata.vn\/blog\/wp-json\/wp\/v2\/posts\/27427","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/interdata.vn\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/interdata.vn\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/interdata.vn\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/interdata.vn\/blog\/wp-json\/wp\/v2\/comments?post=27427"}],"version-history":[{"count":1,"href":"https:\/\/interdata.vn\/blog\/wp-json\/wp\/v2\/posts\/27427\/revisions"}],"predecessor-version":[{"id":27432,"href":"https:\/\/interdata.vn\/blog\/wp-json\/wp\/v2\/posts\/27427\/revisions\/27432"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/interdata.vn\/blog\/wp-json\/wp\/v2\/media\/27430"}],"wp:attachment":[{"href":"https:\/\/interdata.vn\/blog\/wp-json\/wp\/v2\/media?parent=27427"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/interdata.vn\/blog\/wp-json\/wp\/v2\/categories?post=27427"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/interdata.vn\/blog\/wp-json\/wp\/v2\/tags?post=27427"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}