{"id":27430,"date":"2023-09-08T21:24:36","date_gmt":"2023-09-08T14:24:36","guid":{"rendered":"https:\/\/ungdung.hotronghiencuu.com\/open\/monitor-la-gi-2"},"modified":"2023-09-08T21:24:36","modified_gmt":"2023-09-08T14:24:36","slug":"monitor-la-gi-2","status":"publish","type":"post","link":"https:\/\/ungdung.hotronghiencuu.com\/open\/monitor-la-gi-2","title":{"rendered":"Thu\u1eadt to\u00e1n trong l\u1eadp tr\u00ecnh v\u00e0 nh\u1eefng \u0111i\u1ec1u c\u1ea7n bi\u1ebft"},"content":{"rendered":"<p>Monitor l\u00e0 m\u1ed9t thi\u1ebft b\u1ecb hi\u1ec3n th\u1ecb \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i trong c\u00f4ng ngh\u1ec7 th\u00f4ng tin. N\u00f3 cho ph\u00e9p ch\u00fang ta xem v\u00e0 ki\u1ec3m so\u00e1t c\u00e1c ho\u1ea1t \u0111\u1ed9ng tr\u00ean m\u00e1y t\u00ednh, \u0111i\u1ec7n tho\u1ea1i di \u0111\u1ed9ng v\u00e0 c\u00e1c thi\u1ebft b\u1ecb kh\u00e1c. M\u00e0n h\u00ecnh n\u00e0y gi\u00fap ch\u00fang ta truy\u1ec1n t\u1ea3i v\u00e0 nh\u1eadn th\u00f4ng tin m\u1ed9t c\u00e1ch d\u1ec5 d\u00e0ng v\u00e0 thu\u1eadn ti\u1ec7n, l\u00e0m cho c\u00f4ng vi\u1ec7c v\u00e0 gi\u1ea3i tr\u00ed tr\u1edf n\u00ean hi\u1ec7u qu\u1ea3 h\u01a1n.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_40 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\">Table of Contents<\/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\" area-label=\"ez-toc-toggle-icon-1\"><label for=\"item-6ad1439ebb86c\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><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><\/label><input  type=\"checkbox\" id=\"item-6ad1439ebb86c\"><\/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:\/\/ungdung.hotronghiencuu.com\/open\/monitor-la-gi-2\/#Thuat_toan_la_gi\" title=\"Thu\u1eadt to\u00e1n l\u00e0 g\u00ec?\">Thu\u1eadt to\u00e1n 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:\/\/ungdung.hotronghiencuu.com\/open\/monitor-la-gi-2\/#Vai_tro_cua_thuat_toan_trong_lap_trinh\" title=\"Vai tr\u00f2 c\u1ee7a thu\u1eadt to\u00e1n trong l\u1eadp tr\u00ecnh\">Vai tr\u00f2 c\u1ee7a thu\u1eadt to\u00e1n 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:\/\/ungdung.hotronghiencuu.com\/open\/monitor-la-gi-2\/#So_luong_thuat_toan_duoc_su_dung_trong_lap_trinh\" title=\"S\u1ed1 l\u01b0\u1ee3ng thu\u1eadt to\u00e1n \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong l\u1eadp tr\u00ecnh\">S\u1ed1 l\u01b0\u1ee3ng thu\u1eadt to\u00e1n \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong l\u1eadp tr\u00ecnh<\/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:\/\/ungdung.hotronghiencuu.com\/open\/monitor-la-gi-2\/#Cac_loai_thuat_toan_pho_bien\" title=\"C\u00e1c lo\u1ea1i thu\u1eadt to\u00e1n ph\u1ed5 bi\u1ebfn\">C\u00e1c lo\u1ea1i thu\u1eadt to\u00e1n ph\u1ed5 bi\u1ebfn<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/monitor-la-gi-2\/#Vi_du_ve_thuat_toan_tim_kiem\" title=\"V\u00ed d\u1ee5 v\u1ec1 thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm\">V\u00ed d\u1ee5 v\u1ec1 thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/monitor-la-gi-2\/#Thuat_toan_sap_xep\" title=\"Thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp\">Thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/monitor-la-gi-2\/#Thuat_toan_sap_xep_noi_bot\" title=\"Thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp n\u1ed5i b\u1ecdt\">Thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp n\u1ed5i b\u1ecdt<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/monitor-la-gi-2\/#Vi_du\" title=\"V\u00ed d\u1ee5:\">V\u00ed d\u1ee5:<\/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:\/\/ungdung.hotronghiencuu.com\/open\/monitor-la-gi-2\/#Thuat_toan_sap_xep_chon\" title=\"Thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp ch\u1ecdn\">Thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp ch\u1ecdn<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/monitor-la-gi-2\/#Vi_du-2\" title=\"V\u00ed d\u1ee5:\">V\u00ed d\u1ee5:<\/a><\/li><\/ul><\/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:\/\/ungdung.hotronghiencuu.com\/open\/monitor-la-gi-2\/#Thuat_toan_tim_kiem\" title=\"Thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm\">Thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/monitor-la-gi-2\/#Thuat_toan_tim_kiem_tuan_tu\" title=\"Thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm tu\u1ea7n t\u1ef1\">Thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm tu\u1ea7n t\u1ef1<\/a><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:\/\/ungdung.hotronghiencuu.com\/open\/monitor-la-gi-2\/#Vi_du-3\" title=\"V\u00ed d\u1ee5:\">V\u00ed d\u1ee5:<\/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:\/\/ungdung.hotronghiencuu.com\/open\/monitor-la-gi-2\/#Thuat_toan_tim_kiem_nhi_phan\" title=\"Thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm nh\u1ecb ph\u00e2n\">Thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm nh\u1ecb ph\u00e2n<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/monitor-la-gi-2\/#Vi_du-4\" title=\"V\u00ed d\u1ee5:\">V\u00ed d\u1ee5:<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Thuat_toan_la_gi\"><\/span>Thu\u1eadt to\u00e1n l\u00e0 g\u00ec?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Trong l\u1eadp tr\u00ecnh, thu\u1eadt to\u00e1n l\u00e0 m\u1ed9t t\u1eadp h\u1ee3p c\u00e1c b\u01b0\u1edbc c\u1ee5 th\u1ec3 \u0111\u1ec3 gi\u1ea3i quy\u1ebft m\u1ed9t v\u1ea5n \u0111\u1ec1 ho\u1eb7c th\u1ef1c hi\u1ec7n m\u1ed9t nhi\u1ec7m v\u1ee5. N\u00f3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh c\u00e1ch th\u1ee9c th\u1ef1c hi\u1ec7n m\u1ed9t c\u00f4ng vi\u1ec7c t\u1eeb \u0111\u1ea7u \u0111\u1ebfn cu\u1ed1i, t\u1eeb vi\u1ec7c x\u1eed l\u00fd d\u1eef li\u1ec7u \u0111\u1ea7u v\u00e0o cho \u0111\u1ebfn k\u1ebft qu\u1ea3 mong mu\u1ed1n. Thu\u1eadt to\u00e1n c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n b\u1eb1ng ng\u00f4n ng\u1eef t\u1ef1 nhi\u00ean ho\u1eb7c ng\u00f4n ng\u1eef l\u1eadp tr\u00ecnh.<\/p>\n<p>Thu\u1eadt to\u00e1n l\u00e0 m\u1ed9t ph\u1ea7n quan tr\u1ecdng c\u1ee7a l\u1eadp tr\u00ecnh, v\u00ec n\u00f3 gi\u00fap x\u00e1c \u0111\u1ecbnh c\u00e1ch ti\u1ebfp c\u1eadn v\u00e0 gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1 m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3. M\u1ed9t thu\u1eadt to\u00e1n t\u1ed1t c\u00f3 th\u1ec3 gi\u00fap t\u1ed1i \u01b0u h\u00f3a th\u1eddi gian ch\u1ea1y v\u00e0 t\u00e0i nguy\u00ean s\u1eed d\u1ee5ng c\u1ee7a ch\u01b0\u01a1ng tr\u00ecnh, t\u1eeb \u0111\u00f3 c\u1ea3i thi\u1ec7n hi\u1ec7u su\u1ea5t v\u00e0 t\u00ednh \u1ed5n \u0111\u1ecbnh c\u1ee7a \u1ee9ng d\u1ee5ng. Thu\u1eadt to\u00e1n kh\u00f4ng ch\u1ec9 \u00e1p d\u1ee5ng trong l\u0129nh v\u1ef1c l\u1eadp tr\u00ecnh m\u00e1y t\u00ednh, m\u00e0 c\u00f2n trong nhi\u1ec1u ng\u00e0nh kh\u00e1c nhau nh\u01b0 khoa h\u1ecdc d\u1eef li\u1ec7u, k\u1ef9 thu\u1eadt \u0111i\u1ec7n t\u1eed, kinh t\u1ebf v\u00e0 sinh h\u1ecdc.<\/p>\n<p>\u0110\u1ec3 x\u00e2y d\u1ef1ng m\u1ed9t thu\u1eadt to\u00e1n, l\u1eadp tr\u00ecnh vi\u00ean c\u1ea7n ph\u1ea3i c\u00f3 ki\u1ebfn th\u1ee9c v\u1ec1 c\u1ea5u tr\u00fac d\u1eef li\u1ec7u v\u00e0 ng\u00f4n ng\u1eef l\u1eadp tr\u00ecnh. H\u1ecd c\u0169ng c\u1ea7n c\u00f3 kh\u1ea3 n\u0103ng t\u01b0 duy logic v\u00e0 s\u00e1ng t\u1ea1o \u0111\u1ec3 t\u00ecm ra c\u00e1c gi\u1ea3i ph\u00e1p m\u1edbi cho c\u00e1c v\u1ea5n \u0111\u1ec1 kh\u00f3 kh\u0103n. Thu\u1eadt to\u00e1n kh\u00f4ng ch\u1ec9 gi\u00fap gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1 hi\u1ec7n t\u1ea1i m\u00e0 c\u00f2n mang l\u1ea1i nh\u1eefng tri th\u1ee9c v\u00e0 k\u1ef9 n\u0103ng quan tr\u1ecdng cho vi\u1ec7c gi\u1ea3i quy\u1ebft c\u00e1c v\u1ea5n \u0111\u1ec1 trong t\u01b0\u01a1ng lai.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Vai_tro_cua_thuat_toan_trong_lap_trinh\"><\/span>Vai tr\u00f2 c\u1ee7a thu\u1eadt to\u00e1n trong l\u1eadp tr\u00ecnh<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Thu\u1eadt to\u00e1n \u0111\u00f3ng vai tr\u00f2 quan tr\u1ecdng trong vi\u1ec7c gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1 v\u00e0 thi\u1ebft k\u1ebf ch\u01b0\u01a1ng tr\u00ecnh. N\u00f3 l\u00e0 b\u01b0\u1edbc \u0111\u1ea7u ti\u00ean \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh c\u00e1ch ti\u1ebfp c\u1eadn v\u00e0 gi\u1ea3i quy\u1ebft m\u1ed9t v\u1ea5n \u0111\u1ec1. M\u1ed9t thu\u1eadt to\u00e1n t\u1ed1t c\u00f3 th\u1ec3 gi\u00fap t\u1ed1i \u01b0u h\u00f3a th\u1eddi gian ch\u1ea1y v\u00e0 t\u00e0i nguy\u00ean s\u1eed d\u1ee5ng c\u1ee7a ch\u01b0\u01a1ng tr\u00ecnh, t\u1eeb \u0111\u00f3 c\u1ea3i thi\u1ec7n hi\u1ec7u su\u1ea5t v\u00e0 t\u00ednh \u1ed5n \u0111\u1ecbnh c\u1ee7a \u1ee9ng d\u1ee5ng.<\/p>\n<p>Khi x\u00e2y d\u1ef1ng m\u1ed9t thu\u1eadt to\u00e1n, l\u1eadp tr\u00ecnh vi\u00ean c\u1ea7n xem x\u00e9t c\u00e1c y\u1ebfu t\u1ed1 nh\u01b0 t\u00ednh hi\u1ec7u qu\u1ea3, t\u00ednh kh\u1ea3 thi v\u00e0 t\u00ednh \u0111\u00fang \u0111\u1eafn. Thu\u1eadt to\u00e1n c\u0169ng c\u1ea7n \u0111\u01b0\u1ee3c ki\u1ec3m tra v\u00e0 t\u1ed1i \u01b0u h\u00f3a \u0111\u1ec3 \u0111\u1ea3m b\u1ea3o r\u1eb1ng n\u00f3 ho\u1ea1t \u0111\u1ed9ng ch\u00ednh x\u00e1c v\u00e0 nhanh ch\u00f3ng.<\/p>\n<p>Thu\u1eadt to\u00e1n kh\u00f4ng ch\u1ec9 gi\u00fap gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1 hi\u1ec7n t\u1ea1i m\u00e0 c\u00f2n mang l\u1ea1i nh\u1eefng tri th\u1ee9c v\u00e0 k\u1ef9 n\u0103ng quan tr\u1ecdng cho vi\u1ec7c gi\u1ea3i quy\u1ebft c\u00e1c v\u1ea5n \u0111\u1ec1 trong t\u01b0\u01a1ng lai. N\u00f3 l\u00e0 m\u1ed9t c\u00f4ng c\u1ee5 m\u1ea1nh m\u1ebd \u0111\u1ec3 l\u1eadp tr\u00ecnh vi\u00ean c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng \u0111\u1ec3 ph\u00e1t tri\u1ec3n c\u00e1c \u1ee9ng d\u1ee5ng ph\u1ee9c t\u1ea1p v\u00e0 gi\u1ea3i quy\u1ebft c\u00e1c v\u1ea5n \u0111\u1ec1 kh\u00f3 kh\u0103n.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"So_luong_thuat_toan_duoc_su_dung_trong_lap_trinh\"><\/span>S\u1ed1 l\u01b0\u1ee3ng thu\u1eadt to\u00e1n \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong l\u1eadp tr\u00ecnh<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><img decoding=\"async\" alt=\"S\u1ed1 l\u01b0\u1ee3ng thu\u1eadt to\u00e1n \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong l\u1eadp tr\u00ecnh\" src=\"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-content\/uploads\/2023\/09\/thuat_toan_trong_lap_trinh_va_nhung_dieu_can_biet.jpeg\" style=\"text-align: center; clear: both; display: block; margin: 0 auto;\" title=\"S\u1ed1 l\u01b0\u1ee3ng thu\u1eadt to\u00e1n \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong l\u1eadp tr\u00ecnh\"\/><\/p>\n<p>Trong l\u0129nh v\u1ef1c l\u1eadp tr\u00ecnh, c\u00f3 r\u1ea5t nhi\u1ec1u thu\u1eadt to\u00e1n kh\u00e1c nhau \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 gi\u1ea3i quy\u1ebft c\u00e1c v\u1ea5n \u0111\u1ec1 v\u00e0 t\u1ed1i \u01b0u h\u00f3a hi\u1ec7u su\u1ea5t c\u1ee7a ch\u01b0\u01a1ng tr\u00ecnh. S\u1ed1 l\u01b0\u1ee3ng thu\u1eadt to\u00e1n n\u00e0y l\u00e0 v\u00f4 h\u1ea1n, v\u00e0 m\u1ed7i ng\u00e0y c\u00e0ng c\u00f3 nhi\u1ec1u thu\u1eadt to\u00e1n m\u1edbi \u0111\u01b0\u1ee3c ph\u00e1t tri\u1ec3n. C\u00e1c thu\u1eadt to\u00e1n n\u00e0y c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng cho nhi\u1ec1u ng\u00f4n ng\u1eef l\u1eadp tr\u00ecnh kh\u00e1c nhau nh\u01b0 C++, Java, Python, v\u00e0 nhi\u1ec1u ng\u00f4n ng\u1eef kh\u00e1c.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Cac_loai_thuat_toan_pho_bien\"><\/span>C\u00e1c lo\u1ea1i thu\u1eadt to\u00e1n ph\u1ed5 bi\u1ebfn<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 lo\u1ea1i thu\u1eadt to\u00e1n ph\u1ed5 bi\u1ebfn m\u00e0 l\u1eadp tr\u00ecnh vi\u00ean th\u01b0\u1eddng g\u1eb7p:<\/p>\n<ul>\n<li>Thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm: D\u00f9ng \u0111\u1ec3 t\u00ecm ki\u1ebfm m\u1ed9t ph\u1ea7n t\u1eed trong m\u1ed9t danh s\u00e1ch ho\u1eb7c m\u1ea3ng.<\/li>\n<li>Thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp: D\u00f9ng \u0111\u1ec3 s\u1eafp x\u1ebfp c\u00e1c ph\u1ea7n t\u1eed trong danh s\u00e1ch ho\u1eb7c m\u1ea3ng theo th\u1ee9 t\u1ef1 t\u0103ng d\u1ea7n ho\u1eb7c gi\u1ea3m d\u1ea7n.<\/li>\n<li>Thu\u1eadt to\u00e1n \u0111\u1ed3 th\u1ecb: D\u00f9ng \u0111\u1ec3 gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn \u0111\u1ed3 th\u1ecb nh\u01b0 t\u00ecm \u0111\u01b0\u1eddng \u0111i ng\u1eafn nh\u1ea5t, c\u00e2y khung nh\u1ecf nh\u1ea5t, v\u00e0 t\u00ecm th\u00e0nh ph\u1ea7n li\u00ean th\u00f4ng.<\/li>\n<li>Thu\u1eadt to\u00e1n quy ho\u1ea1ch \u0111\u1ed9ng: D\u00f9ng \u0111\u1ec3 gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n t\u1ed1i \u01b0u h\u00f3a b\u1eb1ng c\u00e1ch chia b\u00e0i to\u00e1n th\u00e0nh c\u00e1c ph\u1ea7n con nh\u1ecf h\u01a1n v\u00e0 l\u01b0u tr\u1eef k\u1ebft qu\u1ea3 c\u1ee7a c\u00e1c ph\u1ea7n con n\u00e0y \u0111\u1ec3 s\u1eed d\u1ee5ng l\u1ea1i trong qu\u00e1 tr\u00ecnh gi\u1ea3i quy\u1ebft b\u00e0i to\u00e1n g\u1ed1c.<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"Vi_du_ve_thuat_toan_tim_kiem\"><\/span>V\u00ed d\u1ee5 v\u1ec1 thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>M\u1ed9t v\u00ed d\u1ee5 v\u1ec1 thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm l\u00e0 thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm nh\u1ecb ph\u00e2n. Thu\u1eadt to\u00e1n n\u00e0y \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u00ecm ki\u1ebfm m\u1ed9t ph\u1ea7n t\u1eed trong m\u1ed9t danh s\u00e1ch \u0111\u00e3 \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp. \u00dd t\u01b0\u1edfng c\u1ee7a thu\u1eadt to\u00e1n l\u00e0 so s\u00e1nh ph\u1ea7n t\u1eed \u1edf gi\u1eefa danh s\u00e1ch v\u1edbi gi\u00e1 tr\u1ecb c\u1ea7n t\u00ecm. N\u1ebfu ph\u1ea7n t\u1eed n\u00e0y b\u1eb1ng gi\u00e1 tr\u1ecb c\u1ea7n t\u00ecm, th\u00ec ta \u0111\u00e3 t\u00ecm th\u1ea5y. N\u1ebfu kh\u00f4ng, ta ti\u1ebfp t\u1ee5c so s\u00e1nh v\u1edbi n\u1eeda danh s\u00e1ch c\u00f2n l\u1ea1i v\u00e0 ti\u1ebfp t\u1ee5c qu\u00e1 tr\u00ecnh cho \u0111\u1ebfn khi t\u00ecm th\u1ea5y ho\u1eb7c kh\u00f4ng c\u00f2n ph\u1ea7n t\u1eed n\u00e0o \u0111\u1ec3 so s\u00e1nh.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Thuat_toan_sap_xep\"><\/span>Thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><img decoding=\"async\" alt=\"Thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp\" src=\"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-content\/uploads\/2023\/09\/thuat_toan_trong_lap_trinh_va_nhung_dieu_can_biet.jpg\" style=\"text-align: center; clear: both; display: block; margin: 0 auto;\" title=\"Thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp\"\/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Thuat_toan_sap_xep_noi_bot\"><\/span>Thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp n\u1ed5i b\u1ecdt<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp n\u1ed5i b\u1ecdt l\u00e0 m\u1ed9t thu\u1eadt to\u00e1n c\u01a1 b\u1ea3n trong l\u1eadp tr\u00ecnh. N\u00f3 ho\u1ea1t \u0111\u1ed9ng b\u1eb1ng c\u00e1ch so s\u00e1nh t\u1eebng c\u1eb7p ph\u1ea7n t\u1eed li\u00ean ti\u1ebfp nhau v\u00e0 ho\u00e1n \u0111\u1ed5i ch\u00fang n\u1ebfu ch\u00fang kh\u00f4ng \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp theo th\u1ee9 t\u1ef1 mong mu\u1ed1n. Thu\u1eadt to\u00e1n n\u00e0y ti\u1ebfp t\u1ee5c l\u1eb7p l\u1ea1i qu\u00e1 tr\u00ecnh n\u00e0y cho \u0111\u1ebfn khi kh\u00f4ng c\u00f2n ph\u1ea7n t\u1eed n\u00e0o c\u1ea7n ho\u00e1n \u0111\u1ed5i, t\u1ee9c l\u00e0 d\u00e3y \u0111\u00e3 \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Vi_du\"><\/span>V\u00ed d\u1ee5:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>Input: [5, 3, 8, 1, 2]<\/li>\n<li>B\u01b0\u1edbc 1: [3, 5, 8, 1, 2] (ho\u00e1n \u0111\u1ed5i v\u1ecb tr\u00ed c\u1ee7a s\u1ed1 5 v\u00e0 s\u1ed1 3)<\/li>\n<li>B\u01b0\u1edbc 2: [3, 5, 1, 8, 2] (ho\u00e1n \u0111\u1ed5i v\u1ecb tr\u00ed c\u1ee7a s\u1ed1 8 v\u00e0 s\u1ed1 1)<\/li>\n<li>B\u01b0\u1edbc 3: [3, 5, 1, 2, 8] (ho\u00e1n \u0111\u1ed5i v\u1ecb tr\u00ed c\u1ee7a s\u1ed1 8 v\u00e0 s\u1ed1 2)<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Thuat_toan_sap_xep_chon\"><\/span>Thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp ch\u1ecdn<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp ch\u1ecdn l\u00e0 m\u1ed9t thu\u1eadt to\u00e1n \u0111\u01a1n gi\u1ea3n nh\u01b0ng hi\u1ec7u qu\u1ea3. N\u00f3 ho\u1ea1t \u0111\u1ed9ng b\u1eb1ng c\u00e1ch t\u00ecm ph\u1ea7n t\u1eed nh\u1ecf nh\u1ea5t trong d\u00e3y v\u00e0 \u0111\u1eb7t n\u00f3 v\u00e0o v\u1ecb tr\u00ed \u0111\u1ea7u ti\u00ean, sau \u0111\u00f3 t\u00ecm ph\u1ea7n t\u1eed nh\u1ecf th\u1ee9 hai v\u00e0 \u0111\u1eb7t n\u00f3 v\u00e0o v\u1ecb tr\u00ed th\u1ee9 hai, v\u00e0 ti\u1ebfp t\u1ee5c cho \u0111\u1ebfn khi d\u00e3y \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Vi_du-2\"><\/span>V\u00ed d\u1ee5:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>Input: [5, 3, 8, 1, 2]<\/li>\n<li>B\u01b0\u1edbc 1: [1, 3, 8, 5, 2] (\u0111\u1eb7t s\u1ed1 nh\u1ecf nh\u1ea5t l\u00e0 s\u1ed1 1 v\u00e0o v\u1ecb tr\u00ed \u0111\u1ea7u ti\u00ean)<\/li>\n<li>B\u01b0\u1edbc 2: [1, 2, 8, 5, 3] (\u0111\u1eb7t s\u1ed1 nh\u1ecf th\u1ee9 hai l\u00e0 s\u1ed1 2 v\u00e0o v\u1ecb tr\u00ed th\u1ee9 hai)<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Thuat_toan_tim_kiem\"><\/span>Thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"Thuat_toan_tim_kiem_tuan_tu\"><\/span>Thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm tu\u1ea7n t\u1ef1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm tu\u1ea7n t\u1ef1 l\u00e0 m\u1ed9t thu\u1eadt to\u00e1n c\u01a1 b\u1ea3n \u0111\u1ec3 t\u00ecm ki\u1ebfm m\u1ed9t ph\u1ea7n t\u1eed trong m\u1ed9t d\u00e3y. N\u00f3 ho\u1ea1t \u0111\u1ed9ng b\u1eb1ng c\u00e1ch so s\u00e1nh t\u1eebng ph\u1ea7n t\u1eed trong d\u00e3y v\u1edbi ph\u1ea7n t\u1eed c\u1ea7n t\u00ecm ki\u1ebfm cho \u0111\u1ebfn khi t\u00ecm th\u1ea5y ho\u1eb7c duy\u1ec7t qua to\u00e0n b\u1ed9 d\u00e3y. N\u1ebfu ph\u1ea7n t\u1eed \u0111\u01b0\u1ee3c t\u00ecm th\u1ea5y, thu\u1eadt to\u00e1n tr\u1ea3 v\u1ec1 v\u1ecb tr\u00ed c\u1ee7a n\u00f3 trong d\u00e3y; n\u1ebfu kh\u00f4ng, thu\u1eadt to\u00e1n tr\u1ea3 v\u1ec1 m\u1ed9t gi\u00e1 tr\u1ecb \u0111\u1eb7c bi\u1ec7t \u0111\u1ec3 ch\u1ec9 ra r\u1eb1ng ph\u1ea7n t\u1eed kh\u00f4ng c\u00f3 trong d\u00e3y.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Vi_du-3\"><\/span>V\u00ed d\u1ee5:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>Input: [5, 3, 8, 1, 2]<\/li>\n<li>T\u00ecm ki\u1ebfm s\u1ed1 8<\/li>\n<li>K\u1ebft qu\u1ea3: V\u1ecb tr\u00ed c\u1ee7a s\u1ed1 8 l\u00e0 2<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Thuat_toan_tim_kiem_nhi_phan\"><\/span>Thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm nh\u1ecb ph\u00e2n<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm nh\u1ecb ph\u00e2n l\u00e0 m\u1ed9t thu\u1eadt to\u00e1n hi\u1ec7u qu\u1ea3 \u0111\u1ec3 t\u00ecm ki\u1ebfm m\u1ed9t ph\u1ea7n t\u1eed trong m\u1ed9t d\u00e3y \u0111\u00e3 \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp. N\u00f3 ho\u1ea1t \u0111\u1ed9ng b\u1eb1ng c\u00e1ch so s\u00e1nh ph\u1ea7n t\u1eed c\u1ea7n t\u00ecm ki\u1ebfm v\u1edbi ph\u1ea7n t\u1eed gi\u1eefa c\u1ee7a d\u00e3y v\u00e0 lo\u1ea1i b\u1ecf n\u1eeda d\u00e3y kh\u00f4ng ch\u1ee9a ph\u1ea7n t\u1eed c\u1ea7n t\u00ecm ki\u1ebfm sau m\u1ed7i l\u01b0\u1ee3t so s\u00e1nh. Thu\u1eadt to\u00e1n ti\u1ebfp t\u1ee5c l\u1eb7p l\u1ea1i qu\u00e1 tr\u00ecnh n\u00e0y cho \u0111\u1ebfn khi t\u00ecm th\u1ea5y ho\u1eb7c ch\u1ec9 c\u00f2n l\u1ea1i m\u1ed9t ph\u1ea7n t\u1eed trong d\u00e3y.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Vi_du-4\"><\/span>V\u00ed d\u1ee5:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>Input: [1, 2, 3, 5, 8]<\/li>\n<li>T\u00ecm ki\u1ebfm s\u1ed1 5<\/li>\n<li>K\u1ebft qu\u1ea3: V\u1ecb tr\u00ed c\u1ee7a s\u1ed1 5 l\u00e0 3<\/li>\n<\/ul>\n<p>Trong b\u00e0i vi\u1ebft n\u00e0y, ch\u00fang ta \u0111\u00e3 t\u00ecm hi\u1ec3u v\u1ec1 monitor l\u00e0 g\u00ec v\u00e0 vai tr\u00f2 quan tr\u1ecdng c\u1ee7a n\u00f3 trong c\u00f4ng ngh\u1ec7 th\u00f4ng tin. Monitor l\u00e0 m\u1ed9t thi\u1ebft b\u1ecb xu\u1ea5t ra h\u00ecnh \u1ea3nh v\u00e0 \u00e2m thanh cho ng\u01b0\u1eddi d\u00f9ng, gi\u00fap hi\u1ec3n th\u1ecb th\u00f4ng tin t\u1eeb m\u00e1y t\u00ednh ho\u1eb7c c\u00e1c thi\u1ebft b\u1ecb kh\u00e1c. N\u00f3 \u0111\u00f3ng vai tr\u00f2 quan tr\u1ecdng trong vi\u1ec7c cung c\u1ea5p m\u1ed9t giao di\u1ec7n tr\u1ef1c quan \u0111\u1ec3 t\u01b0\u01a1ng t\u00e1c v\u1edbi m\u00e1y t\u00ednh v\u00e0 th\u01b0\u1edfng th\u1ee9c n\u1ed9i dung \u0111a ph\u01b0\u01a1ng ti\u1ec7n.<br \/>\n<iframe loading=\"lazy\" title=\"Loa Monitor l\u00e0 g\u00ec? | C\u00f3 n\u00ean s\u1eed d\u1ee5ng Loa Monitor v\u1edbi nhu c\u1ea7u Gia \u0111\u00ecnh? | Fb: 0974743311\" width=\"790\" height=\"444\" src=\"https:\/\/www.youtube.com\/embed\/dEMt5x24SAo?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Monitor l\u00e0 m\u1ed9t thi\u1ebft b\u1ecb hi\u1ec3n th\u1ecb \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i trong c\u00f4ng ngh\u1ec7 th\u00f4ng tin. N\u00f3 cho ph\u00e9p ch\u00fang ta xem v\u00e0 ki\u1ec3m so\u00e1t c\u00e1c&#8230; <\/p>\n","protected":false},"author":1,"featured_media":27428,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[29],"tags":[],"class_list":["post-27430","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-khai-niem-1"],"_links":{"self":[{"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/posts\/27430","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/comments?post=27430"}],"version-history":[{"count":0,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/posts\/27430\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/media\/27428"}],"wp:attachment":[{"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/media?parent=27430"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/categories?post=27430"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/tags?post=27430"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}