{"id":476870,"date":"2023-08-09T09:04:34","date_gmt":"2023-08-09T09:04:34","guid":{"rendered":""},"modified":"2023-09-05T11:13:36","modified_gmt":"2023-09-05T11:13:36","slug":"divide-and-conquer-algorithm","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/vn\/wiki\/divide-and-conquer-algorithm\/","title":{"rendered":"Thu\u1eadt to\u00e1n chia \u0111\u1ec3 tr\u1ecb"},"content":{"rendered":"<p>Chia \u0111\u1ec3 tr\u1ecb (D&amp;C) l\u00e0 m\u1ed9t m\u00f4 h\u00ecnh thu\u1eadt to\u00e1n quan tr\u1ecdng v\u1edbi nhi\u1ec1u \u1ee9ng d\u1ee5ng trong khoa h\u1ecdc m\u00e1y t\u00ednh v\u00e0 h\u01a1n th\u1ebf n\u1eefa. N\u00f3 ho\u1ea1t \u0111\u1ed9ng b\u1eb1ng c\u00e1ch chia \u0111\u1ec7 quy m\u1ed9t b\u00e0i to\u00e1n th\u00e0nh hai ho\u1eb7c nhi\u1ec1u b\u00e0i to\u00e1n con c\u00f9ng lo\u1ea1i ho\u1eb7c c\u00f3 li\u00ean quan v\u1edbi nhau, cho \u0111\u1ebfn khi nh\u1eefng b\u00e0i to\u00e1n n\u00e0y tr\u1edf n\u00ean \u0111\u1ee7 \u0111\u01a1n gi\u1ea3n \u0111\u1ec3 c\u00f3 th\u1ec3 gi\u1ea3i tr\u1ef1c ti\u1ebfp. C\u00e1c gi\u1ea3i ph\u00e1p cho c\u00e1c v\u1ea5n \u0111\u1ec1 ph\u1ee5 sau \u0111\u00f3 \u0111\u01b0\u1ee3c k\u1ebft h\u1ee3p \u0111\u1ec3 \u0111\u01b0a ra gi\u1ea3i ph\u00e1p cho v\u1ea5n \u0111\u1ec1 ban \u0111\u1ea7u.<\/p>\n<h2>Ngu\u1ed3n g\u1ed1c v\u00e0 nh\u1eefng \u0111\u1ec1 c\u1eadp \u0111\u1ea7u ti\u00ean v\u1ec1 thu\u1eadt to\u00e1n chia \u0111\u1ec3 tr\u1ecb<\/h2>\n<p>Ngu\u1ed3n g\u1ed1c c\u1ee7a m\u00f4 h\u00ecnh chia \u0111\u1ec3 tr\u1ecb c\u00f3 ngu\u1ed3n g\u1ed1c s\u00e2u xa t\u1eeb l\u1ecbch s\u1eed t\u00ednh to\u00e1n v\u00e0 to\u00e1n h\u1ecdc. C\u00e1ch ti\u1ebfp c\u1eadn gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1 n\u00e0y c\u00f3 d\u1ea5u v\u1ebft t\u1eeb th\u1eddi c\u1ed5 \u0111\u1ea1i, n\u01a1i n\u00f3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong b\u1ed1i c\u1ea3nh chi\u1ebfn l\u01b0\u1ee3c v\u00e0 to\u00e1n h\u1ecdc.<\/p>\n<p>Tuy nhi\u00ean, trong khoa h\u1ecdc m\u00e1y t\u00ednh, thu\u1eadt ng\u1eef \u201cchia \u0111\u1ec3 tr\u1ecb\u201d xu\u1ea5t hi\u1ec7n v\u00e0o gi\u1eefa th\u1ebf k\u1ef7 20. N\u00f3 \u0111\u01b0\u1ee3c ph\u1ed5 bi\u1ebfn th\u00f4ng qua vi\u1ec7c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i trong nhi\u1ec1u thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp v\u00e0 t\u00ecm ki\u1ebfm ban \u0111\u1ea7u nh\u01b0 Quicksort v\u00e0 T\u00ecm ki\u1ebfm nh\u1ecb ph\u00e2n. Vi\u1ec7c ch\u00ednh th\u1ee9c c\u00f4ng nh\u1eadn \u201cph\u00e2n chia v\u00e0 chinh ph\u1ee5c\u201d nh\u01b0 m\u1ed9t chi\u1ebfn l\u01b0\u1ee3c thu\u1eadt to\u00e1n ri\u00eang bi\u1ec7t l\u00e0 do c\u00f4ng tr\u00ecnh n\u1ec1n t\u1ea3ng c\u1ee7a c\u00e1c nh\u00e0 khoa h\u1ecdc m\u00e1y t\u00ednh nh\u01b0 John von Neumann v\u00e0 Donald Knuth.<\/p>\n<h2>Ra m\u1eaft thu\u1eadt to\u00e1n Chia \u0111\u1ec3 tr\u1ecb<\/h2>\n<p>V\u1ec1 b\u1ea3n ch\u1ea5t, thu\u1eadt to\u00e1n chia \u0111\u1ec3 tr\u1ecb bao g\u1ed3m ba b\u01b0\u1edbc ri\u00eang bi\u1ec7t:<\/p>\n<ol>\n<li><strong>Chia<\/strong>: \u0110\u00e2y l\u00e0 b\u01b0\u1edbc \u0111\u1ea7u ti\u00ean, trong \u0111\u00f3 b\u00e0i to\u00e1n ch\u00ednh \u0111\u01b0\u1ee3c chia th\u00e0nh c\u00e1c b\u00e0i to\u00e1n ph\u1ee5 nh\u1ecf h\u01a1n.<\/li>\n<li><strong>Chinh ph\u1ee5c<\/strong>: \u1ede b\u01b0\u1edbc n\u00e0y, c\u00e1c b\u00e0i to\u00e1n con \u0111\u01b0\u1ee3c gi\u1ea3i quy\u1ebft ri\u00eang l\u1ebb, th\u01b0\u1eddng b\u1eb1ng l\u1ec7nh g\u1ecdi \u0111\u1ec7 quy.<\/li>\n<li><strong>K\u1ebft h\u1ee3p<\/strong>: L\u1eddi gi\u1ea3i c\u1ee7a c\u00e1c b\u00e0i to\u00e1n con \u0111\u01b0\u1ee3c k\u1ebft h\u1ee3p l\u1ea1i \u0111\u1ec3 t\u1ea1o th\u00e0nh l\u1eddi gi\u1ea3i c\u1ee7a b\u00e0i to\u00e1n ch\u00ednh.<\/li>\n<\/ol>\n<p>C\u00e1ch ti\u1ebfp c\u1eadn n\u00e0y nh\u1ea5n m\u1ea1nh t\u00ednh ch\u1ea5t \u0111\u1ec7 quy c\u1ee7a nhi\u1ec1u v\u1ea5n \u0111\u1ec1 t\u00ednh to\u00e1n, bi\u1ebfn c\u00e1c v\u1ea5n \u0111\u1ec1 ph\u1ee9c t\u1ea1p th\u00e0nh c\u00e1c ph\u1ea7n d\u1ec5 qu\u1ea3n l\u00fd h\u01a1n v\u00e0 c\u00f3 th\u1ec3 gi\u1ea3i quy\u1ebft d\u1ec5 d\u00e0ng h\u01a1n.<\/p>\n<h2>C\u1ea5u tr\u00fac b\u00ean trong v\u00e0 ho\u1ea1t \u0111\u1ed9ng c\u1ee7a thu\u1eadt to\u00e1n chia \u0111\u1ec3 tr\u1ecb<\/h2>\n<p>C\u1ea5u tr\u00fac b\u00ean trong c\u1ee7a thu\u1eadt to\u00e1n chia \u0111\u1ec3 tr\u1ecb \u0111\u01b0\u1ee3c \u0111\u1eb7c tr\u01b0ng b\u1edfi \u0111\u1ec7 quy. V\u1ec1 c\u1ed1t l\u00f5i, n\u00f3 l\u00e0 m\u1ed9t h\u00e0m \u0111\u1ec7 quy t\u1ef1 g\u1ecdi ch\u00ednh n\u00f3 tr\u00ean c\u00e1c \u0111\u1ea7u v\u00e0o nh\u1ecf h\u01a1n.<\/p>\n<p>Thu\u1eadt to\u00e1n D&amp;C \u0111i\u1ec3n h\u00ecnh tu\u00e2n theo c\u1ea5u tr\u00fac n\u00e0y:<\/p>\n<pre><div class=\"bg-black rounded-md mb-4\"><div class=\"flex items-center relative text-gray-200 bg-gray-800 px-4 py-2 text-xs font-sans justify-between rounded-t-md\"><span>m\u00e3 gi\u1ea3<\/span><button class=\"flex ml-auto gap-2\"><svg stroke=\"currentColor\" fill=\"none\" stroke-width=\"2\" viewbox=\"0 0 24 24\" stroke-linecap=\"round\" stroke-linejoin=\"round\" class=\"h-4 w-4\" height=\"1em\" width=\"1em\" ><path d=\"M16 4h2a2 2 0 0 1 2 2v14a2 2 0 0 1-2 2H6a2 2 0 0 1-2-2V6a2 2 0 0 1 2-2h2\"><\/path><rect x=\"8\" y=\"2\" width=\"8\" height=\"4\" rx=\"1\" ry=\"1\"><\/rect><\/svg>Sao ch\u00e9p m\u00e3<\/button><\/div><div class=\"p-4 overflow-y-auto\"><code class=\"!whitespace-pre hljs language-pseudocode\" data-no-translation=\"\">function DivideAndConquer(problem):\n    if problem is small enough:\n        solve problem directly\n        return solution\n    else:\n        divide problem into smaller parts\n        for each part:\n            solution_part = DivideAndConquer(part)\n        combine the solution_parts into a complete solution\n        return solution\n<\/code><\/div><\/div><\/pre>\n<p>M\u1ed7i l\u1ec7nh g\u1ecdi \u0111\u1ec7 quy c\u00f3 tr\u00e1ch nhi\u1ec7m gi\u1ea3i quy\u1ebft m\u1ed9t phi\u00ean b\u1ea3n nh\u1ecf h\u01a1n c\u1ee7a v\u1ea5n \u0111\u1ec1 ban \u0111\u1ea7u. C\u00e1ch ti\u1ebfp c\u1eadn \u0111\u1ec7 quy n\u00e0y ti\u1ebfp t\u1ee5c cho \u0111\u1ebfn khi \u0111\u1ea1t \u0111\u01b0\u1ee3c tr\u01b0\u1eddng h\u1ee3p c\u01a1 s\u1edf, tr\u01b0\u1eddng h\u1ee3p n\u00e0y c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c gi\u1ea3i tr\u1ef1c ti\u1ebfp m\u00e0 kh\u00f4ng c\u1ea7n \u0111\u1ec7 quy th\u00eam.<\/p>\n<h2>C\u00e1c t\u00ednh n\u0103ng ch\u00ednh c\u1ee7a thu\u1eadt to\u00e1n chia \u0111\u1ec3 tr\u1ecb<\/h2>\n<p>C\u00f3 m\u1ed9t s\u1ed1 t\u00ednh n\u0103ng kh\u00e1c bi\u1ec7t c\u1ee7a thu\u1eadt to\u00e1n chia \u0111\u1ec3 tr\u1ecb:<\/p>\n<ol>\n<li>H\u1ecd \u0111\u01a1n gi\u1ea3n h\u00f3a qu\u00e1 tr\u00ecnh gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1 b\u1eb1ng c\u00e1ch chia nh\u1ecf c\u00e1c v\u1ea5n \u0111\u1ec1 ph\u1ee9c t\u1ea1p th\u00e0nh c\u00e1c v\u1ea5n \u0111\u1ec1 nh\u1ecf h\u01a1n, d\u1ec5 qu\u1ea3n l\u00fd h\u01a1n.<\/li>\n<li>H\u1ecd tu\u00e2n theo c\u00e1ch ti\u1ebfp c\u1eadn \u0111\u1ec7 quy, trong \u0111\u00f3 gi\u1ea3i ph\u00e1p cho m\u1ed9t v\u1ea5n \u0111\u1ec1 ph\u1ee5 thu\u1ed9c v\u00e0o gi\u1ea3i ph\u00e1p cho c\u00e1c tr\u01b0\u1eddng h\u1ee3p nh\u1ecf h\u01a1n c\u1ee7a c\u00f9ng m\u1ed9t v\u1ea5n \u0111\u1ec1.<\/li>\n<li>H\u1ecd khai th\u00e1c c\u1ea5u tr\u00fac c\u1ee7a v\u1ea5n \u0111\u1ec1 v\u00e0 th\u01b0\u1eddng d\u1eabn \u0111\u1ebfn c\u00e1c thu\u1eadt to\u00e1n hi\u1ec7u qu\u1ea3.<\/li>\n<li>C\u00e1c thu\u1eadt to\u00e1n D&amp;C c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c song song h\u00f3a v\u00ec c\u00e1c v\u1ea5n \u0111\u1ec1 ph\u1ee5 th\u01b0\u1eddng \u0111\u1ed9c l\u1eadp.<\/li>\n<\/ol>\n<h2>C\u00e1c lo\u1ea1i thu\u1eadt to\u00e1n chia \u0111\u1ec3 tr\u1ecb<\/h2>\n<p>Chi\u1ebfn l\u01b0\u1ee3c chia \u0111\u1ec3 tr\u1ecb r\u1ea5t ph\u1ed5 bi\u1ebfn trong khoa h\u1ecdc m\u00e1y t\u00ednh v\u00e0 l\u00e0 n\u1ec1n t\u1ea3ng c\u1ee7a nhi\u1ec1u thu\u1eadt to\u00e1n. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 thu\u1eadt to\u00e1n D&amp;C th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng:<\/p>\n<ol>\n<li><strong>T\u00ecm ki\u1ebfm nh\u1ecb ph\u00e2n<\/strong>: \u0110\u01b0\u1ee3c s\u1eed d\u1ee5ng trong c\u00e1c thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm \u0111\u1ec3 t\u00ecm m\u1ed9t ph\u1ea7n t\u1eed trong m\u1ed9t m\u1ea3ng \u0111\u00e3 \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp.<\/li>\n<li><strong>S\u1eafp x\u1ebfp nhanh ch\u00f3ng<\/strong>: D\u00f9ng trong thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp \u0111\u1ec3 s\u1eafp x\u1ebfp m\u1ed9t danh s\u00e1ch ho\u1eb7c m\u1ea3ng.<\/li>\n<li><strong>H\u1ee3p nh\u1ea5tS\u1eafp x\u1ebfp<\/strong>: M\u1ed9t thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp hi\u1ec7u qu\u1ea3 kh\u00e1c d\u1ef1a tr\u00ean D&amp;C.<\/li>\n<li><strong>Thu\u1eadt to\u00e1n Strassen<\/strong>: D\u00f9ng trong ph\u00e9p nh\u00e2n ma tr\u1eadn \u0111\u1ec3 nh\u00e2n hai ma tr\u1eadn.<\/li>\n<li><strong>C\u1eb7p \u0111i\u1ec3m g\u1ea7n nh\u1ea5t<\/strong>: \u0110\u01b0\u1ee3c s\u1eed d\u1ee5ng trong h\u00ecnh h\u1ecdc t\u00ednh to\u00e1n \u0111\u1ec3 t\u00ecm c\u1eb7p \u0111i\u1ec3m g\u1ea7n nh\u1ea5t trong m\u1ed9t t\u1eadp h\u1ee3p.<\/li>\n<\/ol>\n<h2>\u1ee8ng d\u1ee5ng, b\u00e0i to\u00e1n v\u00e0 gi\u1ea3i ph\u00e1p li\u00ean quan \u0111\u1ebfn thu\u1eadt to\u00e1n chia \u0111\u1ec3 tr\u1ecb<\/h2>\n<p>Thu\u1eadt to\u00e1n chia \u0111\u1ec3 tr\u1ecb c\u00f3 nhi\u1ec1u \u1ee9ng d\u1ee5ng:<\/p>\n<ol>\n<li><strong>S\u1eafp x\u1ebfp<\/strong>: C\u00e1c thu\u1eadt to\u00e1n nh\u01b0 quicksort v\u00e0 mergesort.<\/li>\n<li><strong>\u0110ang t\u00ecm ki\u1ebfm<\/strong>: Thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm nh\u1ecb ph\u00e2n.<\/li>\n<li><strong>C\u00e1c ph\u00e9p to\u00e1n s\u1ed1<\/strong>: Thu\u1eadt to\u00e1n Karatsuba cho ph\u00e9p nh\u00e2n nhanh.<\/li>\n<li><strong>Ho\u1ea1t \u0111\u1ed9ng ma tr\u1eadn<\/strong>: Thu\u1eadt to\u00e1n Strassen cho ph\u00e9p nh\u00e2n ma tr\u1eadn.<\/li>\n<li><strong>H\u00ecnh h\u1ecdc t\u00ednh to\u00e1n<\/strong>: C\u00e1c v\u1ea5n \u0111\u1ec1 nh\u01b0 c\u1eb7p g\u1ea7n nh\u1ea5t v\u00e0 bao l\u1ed3i.<\/li>\n<\/ol>\n<p>Tuy nhi\u00ean, thu\u1eadt to\u00e1n D&amp;C c\u0169ng c\u00f3 nh\u1eefng th\u00e1ch th\u1ee9c. M\u1ed9t v\u1ea5n \u0111\u1ec1 nghi\u00eam tr\u1ecdng l\u00e0 vi\u1ec7c s\u1eed d\u1ee5ng qu\u00e1 nhi\u1ec1u b\u1ed9 nh\u1edb ng\u0103n x\u1ebfp do \u0111\u1ec7 quy. \u0110i\u1ec1u n\u00e0y c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c gi\u1ea3m thi\u1ec3u th\u00f4ng qua \u0111\u1ec7 quy \u0111u\u00f4i ho\u1eb7c c\u00e1c gi\u1ea3i ph\u00e1p l\u1eb7p l\u1ea1i n\u1ebfu c\u00f3 th\u1ec3.<\/p>\n<p>M\u1ed9t th\u00e1ch th\u1ee9c kh\u00e1c l\u00e0 quy\u1ebft \u0111\u1ecbnh k\u00edch th\u01b0\u1edbc b\u00e0i to\u00e1n t\u1ed1i \u01b0u cho tr\u01b0\u1eddng h\u1ee3p c\u01a1 s\u1edf. \u0110i\u1ec1u n\u00e0y c\u1ea7n thi\u1ebft k\u1ebf thu\u1eadt to\u00e1n c\u1ea9n th\u1eadn d\u1ef1a tr\u00ean ph\u00e2n t\u00edch v\u00e0 \u0111\u00e1nh gi\u00e1 th\u1ef1c nghi\u1ec7m.<\/p>\n<h2>So s\u00e1nh v\u1edbi c\u00e1c kh\u00e1i ni\u1ec7m t\u01b0\u01a1ng t\u1ef1<\/h2>\n<table>\n<thead>\n<tr>\n<th>\u00dd t\u01b0\u1edfng<\/th>\n<th>S\u1ef1 mi\u00eau t\u1ea3<\/th>\n<th>\u0110i\u1ec3m t\u01b0\u01a1ng \u0111\u1ed3ng<\/th>\n<th>S\u1ef1 kh\u00e1c bi\u1ec7t<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>L\u1eadp tr\u00ecnh n\u0103ng \u0111\u1ed9ng<\/td>\n<td>M\u1ed9t ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i c\u00e1c b\u00e0i to\u00e1n ph\u1ee9c t\u1ea1p b\u1eb1ng c\u00e1ch chia ch\u00fang th\u00e0nh c\u00e1c b\u00e0i to\u00e1n con \u0111\u01a1n gi\u1ea3n h\u01a1n v\u00e0 l\u01b0u tr\u1eef k\u1ebft qu\u1ea3 c\u1ee7a c\u00e1c b\u00e0i to\u00e1n con n\u00e0y \u0111\u1ec3 tr\u00e1nh l\u00e0m vi\u1ec7c tr\u00f9ng l\u1eb7p.<\/td>\n<td>C\u1ea3 hai \u0111\u1ec1u gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1 b\u1eb1ng c\u00e1ch chia ch\u00fang th\u00e0nh c\u00e1c v\u1ea5n \u0111\u1ec1 con nh\u1ecf h\u01a1n.<\/td>\n<td>L\u1eadp tr\u00ecnh \u0111\u1ed9ng s\u1eed d\u1ee5ng c\u00e1ch ti\u1ebfp c\u1eadn t\u1eeb d\u01b0\u1edbi l\u00ean v\u00e0 gi\u1ea3i quy\u1ebft t\u1ea5t c\u1ea3 c\u00e1c b\u00e0i to\u00e1n con ph\u1ee5 thu\u1ed9c tr\u01b0\u1edbc khi gi\u1ea3i quy\u1ebft b\u00e0i to\u00e1n hi\u1ec7n t\u1ea1i.<\/td>\n<\/tr>\n<tr>\n<td>Thu\u1eadt to\u00e1n tham lam<\/td>\n<td>M\u1ed9t c\u00e1ch ti\u1ebfp c\u1eadn x\u00e2y d\u1ef1ng gi\u1ea3i ph\u00e1p t\u1eebng ph\u1ea7n m\u1ed9t, lu\u00f4n ch\u1ecdn ph\u1ea7n ti\u1ebfp theo mang l\u1ea1i l\u1ee3i \u00edch tr\u01b0\u1edbc m\u1eaft nh\u1ea5t.<\/td>\n<td>C\u1ea3 hai \u0111\u1ec1u l\u00e0 m\u00f4 h\u00ecnh thi\u1ebft k\u1ebf thu\u1eadt to\u00e1n \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 gi\u1ea3i quy\u1ebft c\u00e1c v\u1ea5n \u0111\u1ec1 t\u1ed1i \u01b0u h\u00f3a.<\/td>\n<td>C\u00e1c thu\u1eadt to\u00e1n tham lam \u0111\u01b0a ra c\u00e1c l\u1ef1a ch\u1ecdn t\u1ed1i \u01b0u c\u1ee5c b\u1ed9 \u1edf m\u1ed7i b\u01b0\u1edbc v\u1edbi hy v\u1ecdng r\u1eb1ng nh\u1eefng l\u1ef1a ch\u1ecdn c\u1ee5c b\u1ed9 n\u00e0y s\u1ebd d\u1eabn \u0111\u1ebfn t\u1ed1i \u01b0u to\u00e0n c\u1ee5c, trong khi D&amp;C chia v\u1ea5n \u0111\u1ec1 th\u00e0nh c\u00e1c b\u00e0i to\u00e1n con v\u00e0 k\u1ebft h\u1ee3p c\u00e1c gi\u1ea3i ph\u00e1p c\u1ee7a ch\u00fang.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Quan \u0111i\u1ec3m t\u01b0\u01a1ng lai v\u00e0 c\u00f4ng ngh\u1ec7 li\u00ean quan \u0111\u1ebfn thu\u1eadt to\u00e1n ph\u00e2n chia \u0111\u1ec3 chinh ph\u1ee5c<\/h2>\n<p>H\u1ec7 th\u1ed1ng t\u00ednh to\u00e1n v\u00e0 ph\u00e2n t\u00e1n song song m\u1edf ra nh\u1eefng ch\u00e2n tr\u1eddi m\u1edbi cho c\u00e1c thu\u1eadt to\u00e1n D&amp;C. V\u1edbi b\u1ea3n ch\u1ea5t v\u1ed1n c\u00f3 c\u1ee7a vi\u1ec7c chia c\u00e1c v\u1ea5n \u0111\u1ec1 th\u00e0nh c\u00e1c v\u1ea5n \u0111\u1ec1 ph\u1ee5 \u0111\u1ed9c l\u1eadp, D&amp;C r\u1ea5t ph\u00f9 h\u1ee3p \u0111\u1ec3 th\u1ef1c hi\u1ec7n song song. Ch\u00fang ta c\u00f3 th\u1ec3 mong \u0111\u1ee3i s\u1ef1 gia t\u0103ng nhanh ch\u00f3ng c\u1ee7a c\u00e1c thu\u1eadt to\u00e1n D&amp;C \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf cho l\u1eadp tr\u00ecnh GPU, \u0111i\u1ec7n to\u00e1n \u0111\u00e1m m\u00e2y v\u00e0 h\u1ec7 th\u1ed1ng ph\u00e2n t\u00e1n.<\/p>\n<p>H\u01a1n n\u1eefa, c\u00e1ch ti\u1ebfp c\u1eadn ph\u00e2n chia \u0111\u1ec3 chinh ph\u1ee5c s\u1ebd ti\u1ebfp t\u1ee5c ph\u00f9 h\u1ee3p trong c\u00e1c l\u0129nh v\u1ef1c \u0111ang ph\u00e1t tri\u1ec3n nh\u01b0 h\u1ecdc m\u00e1y v\u00e0 khoa h\u1ecdc d\u1eef li\u1ec7u. C\u00e1c t\u00e1c v\u1ee5 x\u1eed l\u00fd d\u1eef li\u1ec7u l\u1edbn c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c x\u1eed l\u00fd hi\u1ec7u qu\u1ea3 b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng c\u00e1c ph\u01b0\u01a1ng ph\u00e1p D&amp;C, khi\u1ebfn ch\u00fang tr\u1edf th\u00e0nh c\u00f4ng c\u1ee5 kh\u00f4ng th\u1ec3 thi\u1ebfu trong k\u1ef7 nguy\u00ean d\u1eef li\u1ec7u l\u1edbn.<\/p>\n<h2>Hi\u1ec7p h\u1ed9i c\u00e1c m\u00e1y ch\u1ee7 proxy v\u1edbi thu\u1eadt to\u00e1n ph\u00e2n chia v\u00e0 chinh ph\u1ee5c<\/h2>\n<p>M\u00e1y ch\u1ee7 proxy c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p ph\u00e2n chia v\u00e0 chinh ph\u1ee5c \u0111\u1ec3 c\u00e2n b\u1eb1ng t\u1ea3i. L\u01b0u l\u01b0\u1ee3ng truy c\u1eadp \u0111\u1ebfn c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c chia cho nhi\u1ec1u m\u00e1y ch\u1ee7, \u201cchinh ph\u1ee5c\u201d v\u1ea5n \u0111\u1ec1 x\u1eed l\u00fd t\u1ea3i m\u1ea1ng n\u1eb7ng m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3. Chi\u1ebfn l\u01b0\u1ee3c n\u00e0y cho ph\u00e9p c\u1ea3i thi\u1ec7n th\u1eddi gian ph\u1ea3n h\u1ed3i v\u00e0 hi\u1ec7u su\u1ea5t t\u1ed5ng th\u1ec3.<\/p>\n<p>H\u01a1n n\u1eefa, khi x\u1eed l\u00fd vi\u1ec7c thu th\u1eadp d\u1eef li\u1ec7u ho\u1eb7c thu th\u1eadp d\u1eef li\u1ec7u tr\u00ean quy m\u00f4 l\u1edbn, ph\u01b0\u01a1ng ph\u00e1p ph\u00e2n chia v\u00e0 chinh ph\u1ee5c c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng. C\u00e1c m\u00e1y ch\u1ee7 proxy kh\u00e1c nhau c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c ch\u1ec9 \u0111\u1ecbnh \u0111\u1ec3 thu th\u1eadp d\u1eef li\u1ec7u t\u1eeb c\u00e1c ph\u1ea7n kh\u00e1c nhau c\u1ee7a trang web v\u00e0 d\u1eef li\u1ec7u \u0111\u01b0\u1ee3c thu th\u1eadp c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c k\u1ebft h\u1ee3p sau \u0111\u00f3, gi\u00fap thu th\u1eadp d\u1eef li\u1ec7u nhanh h\u01a1n v\u00e0 hi\u1ec7u qu\u1ea3 h\u01a1n.<\/p>\n<h2>Li\u00ean k\u1ebft li\u00ean quan<\/h2>\n<ol>\n<li><a href=\"https:\/\/mitpress.mit.edu\/books\/introduction-algorithms-third-edition\" target=\"_new\" rel=\"noopener nofollow\">Gi\u1edbi thi\u1ec7u v\u1ec1 thu\u1eadt to\u00e1n c\u1ee7a Cormen, Leiserson, Rivest v\u00e0 Stein<\/a><\/li>\n<li><a href=\"https:\/\/www.geeksforgeeks.org\/divide-and-conquer-introduction\/\" target=\"_new\" rel=\"noopener nofollow\">M\u00f4 h\u00ecnh ph\u00e2n chia v\u00e0 chinh ph\u1ee5c tr\u00ean GeeksforGeeks<\/a><\/li>\n<li><a href=\"https:\/\/www.khanacademy.org\/computing\/computer-science\/algorithms\/merge-sort\/a\/divide-and-conquer-algorithms\" target=\"_new\" rel=\"noopener nofollow\">Thu\u1eadt to\u00e1n chia \u0111\u1ec3 tr\u1ecb tr\u00ean Khan Academy<\/a><\/li>\n<\/ol>\n<p>Vi\u1ec7c kh\u00e1m ph\u00e1 to\u00e0n di\u1ec7n c\u00e1c thu\u1eadt to\u00e1n ph\u00e2n chia \u0111\u1ec3 chinh ph\u1ee5c n\u00e0y hy v\u1ecdng s\u1ebd mang \u0111\u1ebfn cho \u0111\u1ed9c gi\u1ea3 s\u1ef1 hi\u1ec3u bi\u1ebft s\u00e2u s\u1eafc h\u01a1n v\u1ec1 m\u00f4 h\u00ecnh c\u01a1 b\u1ea3n n\u00e0y trong khoa h\u1ecdc m\u00e1y t\u00ednh. Cho d\u00f9 \u0111\u00f3 l\u00e0 s\u1eafp x\u1ebfp danh s\u00e1ch c\u00e1c ph\u1ea7n t\u1eed, t\u00ecm ki\u1ebfm ph\u1ea7n t\u1eed trong c\u01a1 s\u1edf d\u1eef li\u1ec7u hay x\u1eed l\u00fd l\u01b0u l\u01b0\u1ee3ng truy c\u1eadp tr\u00ean m\u00e1y ch\u1ee7 proxy, ph\u01b0\u01a1ng ph\u00e1p ph\u00e2n chia v\u00e0 chinh ph\u1ee5c \u0111\u1ec1u mang l\u1ea1i gi\u1ea3i ph\u00e1p h\u1eefu hi\u1ec7u v\u00e0 hi\u1ec7u qu\u1ea3.<\/p>","protected":false},"featured_media":0,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-476870","wiki","type-wiki","status-publish","hentry"],"acf":{"faq_title":"Frequently Asked Questions about <mark>Divide and Conquer Algorithm: An In-depth Exploration<\/mark>","faq_items":[{"question":"What is the divide and conquer algorithm?","answer":"<p>The divide and conquer (D&amp;C) algorithm is an algorithmic paradigm that solves a problem by breaking it down into smaller sub-problems of the same type, solving these sub-problems, and combining their solutions to solve the original problem.<\/p>"},{"question":"Where did the divide and conquer algorithm originate from?","answer":"<p>The divide and conquer approach traces its roots back to ancient times, where it was used in strategic and mathematical contexts. However, in computer science, it was popularized in the mid-20th century through its use in early sorting and search algorithms.<\/p>"},{"question":"How does the divide and conquer algorithm work?","answer":"<p>The divide and conquer algorithm works in three main steps: divide the problem into smaller sub-problems, solve the sub-problems (usually by recursive calls), and then combine the solutions to form the solution for the main problem.<\/p>"},{"question":"What are the key features of the divide and conquer algorithm?","answer":"<p>The key features of the divide and conquer algorithm include its ability to simplify complex problems, its recursive approach, its efficiency, and its capability to be parallelized, as sub-problems are usually independent.<\/p>"},{"question":"What are some types of divide and conquer algorithms?","answer":"<p>Some types of divide and conquer algorithms include Binary Search, QuickSort, MergeSort, Strassen's Algorithm, and the algorithm to find the Closest Pair of Points.<\/p>"},{"question":"How are divide and conquer algorithms applied and what are some related problems?","answer":"<p>Divide and conquer algorithms are applied in various fields, including sorting, searching, numerical operations, matrix operations, and computational geometry. They can face challenges like excessive use of stack memory due to recursion and the need to decide the optimal problem size for the base case.<\/p>"},{"question":"How can divide and conquer algorithms be compared to dynamic programming and greedy algorithms?","answer":"<p>While all three are algorithm design paradigms used to solve optimization problems, dynamic programming solves problems by breaking them down into simpler subproblems and storing the results to avoid duplicate work. Greedy algorithms, on the other hand, make local optimal choices at each step hoping that these local choices will lead to a global optimum.<\/p>"},{"question":"What are the future perspectives and technologies related to divide and conquer algorithms?","answer":"<p>The future of divide and conquer algorithms lies in parallel computing and distributed systems, as they are well-suited for parallel execution. They are also expected to be increasingly relevant in fields like machine learning and data science.<\/p>"},{"question":"How can proxy servers be associated with divide and conquer algorithms?","answer":"<p>Proxy servers can use the divide and conquer approach for load balancing, dividing incoming traffic among multiple servers. This strategy improves response times and overall performance. In large scale data scraping or web crawling, different proxy servers can be assigned to gather data from different website sections, allowing for faster and more efficient data collection.<\/p>"}]},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki\/476870","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki"}],"about":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/types\/wiki"}],"version-history":[{"count":0,"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki\/476870\/revisions"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/media?parent=476870"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}