{"id":23507,"date":"2023-01-27T17:41:22","date_gmt":"2023-01-27T10:41:22","guid":{"rendered":"https:\/\/kiencang.net\/?p=23507"},"modified":"2023-08-26T18:36:06","modified_gmt":"2023-08-26T11:36:06","slug":"thuat-toan-sap-xep-quick-sort","status":"publish","type":"post","link":"https:\/\/kiencang.net\/thuat-toan-sap-xep-quick-sort\/","title":{"rendered":"Thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp nhanh (quick sort), gi\u1ea3i th\u00edch k\u00e8m v\u00ed d\u1ee5 trong PHP [serial v\u1ec1 c\u00e1c thu\u1eadt to\u00e1n c\u01a1 b\u1ea3n trong l\u1eadp tr\u00ecnh]"},"content":{"rendered":"\n

T\u00ean nghe \u0111\u00e3 th\u1ea5y h\u1ea5p d\u1eabn r\u1ed3i \u0111\u00fang kh\u00f4ng c\u00e1c b\u1ea1n, d\u00e2n l\u1eadp tr\u00ecnh n\u00f3i r\u1eb1ng, tr\u00ean c\u00e1c m\u1ea3ng ng\u1eabu nhi\u00ean v\u00e0 c\u00f3 s\u1ed1 l\u01b0\u1ee3ng t\u01b0\u01a1ng \u0111\u1ed1i, quick sort c\u00f3 t\u1ed1c \u0111\u1ed9 s\u1eafp x\u1ebfp t\u1ed1t h\u01a1n \u0111\u00e1ng k\u1ec3 so v\u1edbi bubble sort (s\u1eafp x\u1ebfp n\u1ed5i b\u1ecdt)<\/a> v\u00e0 t\u01b0\u01a1ng \u0111\u01b0\u01a1ng merge sort (s\u1eafp x\u1ebfp tr\u1ed9n)<\/a>, c\u1ee5 th\u1ec3 s\u1ed1 b\u01b0\u1edbc c\u1ea7n thi\u1ebft c\u1ee7a quick sort \u0111\u1ec3 s\u1eafp x\u1ebfp ho\u00e0n th\u00e0nh y\u00eau c\u1ea7u l\u00e0 \u00edt h\u01a1n [\u0111\u1ed9 ph\u1ee9c t\u1ea1p c\u1ee7a thu\u1eadt to\u00e1n l\u00e0 O(n log n)]. Gi\u1edd ch\u00fang ta s\u1ebd c\u00f9ng t\u00ecm hi\u1ec3u xem n\u00f3 nh\u01b0 th\u1ebf n\u00e0o nh\u00e9.<\/p>\n\n\n\n

B\u00e0i to\u00e1n, cho d\u00e3y s\u1ed1: 4, 2, 9, 7, 3, 1, 6, 8, 10, 5<\/p>\n\n\n\n

H\u00e3y s\u1eafp x\u1ebfp n\u00f3 theo th\u1ee9 t\u1ef1 t\u1eeb nh\u1ecf \u0111\u1ebfn l\u1edbn.<\/p>\n\n\n\n

\u0110\u00e2y l\u00e0 \u0111o\u1ea1n m\u00e3 m\u1eabu PHP s\u1eed d\u1ee5ng \u00fd t\u01b0\u1edfng v\u1ec1 quick sort:<\/p>\n\n\n\n

<?php\nfunction kc_quickSort($arr) {\n    if (count($arr) <= 1) return $arr;\n    \n    $pivot = $arr[0];\n    $left = $right = array();\n    \n    for ($i = 1; $i < count($arr); $i++) {\n        if ($arr[$i] < $pivot) {\n            $left[] = $arr[$i];\n        } else {\n            $right[] = $arr[$i];\n        }\n    }\n    \n    $left = kc_quickSort($left);\n    $right = kc_quickSort($right);\n    return array_merge($left, array($pivot), $right);\n}\n\n$arr = array(4, 2, 9, 7, 3, 1, 6, 8, 10, 5);\n$arr = kc_quickSort($arr);\n\n\/\/ hi\u1ec3n th\u1ecb k\u1ebft qu\u1ea3\nprint_r($arr);<\/code><\/pre>\n\n\n\n
R\u1ea5t ng\u1eafn g\u1ecdn \u0111\u00fang kh\u00f4ng c\u00e1c b\u1ea1n, nh\u01b0ng kh\u00f4ng d\u1ec5 \u0111\u1ec3 hi\u1ec3u. \u0110i\u1ec3m kh\u00e1c bi\u1ec7t l\u1edbn nh\u1ea5t v\u1edbi bubble sort \u1edf \u0111\u00e2y l\u00e0 quick sort s\u1eed d\u1ee5ng k\u1ef9 thu\u1eadt \u0111\u1ec7 quy<\/a>, m\u1ed9t k\u1ef9 thu\u1eadt trong l\u1eadp tr\u00ecnh m\u00e0 m\u1ed9t h\u00e0m s\u1ebd g\u1ecdi l\u1ea1i ch\u00ednh b\u1ea3n th\u00e2n n\u00f3 \u0111\u1ec3 gi\u1ea3i quy\u1ebft c\u00e1c v\u1ea5n \u0111\u1ec1 con c\u1ee7a ch\u00ednh n\u00f3 cho \u0111\u1ebfn khi v\u1ea5n \u0111\u1ec1 \u0111\u01b0\u1ee3c gi\u1ea3i quy\u1ebft xong.<\/p>\n\n\n\n
Tr\u1eddi \u01a1i, v\u1eady \u0111\u1ec7 quy l\u00e0 c\u00e1i g\u00ec v\u1eady?<\/p>\n\n\n\n
Ch\u00fang ta c\u1ea7n m\u1ed9t v\u00ed d\u1ee5 \u0111\u01a1n gi\u1ea3n v\u1ec1 \u0111\u1ec7 quy trong PHP, ch\u1eb3ng h\u1ea1n \u0111\u00e2y l\u00e0 h\u00e0m t\u00ednh giai th\u1eeba s\u1eed d\u1ee5ng \u0111\u1ec7 quy:<\/p>\n\n\n\n
function factorial($n){\n    if($n == 0){\n        return 1;\n    }\n    else{\n        return $n * factorial($n-1);\n    }\n}\n\necho factorial(6); \/\/ Output: 720<\/code><\/pre>\n\n\n\n
Ch\u00fang ta xem n\u00f3 n\u00f3i g\u00ec:<\/p>\n\n\n\n
    \n
  • N\u1ebfu n = 0 th\u00ec tr\u1ea3 v\u1ec1 k\u1ebft qu\u1ea3 1 v\u00e0 kh\u00f4ng l\u00e0m g\u00ec n\u1eefa;<\/li>\n\n\n\n
  • N\u1ebfu n kh\u00e1c 1 th\u00ec tr\u1ea3 v\u1ec1 n * factorial($n-1)<\/li>\n<\/ul>\n\n\n\n
    C\u00e1i n\u00e0y $n * factorial($n-1);<\/code> ch\u00ednh l\u00e0 \u0111\u1ec7 quy. C\u00e1ch ho\u1ea1t \u0111\u1ed9ng c\u1ee7a n\u00f3 \u0111\u01b0\u1ee3c gi\u1ea3i th\u00edch nh\u01b0 sau:<\/p>\n\n\n\n
      \n
    • factorial(6) = 6 * factorial(5)<\/li>\n\n\n\n
    • factorial(5) = 5 * factorial(4)<\/li>\n\n\n\n
    • factorial(4) = 4 * factorial(3)<\/li>\n\n\n\n
    • factorial(3) = 3 * factorial(2)<\/li>\n\n\n\n
    • factorial(2) = 2 * factorial(1)<\/li>\n\n\n\n
    • factorial(1) = 1 * factorial(0)<\/li>\n\n\n\n
    • factorial(0) = 1<\/li>\n<\/ul>\n\n\n\n
      Nh\u01b0 v\u1eady ch\u00fang ta th\u1ea5y r\u1eb1ng factorial(6) \u0111\u01b0\u1ee3c t\u00ednh th\u00f4ng qua factorial(5) v\u00e0 c\u1ee9 th\u1ebf cho \u0111\u1ebfn m\u1ed1c kh\u1edfi \u0111\u1ea7u c\u1ee7a n\u00f3 l\u00e0 factorial(0) m\u00e0 ta bi\u1ebft gi\u00e1 tr\u1ecb ch\u00ednh x\u00e1c v\u00e0 \u0111\u1ec7 quy d\u1eebng l\u1ea1i \u1edf \u0111\u00e2y, k\u1ebft qu\u1ea3 l\u00e0 factorial(6) = 6*5*4*3*2*1 = 720. Gi\u1ea3 s\u1eed b\u1ea1n thay:<\/p>\n\n\n\n
          if($n == 0){\n        return 2;\n    } <\/code><\/pre>\n\n\n\n
      K\u1ebft qu\u1ea3 s\u1ebd kh\u00e1c, b\u1ea1n h\u00e3y t\u1ef1 th\u1eed xem th\u1ebf n\u00e0o!<\/p>\n\n\n\n
      Giai th\u1eeba c\u00f3 l\u1ebd l\u00e0 v\u00ed d\u1ee5 d\u1ec5 hi\u1ec3u nh\u1ea5t v\u1ec1 \u0111\u1ec7 quy, gi\u1edd ch\u00fang ta quay l\u1ea1i c\u00e1ch gi\u1ea3i quy\u1ebft c\u1ee7a quick sort.<\/p>\n\n\n\n
      Tr\u01b0\u1edbc h\u1ebft ta xem l\u1ea1i \u00fd t\u01b0\u1edfng t\u1ed5ng quan c\u1ee7a n\u00f3:<\/p>\n\n\n\n
        \n
      • N\u00f3 l\u1ea5y m\u1ed9t gi\u00e1 tr\u1ecb \u0111\u1ec3 so s\u00e1nh, \u1edf \u0111\u00e2y l\u00e0 $pivot<\/code><\/li>\n\n\n\n
      • N\u00f3 t\u1ea1o ra 2 m\u1ea3ng ph\u1ee5 l\u00e0 $left<\/code> v\u00e0 $right<\/code><\/li>\n\n\n\n
      • C\u00e1c ph\u1ea7n t\u1eed trong m\u1ea3ng c\u1ea7n s\u1eafp x\u1ebfp ban \u0111\u1ea7u ($arr<\/code>) \u0111\u01b0\u1ee3c so s\u00e1nh l\u1ea7n l\u01b0\u1ee3t v\u1edbi $pivot<\/code>, v\u00e0 n\u1ebfu nh\u1ecf h\u01a1n, ph\u1ea7n t\u1eed n\u00e0y \u0111\u01b0\u1ee3c \u0111\u01b0a v\u00e0o m\u1ea3ng $left<\/code>, v\u00e0 n\u1ebfu l\u1edbn h\u01a1n th\u00ec \u0111\u01b0a v\u00e0o m\u1ea3ng $right<\/code> <\/li>\n\n\n\n
      • Ti\u1ebfp \u0111\u1ebfn n\u00f3 s\u1eed d\u1ee5ng \u0111\u1ec7 quy v\u1edbi c\u1ea3 $left v\u00e0 $right:<\/li>\n<\/ul>\n\n\n\n
        $left = kc_quickSort($left);\n$right = kc_quickSort($right);<\/code><\/pre>\n\n\n\n
        \u0110\u1ec7 quy s\u1ebd d\u1eebng l\u1ea1i khi ch\u1ec9 c\u00f2n m\u1ed9t ph\u1ea7n t\u1eed. Cu\u1ed1i c\u00f9ng n\u00f3 g\u1ed9p c\u00e1c m\u1ea3ng l\u1ea1i v\u1edbi nhau b\u1eb1ng l\u1ec7nh:<\/p>\n\n\n\n
        array_merge($left, array($pivot), $right);<\/code><\/pre>\n\n\n\n
        Gi\u1edd h\u00e3y xem qu\u00e1 tr\u00ecnh c\u1ee7a n\u00f3 v\u1edbi d\u00e3y 4, 2, 9, 7, 3, 1, 6, 8, 10, 5<\/p>\n\n\n\n
        \u1ede \u0111\u00e2y <\/p>\n\n\n\n
          \n
        • $pivot = 4<\/li>\n\n\n\n
        • $left = 2, 3, 1<\/li>\n\n\n\n
        • $right = 9, 7, 6, 8, 10, 5<\/li>\n<\/ul>\n\n\n\n
          Ti\u1ebfp \u0111\u1ebfn $left l\u1ea1i \u0111\u01b0\u1ee3c \u0111\u1ec7 quy:<\/p>\n\n\n\n
            \n
          • $pivot_left = 2<\/li>\n\n\n\n
          • $left_left = 1<\/li>\n\n\n\n
          • $right_left = 3<\/li>\n\n\n\n
          • $arr_left = 1, 2, 3<\/li>\n<\/ul>\n\n\n\n
            \u1ede \u0111\u00e2y $left_left<\/code>, $right_left<\/code> ng\u1eebng \u0111\u1ec7 quy v\u00ec n\u00f3 \u0111\u00e3 ch\u1ea1m \u0111\u1ebfn \u0111i\u1ec1u ki\u1ec7n ch\u1ec9 c\u00f2n m\u1ed9t ph\u1ea7n t\u1eed trong qu\u00e1 tr\u00ecnh chia t\u00e1ch.<\/p>\n\n\n\n
            Ph\u1ea7n \u0111\u1ec7 quy c\u1ee7a $right:<\/p>\n\n\n\n
              \n
            • $pivot_right = 9<\/li>\n\n\n\n
            • $left_right = 7, 6, 8, 5<\/li>\n\n\n\n
            • $right_right = 10<\/li>\n\n\n\n
            • $arr_right = 7, 6, 8, 5, 9, 10<\/li>\n<\/ul>\n\n\n\n
              $arr t\u1ed5ng h\u1ee3p sau l\u1ea7n \u0111\u1ec7 quy \u0111\u1ea7u ti\u00ean (c\u1ee7a $left v\u00e0 $right): 1, 2, 3, 4, 7, 6, 8, 5, 9, 10<\/p>\n\n\n\n
              B\u1ea1n \u0111\u00e3 th\u1ea5y n\u00f3 c\u00f3 s\u1ef1 s\u1eafp x\u1ebfp d\u1ea7n r\u1ed3i \u0111\u00fang kh\u00f4ng? Ng\u1ea1c nhi\u00ean th\u1eadt! S\u1ef1 x\u00e1o tr\u1ed9n ch\u1ec9 c\u00f2n \u1edf ph\u1ea7n 7, 6, 8, 5. S\u1ef1 \u0111\u1ec7 quy ti\u1ebfp c\u1ee7a $left_right s\u1ebd gi\u1ea3i quy\u1ebft n\u1ed1t ph\u1ea7n n\u00e0y.<\/p>\n\n\n\n
              Quick sort th\u1ef1c hi\u1ec7n qu\u00e1 tr\u00ecnh chia \u0111\u1ec3 tr\u1ecb, m\u1ed9t m\u1ea3ng l\u1edbn \u0111\u01b0\u1ee3c chia l\u00e0m \u0111\u00f4i (th\u00e0nh c\u00e1c m\u1ea3ng nh\u1ecf h\u01a1n) \u0111\u1ec3 s\u1eafp x\u1ebfp, sau \u0111\u00f3 c\u00e1c m\u1ea3ng nh\u1ecf h\u01a1n c\u0169ng \u0111\u01b0\u1ee3c l\u00e0m nh\u01b0 v\u1eady (\u0111\u1ec7 quy), trong qu\u00e1 tr\u00ecnh \u0111\u00f3 vi\u1ec7c s\u1eafp x\u1ebfp \u0111\u01b0\u1ee3c x\u1eed l\u00fd d\u1ea7n d\u1ea7n, v\u00e0 \u0111\u1ebfn cu\u1ed1i c\u00f9ng th\u1ee9 t\u1ef1 \u0111\u01b0\u1ee3c thi\u1ebft l\u1eadp.<\/p>\n","protected":false},"excerpt":{"rendered":"
              T\u00ean nghe \u0111\u00e3 th\u1ea5y h\u1ea5p d\u1eabn r\u1ed3i \u0111\u00fang kh\u00f4ng c\u00e1c b\u1ea1n, d\u00e2n l\u1eadp tr\u00ecnh n\u00f3i r\u1eb1ng, tr\u00ean c\u00e1c m\u1ea3ng ng\u1eabu nhi\u00ean v\u00e0 c\u00f3 s\u1ed1 l\u01b0\u1ee3ng t\u01b0\u01a1ng \u0111\u1ed1i, quick sort c\u00f3 t\u1ed1c \u0111\u1ed9 s\u1eafp x\u1ebfp t\u1ed1t h\u01a1n \u0111\u00e1ng k\u1ec3 so v\u1edbi bubble sort (s\u1eafp x\u1ebfp n\u1ed5i b\u1ecdt) v\u00e0 t\u01b0\u01a1ng \u0111\u01b0\u01a1ng merge sort (s\u1eafp x\u1ebfp tr\u1ed9n), c\u1ee5 …<\/p>\n","protected":false},"author":1,"featured_media":24648,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[333],"tags":[334],"yoast_head":"\nThu\u1eadt to\u00e1n s\u1eafp x\u1ebfp nhanh (quick sort), gi\u1ea3i th\u00edch k\u00e8m v\u00ed d\u1ee5 trong PHP [serial v\u1ec1 c\u00e1c thu\u1eadt to\u00e1n c\u01a1 b\u1ea3n trong l\u1eadp tr\u00ecnh] • Ki\u1ebfn 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