{"id":50943,"date":"2023-12-19T21:27:42","date_gmt":"2023-12-19T14:27:42","guid":{"rendered":"https:\/\/masterskills.org\/blog\/top-10-cau-hoi-phong-van-thuat-toan-va-goi-y-cach-tra-loi.html"},"modified":"2023-12-19T21:27:42","modified_gmt":"2023-12-19T14:27:42","slug":"top-10-cau-hoi-phong-van-thuat-toan-va-goi-y-cach-tra-loi","status":"publish","type":"post","link":"https:\/\/masterskills.org\/blog\/top-10-cau-hoi-phong-van-thuat-toan-va-goi-y-cach-tra-loi.html","title":{"rendered":"Top 10+ C\u00e2u H\u1ecfi Ph\u1ecfng V\u1ea5n Thu\u1eadt To\u00e1n V\u00e0 G\u1ee3i \u00dd C\u00e1ch Tr\u1ea3 L\u1eddi"},"content":{"rendered":"
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N\u1ebfu b\u1ea1n chu\u1ea9n b\u1ecb tham gia v\u00e0o m\u1ed9t cu\u1ed9c ph\u1ecfng v\u1ea5n thu\u1eadt to\u00e1n, v\u1eady th\u00ec \u0111\u1eebng b\u1ecf qua b\u00e0i vi\u1ebft d\u01b0\u1edbi \u0111\u00e2y. Trong b\u00e0i vi\u1ebft n\u00e0y, Masterskills s\u1ebd chia s\u1ebb \u0111\u1ebfn b\u1ea1n c\u00e1c c\u00e2u h\u1ecfi ph\u1ecfng v\u1ea5n thu\u1eadt to\u00e1n<\/strong> th\u01b0\u1eddng g\u1eb7p, c\u0169ng nh\u01b0 c\u00e1ch tr\u1ea3 l\u1eddi \u201cghi \u0111i\u1ec3m\u201d.<\/p>\n

1. Thu\u1eadt to\u00e1n \u0111\u01b0\u1ee3c hi\u1ec3u l\u00e0 g\u00ec?<\/strong><\/h2>\n

Thu\u1eadt to\u00e1n l\u00e0 m\u1ed9t lo\u1ea1t c\u00e1c b\u01b0\u1edbc t\u00ednh to\u00e1n, s\u1eed d\u1ee5ng m\u1ed9t ho\u1eb7c nhi\u1ec1u \u0111\u1ea7u v\u00e0o, \u0111\u1ec3 t\u1ea1o ra m\u1ed9t \u0111\u1ea7u ra. C\u00f3 nhi\u1ec1u c\u00e1ch \u0111\u1ec3 bi\u1ec3u di\u1ec5n thu\u1eadt to\u00e1n, c\u00f3 th\u1ec3 l\u00e0 b\u1eb1ng ng\u00f4n ng\u1eef t\u1ef1 nhi\u00ean \u0111\u01a1n gi\u1ea3n ho\u1eb7c d\u01b0\u1edbi d\u1ea1ng m\u00e3 gi\u1ea3, t\u00f9y thu\u1ed9c v\u00e0o y\u00eau c\u1ea7u c\u1ee5 th\u1ec3 c\u1ee7a b\u00e0i to\u00e1n v\u00e0 ng\u01b0\u1eddi vi\u1ebft thu\u1eadt to\u00e1n.<\/p>\n

2. Quicksort l\u00e0 g\u00ec?<\/strong><\/h2>\n

\u0110\u00e2y l\u00e0 m\u1ed9t trong c\u00e1c c\u00e2u h\u1ecfi thu\u1eadt to\u00e1n khi ph\u1ecfng v\u1ea5n \u0111\u1ec3 ki\u1ec3m tra kh\u1ea3 n\u0103ng \u00e1p d\u1ee5ng thu\u1eadt to\u00e1n c\u1ee7a b\u1ea1n \u1edf m\u1ee9c c\u01a1 b\u1ea3n. Thu\u1eadt to\u00e1n Quicksort l\u00e0 m\u1ed9t ph\u01b0\u01a1ng ph\u00e1p s\u1eafp x\u1ebfp nhanh cho c\u00e1c truy v\u1ea5n ho\u1eb7c danh s\u00e1ch. N\u00f3 s\u1eed d\u1ee5ng k\u1ef9 thu\u1eadt \u2018ph\u00e2n chia v\u00e0 chinh ph\u1ee5c\u2019, chia danh s\u00e1ch th\u00e0nh ba ph\u1ea7n:<\/p>\n

    \n
  • M\u1ed9t ph\u1ea7n t\u1eed pivot \u0111\u01b0\u1ee3c ch\u1ecdn t\u1eeb m\u1ea3ng.<\/li>\n
  • C\u00e1c ph\u1ea7n t\u1eed nh\u1ecf h\u01a1n pivot \u0111\u01b0\u1ee3c \u0111\u1eb7t \u1edf b\u00ean tr\u00e1i \u0111\u1ec3 t\u1ea1o m\u1ea3ng con b\u00ean tr\u00e1i.<\/li>\n
  • C\u00e1c ph\u1ea7n t\u1eed l\u1edbn h\u01a1n pivot \u0111\u01b0\u1ee3c \u0111\u1eb7t \u1edf b\u00ean ph\u1ea3i \u0111\u1ec3 t\u1ea1o m\u1ea3ng con b\u00ean ph\u1ea3i.<\/li>\n<\/ul>\n

    Trong m\u1ed7i m\u1ea3ng con, qu\u00e1 tr\u00ecnh l\u1eb7p l\u1ea1i v\u1edbi vi\u1ec7c ch\u1ecdn m\u1ed9t ph\u1ea7n t\u1eed tr\u1ee5c v\u00e0 s\u1eafp x\u1ebfp c\u00e1c gi\u00e1 tr\u1ecb c\u00f2n l\u1ea1i.<\/p>\n

    Ph\u1ee9c t\u1ea1p v\u1ec1 th\u1eddi gian:<\/strong><\/p>\n

      \n
    • Tr\u01b0\u1eddng h\u1ee3p t\u1ed1t nh\u1ea5t: O(nlogn) \u2013 Khi pivot g\u1ea7n trung t\u00e2m.<\/li>\n
    • Tr\u01b0\u1eddng h\u1ee3p t\u1ed3i t\u1ec7 nh\u1ea5t: O(n2) \u2013 Khi pivot l\u00e0 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t ho\u1eb7c nh\u1ecf nh\u1ea5t.<\/li>\n
    • Tr\u01b0\u1eddng h\u1ee3p Trung b\u00ecnh: O(nlogn).<\/li>\n<\/ul>\n

      3. Ph\u1ea7n t\u1eed Pivot c\u00f3 ch\u1ee9c n\u0103ng g\u00ec?<\/strong><\/h2>\n

      B\u1ea1n c\u00f3 th\u1ec3 tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi n\u00e0y b\u1eb1ng c\u00e1ch gi\u1ea3i th\u00edch r\u1eb1ng ph\u1ea7n t\u1eed pivot l\u00e0 ph\u1ea7n t\u1eed \u0111\u01b0\u1ee3c l\u1ef1a ch\u1ecdn t\u1eeb m\u1ea3ng ho\u1eb7c ma tr\u1eadn \u0111ang \u0111\u01b0\u1ee3c x\u1eed l\u00fd, v\u00e0 n\u00f3 \u0111\u00f3ng vai tr\u00f2 l\u00e0 ph\u1ea7n t\u1eed \u0111\u1ea7u ti\u00ean m\u00e0 thu\u1eadt to\u00e1n s\u1ebd s\u1eed d\u1ee5ng \u0111\u1ec3 th\u1ef1c hi\u1ec7n c\u00e1c ph\u00e9p t\u00ednh.<\/p>\n

      C\u00f3 nhi\u1ec1u c\u00e1ch \u0111\u1ec3 l\u1ef1a ch\u1ecdn m\u1ed9t ph\u1ea7n t\u1eed pivot. Trong tr\u01b0\u1eddng h\u1ee3p m\u1ea3ng, c\u00f3 th\u1ec3 l\u00e0 ph\u1ea7n t\u1eed cu\u1ed1i c\u00f9ng ho\u1eb7c \u0111\u1ea7u ti\u00ean, \u0111\u01b0\u1ee3c ch\u1ecdn t\u1eeb ph\u1ea7n gi\u1eefa, ho\u1eb7c th\u1eadm ch\u00ed l\u00e0 l\u1ef1a ch\u1ecdn ng\u1eabu nhi\u00ean. Ph\u1ee5 thu\u1ed9c v\u00e0o thu\u1eadt to\u00e1n c\u1ee5 th\u1ec3, c\u00e1ch ch\u1ecdn ph\u1ea7n t\u1eed pivot c\u00f3 th\u1ec3 \u1ea3nh h\u01b0\u1edfng \u0111\u1ebfn hi\u1ec7u su\u1ea5t c\u1ee7a thu\u1eadt to\u00e1n v\u00e0 \u0111\u00f4i khi quy\u1ebft \u0111\u1ecbnh n\u00e0y c\u00f3 th\u1ec3 t\u1ea1o ra k\u1ebft qu\u1ea3 t\u1ed1t h\u01a1n.<\/p>\n

      4. S\u1ef1 ph\u1ee9c t\u1ea1p th\u1eddi gian c\u1ee7a m\u1ed9t thu\u1eadt to\u00e1n th\u1ec3 hi\u1ec7n \u0111i\u1ec1u g\u00ec?<\/strong><\/h2>\n

      \u0110\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian c\u1ee7a m\u1ed9t thu\u1eadt to\u00e1n \u0111\u1ec1 c\u1eadp \u0111\u1ebfn s\u1ed1 l\u1ea7n l\u1eb7p l\u1ea1i c\u1ea7n thi\u1ebft \u0111\u1ec3 thu\u1eadt to\u00e1n ho\u00e0n th\u00e0nh khi \u0111\u1ea7u v\u00e0o c\u00f3 k\u00edch th\u01b0\u1edbc nh\u1ea5t \u0111\u1ecbnh.<\/p>\n

      5. Gi\u1ea3i th\u00edch c\u00e1c k\u00fd hi\u1ec7u kh\u00e1c nhau \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng khi n\u00f3i \u0111\u1ebfn \u0111\u1ed9 ph\u1ee9c t\u1ea1p v\u1ec1 th\u1eddi gian?<\/strong><\/h2>\n

      Qua c\u00e2u tr\u1ea3 l\u1eddi c\u1ee7a b\u1ea1n v\u1edbi c\u00e2u h\u1ecfi n\u00e0y, ng\u01b0\u1eddi ph\u1ecfng v\u1ea5n c\u00f3 th\u1ec3 hi\u1ec3u h\u01a1n v\u1ec1 m\u1ee9c \u0111\u1ed9 hi\u1ec3u bi\u1ebft v\u1ec1 c\u00e1ch ho\u1ea1t \u0111\u1ed9ng c\u1ee7a c\u00e1c thu\u1eadt to\u00e1n v\u00e0 kh\u1ea3 n\u0103ng \u0111i\u1ec1u ch\u1ec9nh ch\u00fang \u0111\u1ec3 \u0111\u1ea1t \u0111\u01b0\u1ee3c k\u1ebft qu\u1ea3 mong mu\u1ed1n.<\/p>\n

      Vi\u1ec7c s\u1eed d\u1ee5ng k\u00fd hi\u1ec7u gi\u00fap d\u1ef1 \u0111o\u00e1n hi\u1ec7u su\u1ea5t c\u1ee7a thu\u1eadt to\u00e1n. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 k\u00fd hi\u1ec7u b\u1ea1n c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng \u0111\u1ec3 \u0111\u00e1nh gi\u00e1 ph\u1ee9c t\u1ea1p th\u1eddi gian:<\/p>\n

        \n
      • Big Omega: Bi\u1ec3u th\u1ecb s\u1ef1 l\u1eb7p l\u1ea1i \u201cnhi\u1ec1u h\u01a1n ho\u1eb7c gi\u1ed1ng nh\u01b0\u201d. L\u00e0 gi\u1edbi h\u1ea1n d\u01b0\u1edbi ch\u1eb7t ch\u1ebd c\u1ee7a s\u1ef1 t\u0103ng tr\u01b0\u1edfng th\u1eddi gian ch\u1ea1y c\u1ee7a thu\u1eadt to\u00e1n, th\u01b0\u1eddng l\u00e0 tr\u01b0\u1eddng h\u1ee3p ph\u1ee9c t\u1ea1p nh\u1ea5t.<\/li>\n
      • Big-O: \u0110\u01b0\u1ee3c hi\u1ec3u l\u00e0 s\u1ed1 l\u1ea7n l\u1eb7p l\u1ea1i \u201c\u00edt h\u01a1n ho\u1eb7c gi\u1ed1ng nh\u01b0\u201d. L\u00e0 gi\u1edbi h\u1ea1n tr\u00ean ch\u1eb7t ch\u1ebd c\u1ee7a s\u1ef1 t\u0103ng tr\u01b0\u1edfng th\u1eddi gian ch\u1ea1y c\u1ee7a thu\u1eadt to\u00e1n, th\u01b0\u1eddng l\u00e0 tr\u01b0\u1eddng h\u1ee3p x\u1ea5u nh\u1ea5t.<\/li>\n
      • Big Theta: \u0110\u1ea1i di\u1ec7n cho s\u1ef1 l\u1eb7p l\u1ea1i \u201cgi\u1ed1ng nh\u01b0\u201d. V\u1eeba l\u00e0 gi\u1edbi h\u1ea1n tr\u00ean ch\u1eb7t ch\u1ebd v\u00e0 l\u00e0 gi\u1edbi h\u1ea1n d\u01b0\u1edbi ch\u1eb7t ch\u1ebd v\u1ec1 s\u1ef1 t\u0103ng tr\u01b0\u1edfng th\u1eddi gian ch\u1ea1y c\u1ee7a thu\u1eadt to\u00e1n.<\/li>\n
      • Little-O: Bi\u1ec3u th\u1ecb s\u1ef1 l\u1eb7p l\u1ea1i \u201c\u00edt h\u01a1n\u201d. L\u00e0 gi\u1edbi h\u1ea1n tr\u00ean kh\u00f4ng ch\u1eb7t ch\u1ebd v\u1ec1 m\u1eb7t ti\u1ec7m c\u1eadn.<\/li>\n
      • Little Omega: \u0110\u1ea1i di\u1ec7n cho s\u1ef1 l\u1eb7p l\u1ea1i \u201cnhi\u1ec1u h\u01a1n\u201d. L\u00e0 gi\u1edbi h\u1ea1n d\u01b0\u1edbi kh\u00f4ng ch\u1eb7t ch\u1ebd v\u1ec1 m\u1eb7t ti\u1ec7m c\u1eadn.<\/li>\n<\/ul>\n

        6. Ho\u1ea1t \u0111\u1ed9ng c\u1ee7a t\u00ecm ki\u1ebfm nh\u1ecb ph\u00e2n nh\u01b0 th\u1ebf n\u00e0o?<\/strong><\/h2>\n

        T\u00ecm ki\u1ebfm nh\u1ecb ph\u00e2n \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng \u0111\u1ec3 \u0111\u1ecbnh v\u1ecb m\u1ed9t ph\u1ea7n t\u1eed trong m\u1ed9t m\u1ea3ng \u0111\u00e3 \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp. Qu\u00e1 tr\u00ecnh b\u1eaft \u0111\u1ea7u b\u1eb1ng vi\u1ec7c ki\u1ec3m tra ph\u1ea7n t\u1eed \u1edf gi\u1eefa m\u1ea3ng. N\u1ebfu ph\u1ea7n t\u1eed c\u1ea7n t\u00ecm kh\u1edbp v\u1edbi m\u1ee5c gi\u1eefa, t\u00ecm ki\u1ebfm k\u1ebft th\u00fac th\u00e0nh c\u00f4ng. Ng\u01b0\u1ee3c l\u1ea1i, n\u1ebfu ph\u1ea7n t\u1eed \u0111\u00edch l\u1edbn h\u01a1n ph\u1ea7n t\u1eed gi\u1eefa, t\u00ecm ki\u1ebfm \u0111\u01b0\u1ee3c chuy\u1ec3n sang n\u1eeda tr\u00ean c\u1ee7a m\u1ea3ng (t\u1ea5t c\u1ea3 gi\u00e1 tr\u1ecb l\u1edbn h\u01a1n). N\u1ebfu ph\u1ea7n t\u1eed \u0111\u00edch th\u1ea5p h\u01a1n ph\u1ea7n t\u1eed gi\u1eefa, qu\u00e1 tr\u00ecnh t\u00ecm ki\u1ebfm di chuy\u1ec3n xu\u1ed1ng n\u1eeda d\u01b0\u1edbi c\u1ee7a m\u1ea3ng (t\u1ea5t c\u1ea3 gi\u00e1 tr\u1ecb nh\u1ecf h\u01a1n).<\/p>\n

        Ph\u1ee9c t\u1ea1p v\u1ec1 th\u1eddi gian:<\/strong><\/p>\n

          \n
        • Tr\u01b0\u1eddng h\u1ee3p t\u1ed1t nh\u1ea5t: O(1) \u2013 X\u1ea3y ra khi gi\u00e1 tr\u1ecb c\u1ea7n t\u00ecm kh\u1edbp v\u1edbi m\u1ee5c \u1edf gi\u1eefa t\u1eeb \u0111\u1ea7u.<\/li>\n
        • Tr\u01b0\u1eddng h\u1ee3p x\u1ea5u nh\u1ea5t: O(logn) \u2013 X\u1ea3y ra khi gi\u00e1 tr\u1ecb n\u1eb1m \u1edf b\u01b0\u1edbc cu\u1ed1i c\u00f9ng ho\u1eb7c kh\u00f4ng t\u1ed3n t\u1ea1i trong m\u1ea3ng.<\/li>\n
        • Tr\u01b0\u1eddng h\u1ee3p trung b\u00ecnh: O(logn).<\/li>\n<\/ul>\n

          7. S\u1eafp x\u1ebfp theo \u0111\u1ed1ng \u0111\u01b0\u1ee3c hi\u1ec3u l\u00e0 g\u00ec?<\/strong><\/h2>\n

          S\u1eafp x\u1ebfp theo \u0111\u1ed1ng li\u00ean quan \u0111\u1ebfn vi\u1ec7c so s\u00e1nh c\u00e1c m\u1ee5c b\u1eb1ng thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp. \u0110\u1ea7u v\u00e0o \u0111\u01b0\u1ee3c ph\u00e2n chia th\u00e0nh v\u00f9ng \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp v\u00e0 v\u00f9ng ch\u01b0a \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp. Quy\u1ebft \u0111\u1ecbnh v\u1ec1 vi\u1ec7c m\u1ee5c n\u00e0o \u0111\u01b0\u1ee3c chuy\u1ec3n sang v\u00f9ng \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp ph\u1ee5 thu\u1ed9c v\u00e0o lo\u1ea1i \u0111\u1ed1ng, c\u00f3 th\u1ec3 l\u00e0 \u0111\u1ed1ng t\u1ed1i \u0111a ho\u1eb7c \u0111\u1ed1ng t\u1ed1i thi\u1ec3u. Trong \u0111\u1ed1ng t\u1ed1i \u0111a, ph\u1ea7n t\u1eed l\u1edbn nh\u1ea5t \u1edf g\u1ed1c, trong khi \u0111\u1ed1i v\u1edbi \u0111\u1ed1ng t\u1ed1i thi\u1ec3u, ph\u1ea7n t\u1eed nh\u1ecf nh\u1ea5t \u1edf g\u1ed1c.<\/p>\n

          Khi s\u1eed d\u1ee5ng s\u1eafp x\u1ebfp theo \u0111\u1ed1ng tr\u00ean \u0111\u1ed1ng t\u1ed1i \u0111a, v\u00f9ng kh\u00f4ng \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp s\u1ebd thu h\u1eb9p l\u1ea1i khi ph\u1ea7n t\u1eed l\u1edbn nh\u1ea5t \u0111\u01b0\u1ee3c chuy\u1ec3n sang v\u00f9ng \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp. \u0110\u1ed1i v\u1edbi \u0111\u1ed1ng t\u1ed1i thi\u1ec3u (min-heap), m\u1ee5c nh\u1ecf nh\u1ea5t s\u1ebd \u0111\u01b0\u1ee3c chuy\u1ec3n v\u00e0o v\u00f9ng \u0111\u00e3 s\u1eafp x\u1ebfp.<\/p>\n

          Trong \u0111\u1ed1ng t\u1ed1i \u0111a, gi\u00e1 tr\u1ecb c\u1ee7a n\u00fat cha lu\u00f4n l\u1edbn h\u01a1n gi\u00e1 tr\u1ecb con c\u1ee7a ch\u00fang. \u0110\u1ec3 s\u1eafp x\u1ebfp c\u00e1c ph\u1ea7n t\u1eed c\u1ee7a \u0111\u1ed1ng t\u1ed1i \u0111a b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng s\u1eafp x\u1ebfp \u0111\u1ed1ng, c\u1ea7n th\u1ef1c hi\u1ec7n c\u00e1c b\u01b0\u1edbc sau:<\/p>\n

            \n
          • Thay th\u1ebf ph\u1ea7n t\u1eed cu\u1ed1i c\u00f9ng c\u1ee7a heap b\u1eb1ng n\u00fat g\u1ed1c.<\/li>\n
          • X\u00f3a ph\u1ea7n t\u1eed cu\u1ed1i c\u00f9ng m\u1edbi \u0111\u01b0\u1ee3c \u0111\u1eb7t kh\u1ecfi \u0111\u1ed1ng.<\/li>\n
          • Chuy\u1ec3n \u0111\u1ed5i \u0111\u1ed1ng nh\u1ecb ph\u00e2n hi\u1ec7n t\u1ea1i tr\u1edf l\u1ea1i th\u00e0nh m\u1ed9t \u0111\u1ed1ng t\u1ed1i \u0111a.<\/li>\n
          • L\u1eb7p l\u1ea1i quy tr\u00ecnh cho \u0111\u1ebfn khi kh\u00f4ng c\u00f2n ph\u1ea7n t\u1eed n\u00e0o.<\/li>\n<\/ul>\n

            Ph\u1ee9c t\u1ea1p v\u1ec1 th\u1eddi gian:<\/strong><\/p>\n

              \n
            • Tr\u01b0\u1eddng h\u1ee3p t\u1ed1t nh\u1ea5t: O(nlogn)<\/li>\n
            • Tr\u01b0\u1eddng h\u1ee3p x\u1ea5u nh\u1ea5t: O(nlogn)<\/li>\n
            • Tr\u01b0\u1eddng h\u1ee3p trung b\u00ecnh: O(nlogn)<\/li>\n<\/ul>\n

              8. Danh s\u00e1ch b\u1ecf qua \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng nh\u1eb1m m\u1ee5c \u0111\u00edch g\u00ec?<\/strong><\/h2>\n

              Danh s\u00e1ch b\u1ecf qua l\u00e0 m\u1ed9t c\u1ea5u tr\u00fac d\u1eef li\u1ec7u s\u1eed d\u1ee5ng danh s\u00e1ch \u0111\u01b0\u1ee3c li\u00ean k\u1ebft v\u00e0 x\u00e1c su\u1ea5t \u0111\u1ec3 x\u00e2y d\u1ef1ng c\u00e1c l\u1edbp li\u00ean k\u1ebft m\u1edbi tr\u00ean danh s\u00e1ch g\u1ed1c. M\u1ed9t c\u00e1ch \u0111\u1ec3 h\u00ecnh dung n\u00f3 c\u00f3 th\u1ec3 l\u00e0 t\u01b0\u1edfng t\u01b0\u1ee3ng v\u1ec1 m\u1ed9t h\u1ec7 th\u1ed1ng tuy\u1ebfn xe bu\u00fdt. M\u1ed7i \u0111i\u1ec3m d\u1eebng t\u01b0\u01a1ng \u1ee9ng v\u1edbi m\u1ed9t n\u00fat trong danh s\u00e1ch, nh\u01b0ng c\u00f3 xe bu\u00fdt ch\u1ec9 d\u1eebng \u1edf m\u1ed9t s\u1ed1 \u0111i\u1ec3m d\u1eebng, t\u1ea1o ra m\u1ed9t tuy\u1ebfn \u0111\u01b0\u1eddng t\u1ed1c h\u00e0nh. Ng\u01b0\u1ee3c l\u1ea1i, xe bu\u00fdt th\u00f4ng th\u01b0\u1eddng d\u1eebng \u1edf m\u1ecdi \u0111i\u1ec3m.<\/p>\n

              Qu\u00e1 tr\u00ecnh t\u1ea1o l\u1edbp m\u1edbi trong danh s\u00e1ch b\u1ecf qua c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c coi nh\u01b0 vi\u1ec7c thi\u1ebft l\u1eadp c\u00e1c tuy\u1ebfn \u0111\u01b0\u1eddng t\u1ed1c h\u00e0nh. Vi\u1ec7c truy c\u1eadp c\u00e1c n\u00fat th\u01b0\u1eddng xuy\u00ean nh\u1ea5t tr\u1edf n\u00ean hi\u1ec7u qu\u1ea3, l\u00e0m cho c\u00e1c t\u00e1c v\u1ee5 nh\u01b0 ch\u00e8n ho\u1eb7c x\u00f3a n\u00fat tr\u1edf n\u00ean d\u1ec5 d\u00e0ng v\u00e0 nhanh ch\u00f3ng h\u01a1n so v\u1edbi m\u1ed9t s\u1ed1 thu\u1eadt to\u00e1n kh\u00e1c.<\/p>\n

              C\u1ea5u tr\u00fac d\u1eef li\u1ec7u n\u00e0y mang l\u1ea1i hi\u1ec7u su\u1ea5t cao cho c\u00e1c thao t\u00e1c \u0111\u1eb7c bi\u1ec7t tr\u00ean c\u00e1c n\u00fat th\u01b0\u1eddng xuy\u00ean \u0111\u01b0\u1ee3c truy c\u1eadp, gi\u1ed1ng nh\u01b0 vi\u1ec7c di chuy\u1ec3n qua c\u00e1c \u0111i\u1ec3m d\u1eebng tr\u00ean m\u1ed9t tuy\u1ebfn \u0111\u01b0\u1eddng t\u1ed1c h\u00e0nh.<\/p>\n

              9. C\u00e1ch \u0111\u1ec3 so s\u00e1nh hai thu\u1eadt to\u00e1n \u0111\u01b0\u1ee3c vi\u1ebft cho c\u00f9ng m\u1ed9t b\u00e0i to\u00e1n<\/strong><\/h2>\n

              \u0110\u1ec3 so s\u00e1nh gi\u1eefa hai thu\u1eadt to\u00e1n vi\u1ebft cho c\u00f9ng m\u1ed9t v\u1ea5n \u0111\u1ec1, ch\u00fang ta c\u00f3 th\u1ec3 xem x\u00e9t m\u1ed9t s\u1ed1 y\u1ebfu t\u1ed1 quan tr\u1ecdng nh\u01b0 \u0111\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian, \u0111\u1ed9 ph\u1ee9c t\u1ea1p kh\u00f4ng gian, t\u00ednh \u1ed5n \u0111\u1ecbnh, v\u00e0 c\u0169ng xem x\u00e9t hi\u1ec7u su\u1ea5t th\u1ef1c t\u1ebf trong c\u00e1c \u0111i\u1ec1u ki\u1ec7n \u0111\u1ea7u v\u00e0o c\u1ee5 th\u1ec3. \u0110\u1ed1i v\u1edbi \u0111\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian, ch\u00fang ta c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng k\u00fd hi\u1ec7u Big O \u0111\u1ec3 \u0111\u00e1nh gi\u00e1 c\u00e1ch m\u00e0 th\u1eddi gian ch\u1ea1y c\u1ee7a thu\u1eadt to\u00e1n t\u0103ng theo k\u00edch th\u01b0\u1edbc c\u1ee7a \u0111\u1ea7u v\u00e0o.\u00a0<\/p>\n

              Ngo\u00e0i ra, vi\u1ec7c ki\u1ec3m tra v\u00e0 so s\u00e1nh hi\u1ec7u su\u1ea5t th\u1ef1c t\u1ebf tr\u00ean d\u1eef li\u1ec7u th\u1ef1c t\u1ebf l\u00e0 m\u1ed9t c\u00e1ch quan tr\u1ecdng \u0111\u1ec3 \u0111\u1ea3m b\u1ea3o r\u1eb1ng thu\u1eadt to\u00e1n ho\u1ea1t \u0111\u1ed9ng hi\u1ec7u qu\u1ea3 trong m\u1ecdi t\u00ecnh hu\u1ed1ng.<\/p>\n

              10. Asymptotic Notations (K\u00fd hi\u1ec7u ti\u1ec7m c\u1eadn) l\u00e0 g\u00ec?<\/strong><\/h2>\n

              Asymptotic Notations, hay K\u00fd hi\u1ec7u ti\u1ec7m c\u1eadn, l\u00e0 c\u00e1c k\u00fd hi\u1ec7u \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 m\u00f4 t\u1ea3 hi\u1ec7u su\u1ea5t c\u1ee7a thu\u1eadt to\u00e1n khi \u0111\u1ea7u v\u00e0o ti\u1ebfn \u0111\u1ebfn v\u00f4 c\u00f9ng. Ch\u00fang gi\u00fap \u0111\u01a1n gi\u1ea3n h\u00f3a vi\u1ec7c so s\u00e1nh hi\u1ec7u su\u1ea5t c\u1ee7a c\u00e1c thu\u1eadt to\u00e1n m\u00e0 kh\u00f4ng c\u1ea7n quan t\u00e2m \u0111\u1ebfn c\u00e1c y\u1ebfu t\u1ed1 c\u1ee5 th\u1ec3 nh\u01b0 h\u1eb1ng s\u1ed1 hay \u0111i\u1ec1u ki\u1ec7n kh\u1edfi \u0111\u1ea7u.<\/p>\n

              C\u00e1c k\u00fd hi\u1ec7u ti\u1ec7m c\u1eadn ph\u1ed5 bi\u1ebfn bao g\u1ed3m:<\/p>\n

                \n
              • Big O (O): Bi\u1ec3u th\u1ecb gi\u1edbi h\u1ea1n tr\u00ean c\u1ee7a \u0111\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian hay kh\u00f4ng gian.<\/li>\n
              • Big Omega (\u03a9): Bi\u1ec3u th\u1ecb gi\u1edbi h\u1ea1n d\u01b0\u1edbi c\u1ee7a \u0111\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian hay kh\u00f4ng gian.<\/li>\n
              • Big Theta (\u0398): Bi\u1ec3u th\u1ecb c\u1ea3 gi\u1edbi h\u1ea1n tr\u00ean v\u00e0 gi\u1edbi h\u1ea1n d\u01b0\u1edbi, ch\u1ec9 ra \u0111\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian hay kh\u00f4ng gian \u1edf m\u1ee9c trung b\u00ecnh.<\/li>\n<\/ul>\n

                c\u00e2u h\u1ecfi ph\u1ecfng v\u1ea5n thu\u1eadt to\u00e1n11. M\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi kh\u00e1c<\/strong><\/h2>\n

                M\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi ph\u1ecfng v\u1ea5n thu\u1eadt to\u00e1n kh\u00e1c m\u00e0 b\u1ea1n c\u00f3 th\u1ec3 g\u1eb7p trong bu\u1ed5i ph\u1ecfng v\u1ea5n c\u00f3 th\u1ec3 k\u1ec3 \u0111\u1ebfn nh\u01b0:<\/p>\n

                  \n
                • Vi\u1ebft thu\u1eadt to\u00e1n ho\u00e1n \u0111\u1ed5i hai s\u1ed1 cho tr\u01b0\u1edbc trong Java m\u00e0 kh\u00f4ng s\u1eed d\u1ee5ng bi\u1ebfn t\u1ea1m th\u1eddi?<\/li>\n
                • M\u00f4 h\u00ecnh thu\u1eadt to\u00e1n chia \u0111\u1ec3 tr\u1ecb \u0111\u01b0\u1ee3c hi\u1ec3u nh\u01b0 th\u1ebf n\u00e0o?<\/li>\n
                • Thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm \u0111\u01b0\u1ee3c hi\u1ec3u l\u00e0 g\u00ec?<\/li>\n
                • Thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm tuy\u1ebfn t\u00ednh \u0111\u01b0\u1ee3c hi\u1ec3u nh\u01b0 th\u1ebf n\u00e0o?<\/li>\n
                • B\u1ea1n hi\u1ec3u nh\u01b0 th\u1ebf n\u00e0o v\u1ec1 m\u00f4 h\u00ecnh thu\u1eadt to\u00e1n l\u1eadp tr\u00ecnh \u0111\u1ed9ng (DP)?<\/li>\n<\/ul>\n

                  T\u1ea1m k\u1ebft<\/strong><\/p>\n

                  Tr\u00ean \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 chia s\u1ebb v\u1ec1 c\u00e1c c\u00e2u h\u1ecfi ph\u1ecfng v\u1ea5n thu\u1eadt to\u00e1n<\/strong> th\u01b0\u1eddng g\u1eb7p m\u00e0 Masterskills mu\u1ed1n g\u1eedi \u0111\u1ebfn b\u1ea1n. Hy v\u1ecdng r\u1eb1ng, b\u00e0i vi\u1ebft \u0111\u00e3 cung c\u1ea5p \u0111\u1ebfn b\u1ea1n nhi\u1ec1u th\u00f4ng tin h\u1eefu \u00edch v\u00e0 chinh ph\u1ee5c v\u00f2ng ph\u1ecfng v\u1ea5n th\u00e0nh c\u00f4ng.<\/p>\n

                  N\u1ebfu b\u1ea1n c\u00f3 th\u00eam b\u1ea5t k\u1ef3 c\u00e2u h\u1ecfi n\u00e0o, \u0111\u1eebng ng\u1ea7n ng\u1ea1i \u0111\u1ec3 l\u1ea1i b\u00ecnh lu\u1eadn \u0111\u1ec3 \u0111\u01b0\u1ee3c Masterskills h\u1ed7 tr\u1ee3 gi\u1ea3i \u0111\u00e1p chi ti\u1ebft nh\u00e9.<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

                  N\u1ebfu b\u1ea1n chu\u1ea9n b\u1ecb tham gia v\u00e0o m\u1ed9t cu\u1ed9c ph\u1ecfng v\u1ea5n thu\u1eadt to\u00e1n, v\u1eady th\u00ec \u0111\u1eebng b\u1ecf qua b\u00e0i vi\u1ebft d\u01b0\u1edbi \u0111\u00e2y. Trong b\u00e0i vi\u1ebft n\u00e0y, Masterskills s\u1ebd chia s\u1ebb \u0111\u1ebfn b\u1ea1n c\u00e1c c\u00e2u h\u1ecfi ph\u1ecfng v\u1ea5n thu\u1eadt to\u00e1n th\u01b0\u1eddng g\u1eb7p, c\u0169ng nh\u01b0 c\u00e1ch tr\u1ea3 l\u1eddi \u201cghi \u0111i\u1ec3m\u201d. 1. Thu\u1eadt to\u00e1n \u0111\u01b0\u1ee3c hi\u1ec3u l\u00e0 g\u00ec? […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[181],"tags":[],"_links":{"self":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/50943"}],"collection":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/comments?post=50943"}],"version-history":[{"count":0,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/50943\/revisions"}],"wp:attachment":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/media?parent=50943"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/categories?post=50943"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/tags?post=50943"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}