{"id":363713,"date":"2024-07-04T19:39:47","date_gmt":"2024-07-04T12:39:47","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=363713"},"modified":"2024-07-04T19:39:47","modified_gmt":"2024-07-04T12:39:47","slug":"thuat-toan-la-gi","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/thuat-toan-la-gi\/","title":{"rendered":"Thu\u1eadt to\u00e1n l\u00e0 g\u00ec? Thu\u1eadt to\u00e1n trong l\u1eadp tr\u00ecnh v\u00e0 nh\u1eefng \u0111i\u1ec1u c\u1ea7n bi\u1ebft"},"content":{"rendered":"

N\u1ebfu ai \u0111ang t\u00ecm hi\u1ec3u s\u00e2u v\u1ec1 l\u1eadp tr\u00ecnh th\u00ec c\u1ea7n ph\u1ea3i bi\u1ebft \u0111\u1ebfn ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n v\u1ec1 <\/span>thu\u1eadt to\u00e1n l\u00e0 g\u00ec.<\/b>\u00a0Theo \u0111\u00f3, thu\u1eadt to\u00e1n \u0111\u01b0\u1ee3c xem l\u00e0 \u201cch\u00eca kh\u00f3a v\u00e0ng\u201d gi\u00fap cho c\u00e1c l\u1eadp tr\u00ecnh vi\u00ean gi\u1ea3i \u0111\u01b0\u1ee3c nh\u1eefng b\u00e0i to\u00e1n kh\u00f3. Trong b\u00e0i vi\u1ebft n\u00e0y, Ho\u00e0ng H\u00e0 Mobile s\u1ebd gi\u1edbi thi\u1ec7u \u0111\u1ebfn b\u1ea1n nh\u1eefng thu\u1eadt to\u00e1n ph\u1ed5 bi\u1ebfn nh\u1ea5t, c\u0169ng nh\u01b0 gi\u00fap b\u1ea1n bi\u1ebft c\u00e1ch v\u1eadn d\u1ee5ng chu\u1ea9n x\u00e1c nh\u1ea5t nh\u00e9.<\/span><\/p>\n

Thu\u1eadt to\u00e1n l\u00e0 g\u00ec?<\/b><\/h2>\n

T\u1eeb “thu\u1eadt to\u00e1n” b\u1eaft ngu\u1ed3n t\u1eeb t\u00ean c\u1ee7a nh\u00e0 to\u00e1n h\u1ecdc ng\u01b0\u1eddi Ba T\u01b0, Al-Khwarizmi, ng\u01b0\u1eddi \u0111\u00e3 ph\u00e1t tri\u1ec3n nhi\u1ec1u quy t\u1eafc v\u00e0 ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i to\u00e1n v\u00e0o th\u1ebf k\u1ef7 th\u1ee9 9. Hi\u1ec7n nay, thu\u1eadt to\u00e1n kh\u00f4ng ch\u1ec9 \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng trong l\u0129nh v\u1ef1c m\u00e1y t\u00ednh m\u00e0 c\u00f2n trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nh\u01b0 to\u00e1n h\u1ecdc, v\u1eadt l\u00fd, sinh h\u1ecdc v\u00e0 c\u1ea3 \u0111\u1eddi s\u1ed1ng h\u00e0ng ng\u00e0y.<\/span><\/p>\n

M\u1ed9t thu\u1eadt to\u00e1n ph\u1ea3i c\u00f3 t\u00ednh x\u00e1c \u0111\u1ecbnh, ngh\u0129a l\u00e0 m\u1ed7i b\u01b0\u1edbc c\u1ee7a thu\u1eadt to\u00e1n ph\u1ea3i r\u00f5 r\u00e0ng v\u00e0 kh\u00f4ng g\u00e2y hi\u1ec3u nh\u1ea7m. \u0110i\u1ec1u n\u00e0y \u0111\u1ea3m b\u1ea3o r\u1eb1ng m\u1ecdi ng\u01b0\u1eddi ho\u1eb7c m\u00e1y t\u00ednh th\u1ef1c hi\u1ec7n thu\u1eadt to\u00e1n \u0111\u1ec1u hi\u1ec3u v\u00e0 l\u00e0m \u0111\u00fang c\u00e1c b\u01b0\u1edbc. B\u00ean c\u1ea1nh \u0111\u00f3, m\u1ed9t thu\u1eadt to\u00e1n ph\u1ea3i c\u00f3 t\u00ednh d\u1eebng, t\u1ee9c l\u00e0 sau m\u1ed9t s\u1ed1 b\u01b0\u1edbc h\u1eefu h\u1ea1n, thu\u1eadt to\u00e1n s\u1ebd k\u1ebft th\u00fac v\u00e0 \u0111\u01b0a ra k\u1ebft qu\u1ea3 cu\u1ed1i c\u00f9ng.\u00a0<\/span><\/p>\n

\"thuat-toan-la-gi-1\"<\/picture><\/p>\n

Thu\u1eadt to\u00e1n c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n d\u01b0\u1edbi nhi\u1ec1u h\u00ecnh th\u1ee9c kh\u00e1c nhau, bao g\u1ed3m ng\u00f4n ng\u1eef t\u1ef1 nhi\u00ean, s\u01a1 \u0111\u1ed3 kh\u1ed1i, ng\u00f4n ng\u1eef l\u1eadp tr\u00ecnh, ho\u1eb7c gi\u1ea3 m\u00e3 (pseudocode). Gi\u1ea3 m\u00e3 l\u00e0 m\u1ed9t c\u00e1ch bi\u1ec3u di\u1ec5n thu\u1eadt to\u00e1n b\u1eb1ng ng\u00f4n ng\u1eef g\u1ea7n gi\u1ed1ng ng\u00f4n ng\u1eef l\u1eadp tr\u00ecnh nh\u01b0ng d\u1ec5 \u0111\u1ecdc h\u01a1n v\u00e0 kh\u00f4ng tu\u00e2n theo c\u00fa ph\u00e1p ch\u1eb7t ch\u1ebd. S\u01a1 \u0111\u1ed3 kh\u1ed1i l\u00e0 m\u1ed9t c\u00e1ch bi\u1ec3u di\u1ec5n thu\u1eadt to\u00e1n b\u1eb1ng c\u00e1c h\u00ecnh v\u1ebd, gi\u00fap d\u1ec5 d\u00e0ng h\u00ecnh dung c\u00e1c b\u01b0\u1edbc v\u00e0 lu\u1ed3ng \u0111i\u1ec1u khi\u1ec3n c\u1ee7a thu\u1eadt to\u00e1n.<\/span><\/p>\n

V\u00ed d\u1ee5, thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm v\u00e0 s\u1eafp x\u1ebfp l\u00e0 nh\u1eefng thu\u1eadt to\u00e1n c\u01a1 b\u1ea3n v\u00e0 \u0111\u01b0\u1ee3c \u1ee9ng d\u1ee5ng r\u1ed9ng r\u00e3i trong vi\u1ec7c qu\u1ea3n l\u00fd d\u1eef li\u1ec7u. Thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm gi\u00fap x\u00e1c \u0111\u1ecbnh v\u1ecb tr\u00ed c\u1ee7a m\u1ed9t ph\u1ea7n t\u1eed trong m\u1ed9t c\u1ea5u tr\u00fac d\u1eef li\u1ec7u. Trong khi thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp gi\u00fap s\u1eafp x\u1ebfp c\u00e1c ph\u1ea7n t\u1eed theo m\u1ed9t th\u1ee9 t\u1ef1 nh\u1ea5t \u0111\u1ecbnh.\u00a0<\/span><\/p>\n

T\u1ea7m quan tr\u1ecdng c\u1ee7a thu\u1eadt to\u00e1n l\u00e0 g\u00ec?<\/b><\/h2>\n

V\u1edbi s\u1ef1 ph\u00e1t tri\u1ec3n m\u1ea1nh m\u1ebd c\u1ee7a c\u00f4ng ngh\u1ec7 hi\u1ec7n nay, thu\u1eadt to\u00e1n c\u00e0ng gi\u1eef vai tr\u00f2 ch\u1ee7 ch\u1ed1t trong s\u1ef1 t\u0103ng tr\u01b0\u1edfng v\u00e0 \u0111\u1ed5i m\u1edbi c\u1ee7a l\u0129nh v\u1ef1c n\u00e0y. D\u01b0\u1edbi \u0111\u00e2y, Ho\u00e0ng H\u00e0 Mobile \u0111\u00e3 t\u1ed5ng h\u1ee3p \u0111\u01b0\u1ee3c nh\u1eefng vai tr\u00f2 c\u1ee7a thu\u1eadt to\u00e1n m\u00e0 b\u1ea1n n\u00ean bi\u1ebft \u0111\u1ebfn.<\/span><\/p>\n

N\u1ec1n t\u1ea3ng c\u1ee7a l\u1eadp tr\u00ecnh<\/b><\/h3>\n

Thu\u1eadt to\u00e1n \u0111\u00f3ng vai tr\u00f2 c\u1ed1t l\u00f5i trong l\u1eadp tr\u00ecnh v\u00e0 c\u00f3 t\u1ea7m \u1ea3nh h\u01b0\u1edfng s\u00e2u r\u1ed9ng \u0111\u1ebfn m\u1ecdi kh\u00eda c\u1ea1nh c\u1ee7a ph\u00e1t tri\u1ec3n ph\u1ea7n m\u1ec1m. M\u1ed9t thu\u1eadt to\u00e1n t\u1ed1t v\u1eeba gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1 v\u1eeba t\u1ed1i \u01b0u h\u00f3a hi\u1ec7u su\u1ea5t c\u1ee7a ch\u01b0\u01a1ng tr\u00ecnh, gi\u1ea3m thi\u1ec3u th\u1eddi gian th\u1ef1c thi v\u00e0 ti\u1ebft ki\u1ec7m b\u1ed9 nh\u1edb. V\u00ed d\u1ee5, trong c\u00e1c b\u00e0i to\u00e1n t\u00ecm ki\u1ebfm v\u00e0 s\u1eafp x\u1ebfp, vi\u1ec7c ch\u1ecdn thu\u1eadt to\u00e1n ph\u00f9 h\u1ee3p c\u00f3 th\u1ec3 l\u00e0m gi\u1ea3m \u0111\u00e1ng k\u1ec3 th\u1eddi gian x\u1eed l\u00fd. C\u00e1c thu\u1eadt to\u00e1n nh\u01b0 QuickSort, MergeSort hay c\u00e1c thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm nh\u1ecb ph\u00e2n \u0111\u1ec1u l\u00e0 nh\u1eefng v\u00ed d\u1ee5 \u0111i\u1ec3n h\u00ecnh cho vi\u1ec7c t\u1ed1i \u01b0u h\u00f3a m\u00e3 ngu\u1ed3n.<\/span><\/p>\n

\"thuat-toan-la-gi-2\"<\/picture><\/p>\n

Thu\u1eadt to\u00e1n gi\u00fap \u0111\u1ea3m b\u1ea3o t\u00ednh \u0111\u00fang \u0111\u1eafn c\u1ee7a ch\u01b0\u01a1ng tr\u00ecnh. Nh\u1eefng thu\u1eadt to\u00e1n \u0111\u00fang s\u1ebd gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1 m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c trong m\u1ecdi tr\u01b0\u1eddng h\u1ee3p c\u00f3 th\u1ec3 x\u1ea3y ra. Vi\u1ec7c s\u1eed d\u1ee5ng c\u00e1c thu\u1eadt to\u00e1n \u0111\u00e3 \u0111\u01b0\u1ee3c ki\u1ec3m ch\u1ee9ng gi\u00fap gi\u1ea3m thi\u1ec3u l\u1ed7i v\u00e0 t\u0103ng \u0111\u1ed9 tin c\u1eady c\u1ee7a ph\u1ea7n m\u1ec1m. Ngo\u00e0i ra, vi\u1ec7c vi\u1ebft c\u00e1c tr\u01b0\u1eddng h\u1ee3p ki\u1ec3m th\u1eed d\u1ef1a tr\u00ean thu\u1eadt to\u00e1n c\u0169ng gi\u00fap ph\u00e1t hi\u1ec7n s\u1edbm c\u00e1c l\u1ed7i ti\u1ec1m \u1ea9n trong qu\u00e1 tr\u00ecnh ph\u00e1t tri\u1ec3n ph\u1ea7n m\u1ec1m.<\/span><\/p>\n

B\u00ean c\u1ea1nh \u0111\u00f3, thu\u1eadt to\u00e1n l\u00e0 n\u1ec1n t\u1ea3ng cho nhi\u1ec1u \u1ee9ng d\u1ee5ng trong l\u1eadp tr\u00ecnh, t\u1eeb c\u00e1c \u1ee9ng d\u1ee5ng nh\u01b0 x\u1eed l\u00fd v\u0103n b\u1ea3n, \u0111\u1ed3 h\u1ecda m\u00e1y t\u00ednh,… M\u1ed7i l\u0129nh v\u1ef1c \u0111\u00f2i h\u1ecfi c\u00e1c thu\u1eadt to\u00e1n chuy\u00ean bi\u1ec7t \u0111\u1ec3 gi\u1ea3i quy\u1ebft c\u00e1c v\u1ea5n \u0111\u1ec1 \u0111\u1eb7c th\u00f9. Ch\u00ednh v\u00ec th\u1ebf, vi\u1ec7c n\u1eafm v\u1eefng c\u00e1c thu\u1eadt to\u00e1n c\u01a1 b\u1ea3n v\u00e0 n\u00e2ng cao gi\u00fap l\u1eadp tr\u00ecnh vi\u00ean d\u1ec5 d\u00e0ng ti\u1ebfp c\u1eadn v\u00e0 ph\u00e1t tri\u1ec3n c\u00e1c \u1ee9ng d\u1ee5ng trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau.<\/span><\/p>\n

Tr\u00ed tu\u1ec7 nh\u00e2n t\u1ea1o v\u00e0 m\u00e1y h\u1ecdc<\/b><\/h3>\n

Thu\u1eadt to\u00e1n l\u00e0 g\u00ec<\/b> v\u00e0 c\u00f3 \u00fd ngh\u0129a nh\u01b0 th\u1ebf n\u00e0o \u0111\u1ed1i v\u1edbi AI? Thu\u1eadt to\u00e1n gi\u00fap x\u1eed l\u00fd v\u00e0 ph\u00e2n t\u00edch l\u01b0\u1ee3ng d\u1eef li\u1ec7u kh\u1ed5ng l\u1ed3, t\u1eeb \u0111\u00f3 t\u00ecm ra c\u00e1c m\u1eabu v\u00e0 xu h\u01b0\u1edbng ti\u1ec1m \u1ea9n. Trong m\u00e1y h\u1ecdc, d\u1eef li\u1ec7u l\u00e0 y\u1ebfu t\u1ed1 c\u1ed1t l\u00f5i v\u00e0 c\u00e1c thu\u1eadt to\u00e1n \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf \u0111\u1ec3 h\u1ecdc t\u1eeb d\u1eef li\u1ec7u n\u00e0y, t\u1ea1o ra c\u00e1c m\u00f4 h\u00ecnh c\u00f3 kh\u1ea3 n\u0103ng d\u1ef1 \u0111o\u00e1n v\u00e0 ra quy\u1ebft \u0111\u1ecbnh. C\u00e1c thu\u1eadt to\u00e1n nh\u01b0 h\u1ed3i quy tuy\u1ebfn t\u00ednh, c\u00e2y quy\u1ebft \u0111\u1ecbnh, v\u00e0 m\u1ea1ng n\u01a1-ron nh\u00e2n t\u1ea1o l\u00e0 nh\u1eefng c\u00f4ng c\u1ee5 quan tr\u1ecdng trong vi\u1ec7c ph\u00e2n t\u00edch, x\u1eed l\u00fd d\u1eef li\u1ec7u.<\/span><\/p>\n

\"thuat-toan-la-gi-3\"<\/picture><\/p>\n

M\u00e1y h\u1ecdc l\u00e0 qu\u00e1 tr\u00ecnh m\u00e0 m\u00e1y t\u00ednh s\u1eed d\u1ee5ng c\u00e1c thu\u1eadt to\u00e1n \u0111\u1ec3 h\u1ecdc t\u1eeb d\u1eef li\u1ec7u v\u00e0 c\u1ea3i thi\u1ec7n hi\u1ec7u su\u1ea5t theo th\u1eddi gian. C\u00e1c thu\u1eadt to\u00e1n h\u1ecdc m\u00e1y nh\u01b0 h\u1ecdc gi\u00e1m s\u00e1t (supervised learning), h\u1ecdc kh\u00f4ng gi\u00e1m s\u00e1t (unsupervised learning), v\u00e0 h\u1ecdc t\u0103ng c\u01b0\u1eddng (reinforcement learning). V\u1edbi nh\u1eefng thu\u1eadt to\u00e1n n\u00e0y gi\u00fap m\u00e1y t\u00ednh t\u1ef1 \u0111\u1ed9ng h\u00f3a vi\u1ec7c h\u1ecdc h\u1ecfi t\u1eeb d\u1eef li\u1ec7u v\u00e0 \u0111\u01b0a ra c\u00e1c d\u1ef1 \u0111o\u00e1n ch\u00ednh x\u00e1c, c\u0169ng nh\u01b0 c\u1ea3i thi\u1ec7n kh\u1ea3 n\u0103ng ra quy\u1ebft \u0111\u1ecbnh.<\/span><\/p>\n

Thu\u1eadt to\u00e1n c\u00f2n gi\u00fap ph\u00e1t tri\u1ec3n c\u00e1c h\u1ec7 th\u1ed1ng AI t\u1ef1 \u0111\u1ed9ng, c\u00f3 kh\u1ea3 n\u0103ng th\u1ef1c hi\u1ec7n c\u00e1c nhi\u1ec7m v\u1ee5 ph\u1ee9c t\u1ea1p m\u00e0 kh\u00f4ng c\u1ea7n s\u1ef1 can thi\u1ec7p c\u1ee7a con ng\u01b0\u1eddi. V\u00ed d\u1ee5, trong xe t\u1ef1 l\u00e1i, c\u00e1c thu\u1eadt to\u00e1n gi\u00fap ph\u00e2n t\u00edch d\u1eef li\u1ec7u t\u1eeb c\u00e1c c\u1ea3m bi\u1ebfn, nh\u1eadn di\u1ec7n \u0111\u1ed1i t\u01b0\u1ee3ng v\u00e0 ra quy\u1ebft \u0111\u1ecbnh l\u00e1i xe an to\u00e0n. T\u01b0\u01a1ng t\u1ef1, trong c\u00e1c h\u1ec7 th\u1ed1ng \u0111\u1ec1 xu\u1ea5t, thu\u1eadt to\u00e1n gi\u00fap ph\u00e2n t\u00edch h\u00e0nh vi ng\u01b0\u1eddi d\u00f9ng v\u00e0 \u0111\u01b0a ra c\u00e1c g\u1ee3i \u00fd ph\u00f9 h\u1ee3p.<\/span><\/p>\n

An ninh m\u1ea1ng v\u00e0 m\u1eadt m\u00e3<\/b><\/h3>\n

Thu\u1eadt to\u00e1n m\u1eadt m\u00e3 l\u00e0 c\u00f4ng c\u1ee5 ch\u00ednh \u0111\u1ec3 m\u00e3 h\u00f3a v\u00e0 gi\u1ea3i m\u00e3 d\u1eef li\u1ec7u. M\u00e3 h\u00f3a gi\u00fap chuy\u1ec3n \u0111\u1ed5i th\u00f4ng tin t\u1eeb d\u1ea1ng d\u1ec5 \u0111\u1ecdc sang d\u1ea1ng m\u00e3 h\u00f3a kh\u00f3 hi\u1ec3u, ch\u1ec9 c\u00f3 th\u1ec3 gi\u1ea3i m\u00e3 b\u1edfi nh\u1eefng ng\u01b0\u1eddi c\u00f3 kh\u00f3a th\u00edch h\u1ee3p. C\u00e1c thu\u1eadt to\u00e1n m\u00e3 h\u00f3a nh\u01b0 AES (Advanced Encryption Standard), RSA (Rivest-Shamir-Adleman) v\u00e0 ECC (Elliptic Curve Cryptography) \u0111\u1ea3m b\u1ea3o r\u1eb1ng d\u1eef li\u1ec7u \u0111\u01b0\u1ee3c b\u1ea3o v\u1ec7 kh\u1ecfi truy c\u1eadp tr\u00e1i ph\u00e9p.<\/span><\/p>\n

\u0110\u1ed3ng th\u1eddi, c\u00e1c giao th\u1ee9c b\u1ea3o m\u1eadt nh\u01b0 SSL\/TLS (Secure Sockets Layer\/Transport Layer Security) s\u1eed d\u1ee5ng c\u00e1c thu\u1eadt to\u00e1n m\u1eadt m\u00e3 \u0111\u1ec3 b\u1ea3o v\u1ec7 d\u1eef li\u1ec7u truy\u1ec1n t\u1ea3i gi\u1eefa c\u00e1c thi\u1ebft b\u1ecb v\u00e0 m\u00e1y ch\u1ee7. \u0110i\u1ec1u n\u00e0y gi\u00fap ng\u0103n ch\u1eb7n c\u00e1c cu\u1ed9c t\u1ea5n c\u00f4ng nghe l\u00e9n v\u00e0 \u0111\u1ea3m b\u1ea3o r\u1eb1ng d\u1eef li\u1ec7u kh\u00f4ng b\u1ecb thay \u0111\u1ed5i ho\u1eb7c gi\u1ea3 m\u1ea1o trong qu\u00e1 tr\u00ecnh truy\u1ec1n.<\/span><\/p>\n

\"thuat-toan-la-gi-4\"<\/picture><\/p>\n

Thu\u1eadt to\u00e1n c\u0169ng \u0111\u00f3ng vai tr\u00f2 quan tr\u1ecdng trong vi\u1ec7c x\u00e1c th\u1ef1c v\u00e0 ki\u1ec3m tra danh t\u00ednh c\u1ee7a ng\u01b0\u1eddi d\u00f9ng. C\u00e1c thu\u1eadt to\u00e1n b\u0103m (hashing algorithms) nh\u01b0 SHA-256 (Secure Hash Algorithm) t\u1ea1o ra c\u00e1c m\u00e3 b\u0103m duy nh\u1ea5t t\u1eeb d\u1eef li\u1ec7u g\u1ed1c, gi\u00fap x\u00e1c th\u1ef1c t\u00ednh to\u00e0n v\u1eb9n c\u1ee7a d\u1eef li\u1ec7u. H\u01a1n n\u1eefa, c\u00e1c h\u1ec7 th\u1ed1ng x\u00e1c th\u1ef1c \u0111a y\u1ebfu t\u1ed1 (MFA) s\u1eed d\u1ee5ng c\u00e1c thu\u1eadt to\u00e1n \u0111\u1ec3 x\u00e1c minh danh t\u00ednh ng\u01b0\u1eddi d\u00f9ng th\u00f4ng qua nhi\u1ec1u ph\u01b0\u01a1ng ph\u00e1p, ch\u1eb3ng h\u1ea1n nh\u01b0 m\u1eadt kh\u1ea9u, m\u00e3 OTP (One-Time Password) v\u00e0 sinh tr\u1eafc h\u1ecdc.<\/span><\/p>\n

Top nh\u1eefng thu\u1eadt to\u00e1n \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng ph\u1ed5 bi\u1ebfn nh\u1ea5t<\/b><\/h2>\n

Sau khi t\u00ecm hi\u1ec3u v\u1ec1 kh\u00e1i ni\u1ec7m <\/span>thu\u1eadt to\u00e1n l\u00e0 g\u00ec, <\/b>Ho\u00e0ng H\u00e0 Mobile s\u1ebd ti\u1ebfp t\u1ee5c chia s\u1ebb th\u00eam cho b\u1ea1n nh\u1eefng ki\u1ebfn th\u1ee9c h\u1eefu \u00edch kh\u00e1c li\u00ean quan \u0111\u1ebfn t\u00ean thu\u1eadt to\u00e1n \u0111ang \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng n\u1ec1n t\u1ea3ng nh\u1ea5t hi\u1ec7n nay.<\/span><\/p>\n

Thu\u1eadt to\u00e1n Hashing<\/b><\/h3>\n

Thu\u1eadt to\u00e1n Hashing l\u00e0 qu\u00e1 tr\u00ecnh bi\u1ebfn \u0111\u1ed5i d\u1eef li\u1ec7u \u0111\u1ea7u v\u00e0o (message) th\u00e0nh m\u1ed9t chu\u1ed7i gi\u00e1 tr\u1ecb hash c\u00f3 \u0111\u1ed9 d\u00e0i c\u1ed1 \u0111\u1ecbnh. \u0110\u1ea7u ra c\u1ee7a thu\u1eadt to\u00e1n n\u00e0y \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 gi\u00e1 tr\u1ecb b\u0103m (hash value) ho\u1eb7c m\u00e3 b\u0103m (hash code). Tuy nhi\u00ean, b\u1ea1n c\u1ea7n l\u01b0u \u00fd l\u00e0 m\u00e3 b\u0103m kh\u00f4ng th\u1ec3 \u0111\u01b0\u1ee3c ph\u1ee5c h\u1ed3i v\u1ec1 d\u1eef li\u1ec7u g\u1ed1c m\u1ed9t c\u00e1ch d\u1ec5 d\u00e0ng. \u0110i\u1ec1u n\u00e0y c\u00f3 ngh\u0129a l\u00e0 khi b\u1ea1n bi\u1ebft gi\u00e1 tr\u1ecb b\u0103m c\u1ee7a m\u1ed9t t\u1eadp d\u1eef li\u1ec7u, kh\u00f4ng th\u1ec3 ph\u1ee5c h\u1ed3i ng\u01b0\u1ee3c l\u1ea1i d\u1eef li\u1ec7u ban \u0111\u1ea7u.<\/span><\/p>\n

\"thuat-toan-la-gi-5\"<\/picture><\/p>\n

Thu\u1eadt to\u00e1n Hashing \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 ki\u1ec3m tra t\u00ednh to\u00e0n v\u1eb9n c\u1ee7a d\u1eef li\u1ec7u. B\u1eb1ng c\u00e1ch t\u00ednh to\u00e1n l\u1ea1i gi\u00e1 tr\u1ecb b\u0103m c\u1ee7a d\u1eef li\u1ec7u v\u00e0 so s\u00e1nh v\u1edbi gi\u00e1 tr\u1ecb b\u0103m ban \u0111\u1ea7u, ta c\u00f3 th\u1ec3 x\u00e1c minh xem d\u1eef li\u1ec7u c\u00f3 b\u1ecb thay \u0111\u1ed5i hay kh\u00f4ng trong qu\u00e1 tr\u00ecnh truy\u1ec1n t\u1ea3i ho\u1eb7c l\u01b0u tr\u1eef. B\u00ean c\u1ea1nh \u0111\u00f3, gi\u00e1 tr\u1ecb b\u0103m \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u1ed1i \u01b0u h\u00f3a t\u00ecm ki\u1ebfm trong c\u01a1 s\u1edf d\u1eef li\u1ec7u. Thay v\u00ec so s\u00e1nh d\u1eef li\u1ec7u t\u1eebng byte, ta ch\u1ec9 c\u1ea7n so s\u00e1nh gi\u00e1 tr\u1ecb b\u0103m c\u1ee7a ch\u00fang, l\u00e0m t\u0103ng t\u1ed1c qu\u00e1 tr\u00ecnh t\u00ecm ki\u1ebfm.<\/span><\/p>\n

Thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm<\/b><\/h3>\n

Thu\u1eadt to\u00e1n l\u00e0 g\u00ec<\/b> v\u00e0 c\u00f3 \u00fd ngh\u0129a nh\u01b0 th\u1ebf n\u00e0o trong t\u00ecm ki\u1ebfm d\u1eef li\u1ec7u? Thu\u1eadt to\u00e1n cung c\u1ea5p c\u01a1 s\u1edf cho vi\u1ec7c thi\u1ebft k\u1ebf v\u00e0 tri\u1ec3n khai c\u00e1c c\u1ea5u tr\u00fac d\u1eef li\u1ec7u hi\u1ec7u qu\u1ea3. C\u00e1c c\u1ea5u tr\u00fac d\u1eef li\u1ec7u n\u00e0y \u0111\u00f3ng vai tr\u00f2 quan tr\u1ecdng trong vi\u1ec7c t\u1ed5 ch\u1ee9c v\u00e0 qu\u1ea3n l\u00fd d\u1eef li\u1ec7u, cho ph\u00e9p t\u00ecm ki\u1ebfm, ch\u00e8n, x\u00f3a d\u1eef li\u1ec7u. H\u01a1n n\u1eefa, trong c\u00e1c \u1ee9ng d\u1ee5ng y\u00eau c\u1ea7u th\u1eddi gian th\u1ef1c thi nhanh nh\u01b0 game, c\u00e1c thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm gi\u00fap c\u1ea3i thi\u1ec7n hi\u1ec7u su\u1ea5t v\u00e0 \u0111\u00e1p \u1ee9ng y\u00eau c\u1ea7u v\u1ec1 th\u1eddi gian th\u1ef1c.<\/span><\/p>\n

\"thuat-toan-la-gi-6\"<\/picture><\/p>\n

\u0110\u1ed3ng th\u1eddi, trong l\u0129nh v\u1ef1c khai th\u00e1c d\u1eef li\u1ec7u v\u00e0 khoa h\u1ecdc d\u1eef li\u1ec7u, c\u00e1c thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 ph\u00e2n t\u00edch v\u00e0 tr\u00edch xu\u1ea5t th\u00f4ng tin quan tr\u1ecdng t\u1eeb c\u00e1c t\u1eadp d\u1eef li\u1ec7u l\u1edbn. C\u00f2n trong c\u00e1c h\u1ec7 th\u1ed1ng truy\u1ec1n th\u00f4ng v\u00e0 m\u1ea1ng, thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm gi\u00fap trong vi\u1ec7c ph\u00e2n t\u00edch, t\u00ecm ki\u1ebfm v\u00e0 truy\u1ec1n t\u1ea3i d\u1eef li\u1ec7u.<\/span><\/p>\n

Thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp<\/b><\/h3>\n

Thu\u1eadt to\u00e1n n\u00e0y nh\u1eb1m m\u1ee5c \u0111\u00edch s\u1eafp x\u1ebfp c\u00e1c ph\u1ea7n t\u1eed trong m\u1ed9t t\u1eadp d\u1eef li\u1ec7u th\u00e0nh m\u1ed9t tr\u00ecnh t\u1ef1 m\u00e0 th\u01b0\u1eddng tu\u00e2n theo m\u1ed9t ti\u00eau ch\u00ed nh\u1ea5t \u0111\u1ecbnh. Ch\u1eb3ng h\u1ea1n nh\u01b0 th\u1ee9 t\u1ef1 t\u0103ng d\u1ea7n, gi\u1ea3m d\u1ea7n ho\u1eb7c theo m\u1ed9t quy lu\u1eadt nh\u1ea5t \u0111\u1ecbnh kh\u00e1c. Th\u00eam v\u00e0o \u0111\u00f3, trong c\u00e1c h\u1ec7 th\u1ed1ng qu\u1ea3n l\u00fd c\u01a1 s\u1edf d\u1eef li\u1ec7u, c\u00e1c thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 s\u1eafp x\u1ebfp k\u1ebft qu\u1ea3 truy v\u1ea5n ho\u1eb7c ch\u1ec9 m\u1ee5c, l\u00e0m t\u0103ng hi\u1ec7u su\u1ea5t v\u00e0 \u0111\u00e1p \u1ee9ng y\u00eau c\u1ea7u v\u1ec1 th\u1eddi gian th\u1ef1c.<\/span><\/p>\n

\"thuat-toan-la-gi-7\"<\/picture><\/p>\n

Song song, trong c\u00e1c \u1ee9ng d\u1ee5ng x\u1eed l\u00fd d\u1eef li\u1ec7u l\u1edbn, nh\u1eefng thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp hi\u1ec7u qu\u1ea3 nh\u01b0 Merge Sort v\u00e0 Quick Sort gi\u00fap c\u1ea3i thi\u1ec7n hi\u1ec7u su\u1ea5t x\u1eed l\u00fd. H\u01a1n n\u1eefa, vi\u1ec7c hi\u1ec3u v\u00e0 \u00e1p d\u1ee5ng c\u00e1c thu\u1eadt to\u00e1n s\u1eafp x\u1ebfp gi\u00fap l\u1eadp tr\u00ecnh vi\u00ean thi\u1ebft k\u1ebf tri\u1ec3n khai c\u00e1c gi\u1ea3i ph\u00e1p t\u1ed1i \u01b0u cho c\u00e1c v\u1ea5n \u0111\u1ec1 ph\u1ee9c t\u1ea1p.<\/span><\/p>\n

Thu\u1eadt to\u00e1n Dijkstra<\/b><\/h3>\n

Thu\u1eadt to\u00e1n l\u00e0 g\u00ec<\/b>, t\u1ea1i sao l\u1ea1i \u0111\u01b0\u1ee3c \u0111\u1eb7t t\u00ean l\u00e0 Dijkstra? \u0110\u01b0\u1ee3c bi\u1ebft thu\u1eadt to\u00e1n n\u00e0y \u0111\u01b0\u1ee3c ph\u00e1t tri\u1ec3n b\u1edfi nh\u00e0 khoa h\u1ecdc Edsger W. Dijkstra v\u00e0o n\u0103m 1956. N\u00f3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i \u0111\u1ec3 t\u00ecm \u0111\u01b0\u1eddng \u0111i ng\u1eafn nh\u1ea5t gi\u1eefa c\u00e1c \u0111\u1ec9nh trong m\u1ed9t \u0111\u1ed3 th\u1ecb c\u00f3 tr\u1ecdng s\u1ed1 kh\u00f4ng \u00e2m. Tuy nhi\u00ean, hi\u1ec7n nay \u1ee9ng d\u1ee5ng c\u1ee7a thu\u1eadt to\u00e1n Dijkstra \u0111\u00e3 \u0111\u01b0\u1ee3c m\u1edf r\u1ed9ng h\u01a1n.<\/span><\/p>\n

\"thuat-toan-la-gi-8\"<\/picture><\/p>\n

Ch\u1eb3ng h\u1ea1n nh\u01b0 trong m\u1ea1ng m\u00e1y t\u00ednh v\u00e0 c\u00e1c h\u1ec7 th\u1ed1ng m\u1ea1ng, thu\u1eadt to\u00e1n Dijkstra \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u00ednh to\u00e1n \u0111\u01b0\u1eddng \u0111i ng\u1eafn nh\u1ea5t gi\u1eefa c\u00e1c n\u00fat trong m\u1ea1ng. Nh\u1edd v\u00e0o \u0111\u00f3 gi\u00fap c\u1ea3i thi\u1ec7n hi\u1ec7u su\u1ea5t truy\u1ec1n th\u00f4ng v\u00e0 gi\u1ea3m \u0111\u1ed9 tr\u1ec5. \u0110\u00e3 th\u1ebf, trong c\u00e1c \u1ee9ng d\u1ee5ng GPS v\u00e0 b\u1ea3n \u0111\u1ed3 s\u1ed1, thu\u1eadt to\u00e1n Dijkstra \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u00ecm \u0111\u01b0\u1eddng \u0111i ng\u1eafn nh\u1ea5t t\u1eeb \u0111i\u1ec3m xu\u1ea5t ph\u00e1t \u0111\u1ebfn \u0111i\u1ec3m \u0111\u00edch, gi\u00fap ng\u01b0\u1eddi d\u00f9ng l\u1ef1a ch\u1ecdn con \u0111\u01b0\u1eddng t\u1ed1i \u01b0u.<\/span><\/p>\n

K\u1ebft lu\u1eadn<\/b><\/h2>\n

Nh\u01b0 v\u1eady, Ho\u00e0ng H\u00e0 Mobile \u0111\u00e3 cung c\u1ea5p cho b\u1ea1n t\u1ea5t c\u1ea3 nh\u1eefng th\u00f4ng tin li\u00ean quan \u0111\u1ebfn <\/span>thu\u1eadt to\u00e1n l\u00e0 g\u00ec<\/b>? Qua vi\u1ec7c nghi\u00ean c\u1ee9u v\u00e0 \u00e1p d\u1ee5ng thu\u1eadt to\u00e1n, con ng\u01b0\u1eddi \u0111\u00e3 c\u00f3 th\u1ec3 t\u1eadn d\u1ee5ng t\u1ed1i \u0111a s\u1ee9c m\u1ea1nh c\u1ee7a m\u00e1y t\u00ednh \u0111\u1ec3 gi\u1ea3i quy\u1ebft c\u00e1c v\u1ea5n \u0111\u1ec1 ph\u1ee9c t\u1ea1p t\u1eeb khoa h\u1ecdc, k\u1ef9 thu\u1eadt \u0111\u1ebfn c\u00e1c l\u0129nh v\u1ef1c x\u00e3 h\u1ed9i. Nh\u1eefng ti\u1ebfn b\u1ed9 trong l\u0129nh v\u1ef1c thu\u1eadt to\u00e1n \u0111\u00e3 m\u1edf ra nh\u1eefng c\u00e1nh c\u1eeda m\u1edbi cho s\u1ef1 ph\u00e1t tri\u1ec3n c\u00f4ng ngh\u1ec7 hi\u1ec7n nay.<\/span><\/p>\n

Xem th\u00eam:<\/b><\/p>\n