{"id":476013,"date":"2023-08-09T07:25:33","date_gmt":"2023-08-09T07:25:33","guid":{"rendered":""},"modified":"2023-09-05T11:11:50","modified_gmt":"2023-09-05T11:11:50","slug":"big-o-notation","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/vn\/wiki\/big-o-notation\/","title":{"rendered":"K\u00fd hi\u1ec7u O l\u1edbn"},"content":{"rendered":"<p>K\u00fd hi\u1ec7u Big O l\u00e0 k\u00fd hi\u1ec7u to\u00e1n h\u1ecdc m\u00f4 t\u1ea3 h\u00e0nh vi gi\u1edbi h\u1ea1n c\u1ee7a h\u00e0m khi \u0111\u1ed1i s\u1ed1 c\u00f3 xu h\u01b0\u1edbng h\u01b0\u1edbng t\u1edbi m\u1ed9t gi\u00e1 tr\u1ecb c\u1ee5 th\u1ec3 ho\u1eb7c v\u00f4 c\u00f9ng, th\u01b0\u1eddng l\u00e0 v\u1ec1 c\u00e1c h\u00e0m \u0111\u01a1n gi\u1ea3n h\u01a1n. Trong l\u0129nh v\u1ef1c khoa h\u1ecdc m\u00e1y t\u00ednh, n\u00f3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i trong vi\u1ec7c ph\u00e2n t\u00edch c\u00e1c thu\u1eadt to\u00e1n, c\u1ee5 th\u1ec3 h\u01a1n l\u00e0 \u0111\u1ec3 bi\u1ec3u th\u1ecb s\u1ef1 ph\u1ee9c t\u1ea1p ho\u1eb7c s\u1ef1 c\u00e2n b\u1eb1ng gi\u1eefa kh\u00f4ng gian v\u00e0 th\u1eddi gian c\u1ee7a m\u1ed9t thu\u1eadt to\u00e1n.<\/p>\n<h2>L\u1ecbch s\u1eed v\u00e0 ngu\u1ed3n g\u1ed1c c\u1ee7a k\u00fd hi\u1ec7u Big O<\/h2>\n<p>K\u00fd hi\u1ec7u Big O c\u00f3 ngu\u1ed3n g\u1ed1c t\u1eeb c\u00f4ng tr\u00ecnh c\u1ee7a nh\u00e0 to\u00e1n h\u1ecdc ng\u01b0\u1eddi \u0110\u1ee9c Paul Bachmann, ng\u01b0\u1eddi \u0111\u00e3 gi\u1edbi thi\u1ec7u n\u00f3 trong t\u00e1c ph\u1ea9m n\u0103m 1894 c\u1ee7a m\u00ecnh, \u201cDie Analytische Zahlentheorie\u201d. Tuy nhi\u00ean, vi\u1ec7c s\u1eed d\u1ee5ng ti\u00eau chu\u1ea9n v\u00e0 ph\u1ed5 bi\u1ebfn k\u00fd hi\u1ec7u n\u00e0y \u0111\u1ebfn t\u1eeb m\u1ed9t nh\u00e0 to\u00e1n h\u1ecdc kh\u00e1c, Edmund Landau, ng\u01b0\u1eddi \u0111\u00e3 \u00e1p d\u1ee5ng n\u00f3 v\u00e0o n\u0103m 1909. Do \u0111\u00f3, n\u00f3 th\u01b0\u1eddng \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 k\u00fd hi\u1ec7u Landau ho\u1eb7c k\u00fd hi\u1ec7u Bachmann\u2013Landau. T\u1eeb ngu\u1ed3n g\u1ed1c to\u00e1n h\u1ecdc c\u1ee7a n\u00f3, n\u00f3 \u0111\u00e3 chuy\u1ec3n sang l\u0129nh v\u1ef1c khoa h\u1ecdc m\u00e1y t\u00ednh v\u00e0 k\u1ec3 t\u1eeb \u0111\u00f3 tr\u1edf th\u00e0nh c\u00f4ng c\u1ee5 c\u01a1 b\u1ea3n \u0111\u1ec3 ph\u00e2n t\u00edch thu\u1eadt to\u00e1n.<\/p>\n<h2>Th\u00f4ng tin chi ti\u1ebft v\u1ec1 k\u00fd hi\u1ec7u Big O<\/h2>\n<p>K\u00fd hi\u1ec7u Big O l\u00e0 m\u1ed9t c\u00e1ch \u0111\u1ec3 truy\u1ec1n \u0111\u1ea1t m\u1ee9c \u0111\u1ed9 hi\u1ec7u qu\u1ea3 c\u1ee7a thu\u1eadt to\u00e1n m\u00e1y t\u00ednh khi s\u1ed1 l\u01b0\u1ee3ng d\u1eef li\u1ec7u m\u00e0 n\u00f3 ho\u1ea1t \u0111\u1ed9ng t\u0103ng l\u00ean. N\u00f3 \u0111\u01b0a ra gi\u1edbi h\u1ea1n tr\u00ean c\u1ee7a \u0111\u1ed9 ph\u1ee9c t\u1ea1p trong tr\u01b0\u1eddng h\u1ee3p x\u1ea5u nh\u1ea5t, gi\u00fap \u0111\u1ecbnh l\u01b0\u1ee3ng hi\u1ec7u su\u1ea5t c\u1ee7a thu\u1eadt to\u00e1n. K\u00fd hi\u1ec7u bi\u1ec3u th\u1ecb m\u1ed1i quan h\u1ec7 gi\u1eefa k\u00edch th\u01b0\u1edbc \u0111\u1ea7u v\u00e0o (n) v\u00e0 \u0111\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian (T) c\u1ee7a thu\u1eadt to\u00e1n.<\/p>\n<p>V\u00ed d\u1ee5: \u0111\u1ed1i v\u1edbi thu\u1eadt to\u00e1n t\u00ecm ki\u1ebfm tuy\u1ebfn t\u00ednh tr\u00ean danh s\u00e1ch n ph\u1ea7n t\u1eed, tr\u01b0\u1eddng h\u1ee3p x\u1ea5u nh\u1ea5t s\u1ebd l\u00e0 m\u1ee5c kh\u00f4ng c\u00f3 trong danh s\u00e1ch, ngh\u0129a l\u00e0 thu\u1eadt to\u00e1n s\u1ebd ph\u1ea3i t\u00ecm ki\u1ebfm qua t\u1ea5t c\u1ea3 n ph\u1ea7n t\u1eed. Do \u0111\u00f3, ch\u00fang t\u00f4i bi\u1ec3u th\u1ecb \u0111\u1ed9 ph\u1ee9c t\u1ea1p v\u1ec1 th\u1eddi gian c\u1ee7a t\u00ecm ki\u1ebfm tuy\u1ebfn t\u00ednh l\u00e0 O(n).<\/p>\n<h2>C\u1ea5u tr\u00fac b\u00ean trong c\u1ee7a k\u00fd hi\u1ec7u Big O<\/h2>\n<p>Trong k\u00fd hi\u1ec7u Big O, k\u00fd hi\u1ec7u O \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng c\u00f9ng v\u1edbi h\u00e0m x\u00e1c \u0111\u1ecbnh t\u1ed1c \u0111\u1ed9 t\u0103ng tr\u01b0\u1edfng c\u1ee7a thu\u1eadt to\u00e1n. S\u1ef1 ph\u1ee9c t\u1ea1p v\u1ec1 th\u1eddi gian (h\u00e0m) ph\u1ed5 bi\u1ebfn nh\u1ea5t m\u00e0 ch\u00fang ta g\u1eb7p ph\u1ea3i l\u00e0:<\/p>\n<ol>\n<li>O(1): \u0110\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian kh\u00f4ng \u0111\u1ed5i.<\/li>\n<li>O(log n): \u0110\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian logarit.<\/li>\n<li>O(n): \u0110\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian tuy\u1ebfn t\u00ednh.<\/li>\n<li>O(n log n): \u0110\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian log-tuy\u1ebfn t\u00ednh.<\/li>\n<li>O(n\u00b2): \u0110\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian b\u1eadc hai.<\/li>\n<li>O(n\u00b3): \u0110\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian kh\u1ed1i.<\/li>\n<li>O(2^n): \u0110\u1ed9 ph\u1ee9c t\u1ea1p theo c\u1ea5p s\u1ed1 nh\u00e2n theo th\u1eddi gian.<\/li>\n<\/ol>\n<p>H\u00e0m trong d\u1ea5u ngo\u1eb7c \u0111\u01a1n x\u00e1c \u0111\u1ecbnh t\u1ed1c \u0111\u1ed9 t\u0103ng c\u1ee7a \u0111\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian, c\u00f3 th\u1ec3 thay \u0111\u1ed5i t\u1eeb h\u1eb1ng s\u1ed1, tuy\u1ebfn t\u00ednh, b\u1eadc hai, b\u1eadc ba ho\u1eb7c h\u00e0m m\u0169.<\/p>\n<h2>C\u00e1c t\u00ednh n\u0103ng ch\u00ednh c\u1ee7a k\u00fd hi\u1ec7u Big O<\/h2>\n<p>K\u00fd hi\u1ec7u Big O \u0111\u01b0\u1ee3c \u0111\u1eb7c tr\u01b0ng b\u1edfi m\u1ed9t s\u1ed1 t\u00ednh n\u0103ng ch\u00ednh:<\/p>\n<ol>\n<li><strong>Gi\u1edbi h\u1ea1n tr\u00ean ti\u1ec7m c\u1eadn<\/strong>: N\u00f3 cung c\u1ea5p gi\u1edbi h\u1ea1n tr\u00ean v\u1ec1 \u0111\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian c\u1ee7a thu\u1eadt to\u00e1n trong tr\u01b0\u1eddng h\u1ee3p x\u1ea5u nh\u1ea5t.<\/li>\n<li><strong>S\u1ef1 \u0111\u01a1n gi\u1ea3n<\/strong>: N\u00f3 \u0111\u01a1n gi\u1ea3n h\u00f3a vi\u1ec7c so s\u00e1nh c\u00e1c thu\u1eadt to\u00e1n b\u1eb1ng c\u00e1ch t\u1eadp trung v\u00e0o t\u1ed1c \u0111\u1ed9 t\u0103ng tr\u01b0\u1edfng, b\u1ecf qua c\u00e1c y\u1ebfu t\u1ed1 kh\u00f4ng \u0111\u1ed5i v\u00e0 c\u00e1c s\u1ed1 h\u1ea1ng nh\u1ecf h\u01a1n.<\/li>\n<li><strong>Th\u00f4ng tin chi ti\u1ebft v\u1ec1 kh\u1ea3 n\u0103ng m\u1edf r\u1ed9ng<\/strong>: N\u00f3 \u0111\u01b0a ra th\u01b0\u1edbc \u0111o v\u1ec1 hi\u1ec7u qu\u1ea3 c\u1ee7a thu\u1eadt to\u00e1n khi k\u00edch th\u01b0\u1edbc \u0111\u1ea7u v\u00e0o t\u0103ng l\u00ean.<\/li>\n<li><strong>Ph\u00e2n t\u00edch tr\u01b0\u1eddng h\u1ee3p x\u1ea5u nh\u1ea5t<\/strong>: N\u00f3 cung c\u1ea5p m\u1ed9t c\u00e1i nh\u00ecn bi quan (th\u1eddi gian t\u1ed1i \u0111a) v\u1ec1 \u0111\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian c\u1ee7a thu\u1eadt to\u00e1n.<\/li>\n<\/ol>\n<h2>C\u00e1c lo\u1ea1i k\u00fd hi\u1ec7u Big O<\/h2>\n<p>C\u00f3 m\u1ed9t s\u1ed1 lo\u1ea1i k\u00fd hi\u1ec7u Big O \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 bi\u1ec3u th\u1ecb \u0111\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian kh\u00e1c nhau:<\/p>\n<table>\n<thead>\n<tr>\n<th>\u0110\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian<\/th>\n<th>T\u00ean<\/th>\n<th>Thu\u1eadt to\u00e1n m\u1eabu<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>O(1)<\/td>\n<td>Kh\u00f4ng thay \u0111\u1ed5i<\/td>\n<td>Truy c\u1eadp ch\u1ec9 m\u1ee5c m\u1ea3ng<\/td>\n<\/tr>\n<tr>\n<td>O(logn)<\/td>\n<td>logarit<\/td>\n<td>T\u00ecm ki\u1ebfm nh\u1ecb ph\u00e2n<\/td>\n<\/tr>\n<tr>\n<td>TR\u00caN)<\/td>\n<td>tuy\u1ebfn t\u00ednh<\/td>\n<td>T\u00ecm ki\u1ebfm tuy\u1ebfn t\u00ednh<\/td>\n<\/tr>\n<tr>\n<td>O(n log n)<\/td>\n<td>\u0110\u0103ng nh\u1eadp tuy\u1ebfn t\u00ednh<\/td>\n<td>S\u1eafp x\u1ebfp nhanh ch\u00f3ng<\/td>\n<\/tr>\n<tr>\n<td>O(n\u00b2)<\/td>\n<td>b\u1eadc hai<\/td>\n<td>S\u1eafp x\u1ebfp bong b\u00f3ng<\/td>\n<\/tr>\n<tr>\n<td>O(n\u00b3)<\/td>\n<td>kh\u1ed1i<\/td>\n<td>Ph\u00e9p nh\u00e2n ma tr\u1eadn<\/td>\n<\/tr>\n<tr>\n<td>O(2^n)<\/td>\n<td>s\u1ed1 m\u0169<\/td>\n<td>V\u1ea5n \u0111\u1ec1 nh\u00e2n vi\u00ean b\u00e1n h\u00e0ng du l\u1ecbch<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>M\u1ed7i k\u00fd hi\u1ec7u n\u00e0y t\u01b0\u01a1ng \u1ee9ng v\u1edbi m\u1ed9t l\u1edbp thu\u1eadt to\u00e1n th\u1ec3 hi\u1ec7n t\u1ed1c \u0111\u1ed9 t\u0103ng tr\u01b0\u1edfng c\u1ee5 th\u1ec3 v\u1ec1 \u0111\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian c\u1ee7a ch\u00fang.<\/p>\n<h2>\u1ee8ng d\u1ee5ng k\u00fd hi\u1ec7u Big O<\/h2>\n<p>K\u00fd hi\u1ec7u Big O \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong khoa h\u1ecdc m\u00e1y t\u00ednh \u0111\u1ec3 m\u00f4 t\u1ea3 hi\u1ec7u su\u1ea5t c\u1ee7a c\u00e1c thu\u1eadt to\u00e1n. N\u00f3 cho ph\u00e9p c\u00e1c l\u1eadp tr\u00ecnh vi\u00ean hi\u1ec3u m\u00e3 c\u1ee7a h\u1ecd s\u1ebd m\u1edf r\u1ed9ng nh\u01b0 th\u1ebf n\u00e0o v\u00e0 cho ph\u00e9p h\u1ecd x\u00e1c \u0111\u1ecbnh c\u00e1c t\u1eafc ngh\u1ebdn ti\u1ec1m \u1ea9n. Ngo\u00e0i ra, n\u00f3 l\u00e0 m\u1ed9t th\u00e0nh ph\u1ea7n quan tr\u1ecdng c\u1ee7a nhi\u1ec1u m\u00f4 h\u00ecnh thi\u1ebft k\u1ebf thu\u1eadt to\u00e1n nh\u01b0 chia \u0111\u1ec3 tr\u1ecb, l\u1eadp tr\u00ecnh \u0111\u1ed9ng v\u00e0 thu\u1eadt to\u00e1n tham lam.<\/p>\n<p>C\u00e1c v\u1ea5n \u0111\u1ec1 th\u01b0\u1eddng g\u1eb7p li\u00ean quan \u0111\u1ebfn k\u00fd hi\u1ec7u Big O th\u01b0\u1eddng li\u00ean quan \u0111\u1ebfn vi\u1ec7c hi\u1ec3u c\u00e1ch t\u00ednh \u0111\u1ed9 ph\u1ee9c t\u1ea1p v\u1ec1 th\u1eddi gian v\u00e0 ph\u00e2n bi\u1ec7t gi\u1eefa c\u00e1c tr\u01b0\u1eddng h\u1ee3p x\u1ea5u nh\u1ea5t, tr\u01b0\u1eddng h\u1ee3p t\u1ed1t nh\u1ea5t v\u00e0 tr\u01b0\u1eddng h\u1ee3p trung b\u00ecnh.<\/p>\n<h2>So s\u00e1nh v\u1edbi c\u00e1c \u0111i\u1ec1u kho\u1ea3n t\u01b0\u01a1ng t\u1ef1<\/h2>\n<p>C\u00f3 m\u1ed9t s\u1ed1 k\u00fd hi\u1ec7u kh\u00e1c \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong ph\u00e2n t\u00edch thu\u1eadt to\u00e1n c\u00f9ng v\u1edbi Big O, \u0111\u00f3 l\u00e0: k\u00fd hi\u1ec7u Big \u03a9 (Omega) v\u00e0 k\u00fd hi\u1ec7u Big \u0398 (Theta). Trong khi Big O cung c\u1ea5p gi\u1edbi h\u1ea1n tr\u00ean ti\u1ec7m c\u1eadn, Big \u03a9 cung c\u1ea5p gi\u1edbi h\u1ea1n d\u01b0\u1edbi ti\u1ec7m c\u1eadn. M\u1eb7t kh\u00e1c, \u0398 l\u1edbn cung c\u1ea5p m\u1ed9t gi\u1edbi h\u1ea1n ch\u1eb7t ch\u1ebd, ngh\u0129a l\u00e0 n\u00f3 v\u1eeba l\u00e0 gi\u1edbi h\u1ea1n tr\u00ean v\u1eeba l\u00e0 gi\u1edbi h\u1ea1n d\u01b0\u1edbi.<\/p>\n<h2>Quan \u0111i\u1ec3m v\u00e0 c\u00f4ng ngh\u1ec7 t\u01b0\u01a1ng lai<\/h2>\n<p>Trong khi k\u00fd hi\u1ec7u Big O \u0111\u00e3 \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng s\u00e2u r\u1ed9ng trong ph\u00e2n t\u00edch thu\u1eadt to\u00e1n v\u00e0 gi\u00e1o d\u1ee5c khoa h\u1ecdc m\u00e1y t\u00ednh, th\u00ec c\u00e1c c\u00f4ng ngh\u1ec7 m\u1edbi n\u1ed5i nh\u01b0 \u0111i\u1ec7n to\u00e1n l\u01b0\u1ee3ng t\u1eed \u0111\u00e3 s\u1eb5n s\u00e0ng m\u1edf r\u1ed9ng h\u01a1n n\u1eefa c\u00e1c \u1ee9ng d\u1ee5ng c\u1ee7a n\u00f3. Ngo\u00e0i ra, s\u1ee9c m\u1ea1nh t\u00ednh to\u00e1n ng\u00e0y c\u00e0ng t\u0103ng v\u00e0 s\u1ef1 ra \u0111\u1eddi c\u1ee7a c\u00e1c thu\u1eadt to\u00e1n ph\u1ee9c t\u1ea1p trong h\u1ecdc m\u00e1y v\u00e0 tr\u00ed tu\u1ec7 nh\u00e2n t\u1ea1o \u0111\u00e3 c\u1ee7ng c\u1ed1 t\u1ea7m quan tr\u1ecdng c\u1ee7a vi\u1ec7c hi\u1ec3u \u0111\u1ed9 ph\u1ee9c t\u1ea1p v\u00e0 hi\u1ec7u qu\u1ea3 t\u00ednh to\u00e1n.<\/p>\n<h2>M\u00e1y ch\u1ee7 proxy v\u00e0 k\u00fd hi\u1ec7u Big O<\/h2>\n<p>S\u1ef1 li\u00ean quan c\u1ee7a k\u00fd hi\u1ec7u Big O trong b\u1ed1i c\u1ea3nh m\u00e1y ch\u1ee7 proxy c\u00f3 v\u1ebb kh\u00f4ng r\u00f5 r\u00e0ng, nh\u01b0ng n\u00f3 c\u00f3 th\u1ec3 \u0111\u00f3ng m\u1ed9t vai tr\u00f2 quan tr\u1ecdng trong vi\u1ec7c hi\u1ec3u hi\u1ec7u su\u1ea5t c\u1ee7a ch\u00fang. V\u00ed d\u1ee5: hi\u1ec7u qu\u1ea3 c\u1ee7a c\u00e1c thu\u1eadt to\u00e1n \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 c\u00e2n b\u1eb1ng t\u1ea3i gi\u1eefa nhi\u1ec1u m\u00e1y ch\u1ee7 proxy ho\u1eb7c \u0111\u1ecbnh tuy\u1ebfn c\u00e1c y\u00eau c\u1ea7u th\u00f4ng qua \u0111\u01b0\u1eddng d\u1eabn t\u1ed1i \u01b0u trong m\u1ea1ng m\u00e1y ch\u1ee7 proxy c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c ph\u00e2n t\u00edch b\u1eb1ng k\u00fd hi\u1ec7u Big O.<\/p>\n<h2>Li\u00ean k\u1ebft li\u00ean quan<\/h2>\n<ul>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Big_O_notation\" target=\"_new\" rel=\"noopener nofollow\">K\u00fd hi\u1ec7u Big O \u2013 Wikipedia<\/a><\/li>\n<li><a href=\"https:\/\/rob-bell.net\/2009\/06\/a-beginners-guide-to-big-o-notation\/\" target=\"_new\" rel=\"noopener nofollow\">H\u01b0\u1edbng d\u1eabn cho ng\u01b0\u1eddi m\u1edbi b\u1eaft \u0111\u1ea7u v\u1ec1 k\u00fd hi\u1ec7u Big O \u2013 Rob Bell<\/a><\/li>\n<li><a href=\"https:\/\/codeburst.io\/big-o-notation-in-javascript-36ff67766051\" target=\"_new\" rel=\"noopener nofollow\">K\u00fd hi\u1ec7u Big O trong JavaScript \u2013 Codeburst<\/a><\/li>\n<\/ul>\n<p>T\u1ed5ng quan n\u00e0y cung c\u1ea5p c\u00e1i nh\u00ecn s\u00e2u s\u1eafc to\u00e0n di\u1ec7n v\u1ec1 k\u00fd hi\u1ec7u Big O. Tuy nhi\u00ean, \u0111\u1ec3 n\u1eafm b\u1eaft \u0111\u1ea7y \u0111\u1ee7 chi\u1ec1u s\u00e2u v\u00e0 \u1ee9ng d\u1ee5ng c\u1ee7a kh\u00e1i ni\u1ec7m n\u00e0y, c\u1ea7n c\u00f3 s\u1ef1 hi\u1ec3u bi\u1ebft v\u1eefng ch\u1eafc v\u1ec1 c\u00e1c nguy\u00ean t\u1eafc khoa h\u1ecdc m\u00e1y t\u00ednh v\u00e0 ph\u00e2n t\u00edch thu\u1eadt to\u00e1n.<\/p>","protected":false},"featured_media":467722,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-476013","wiki","type-wiki","status-publish","has-post-thumbnail","hentry"],"acf":{"faq_title":"Frequently Asked Questions about <mark>Big O Notation: A Comprehensive Insight<\/mark>","faq_items":[{"question":"What is Big O notation?","answer":"<p>Big O notation is a mathematical concept that describes the limiting behavior of a function when the argument tends towards a certain value or infinity. In computer science, it's used to denote the complexity or time-space trade-off of an algorithm.<\/p>"},{"question":"Who introduced Big O notation?","answer":"<p>Big O notation was first introduced by German mathematician Paul Bachmann in his 1894 work, \"Die Analytische Zahlentheorie\". However, the notation was popularized by another mathematician, Edmund Landau, in 1909.<\/p>"},{"question":"How is Big O notation used in computer science?","answer":"<p>In computer science, Big O notation is used to describe how well a computer algorithm scales as the number of data it operates on increases. It gives an upper bound of the complexity in the worst-case scenario, allowing for a quantifiable performance measure of an algorithm.<\/p>"},{"question":"What are the key features of Big O notation?","answer":"<p>The key features of Big O notation include providing an asymptotic upper bound, simplicity in comparing algorithms by focusing on growth rate, providing insight into scalability, and offering a worst-case analysis of an algorithm's time complexity.<\/p>"},{"question":"What are the different types of Big O notation?","answer":"<p>The most common types of Big O notations include O(1) for constant time complexity, O(log n) for logarithmic time complexity, O(n) for linear time complexity, O(n log n) for log-linear time complexity, O(n\u00b2) for quadratic time complexity, O(n\u00b3) for cubic time complexity, and O(2^n) for exponential time complexity.<\/p>"},{"question":"How is Big O notation applied and what are common problems associated with it?","answer":"<p>Big O notation is used to describe the performance or efficiency of algorithms. It helps programmers understand how their code will scale and identify potential performance issues. Common problems often involve understanding how to calculate time complexity and differentiate between worst-case, best-case, and average-case scenarios.<\/p>"},{"question":"How does Big O notation relate to proxy servers?","answer":"<p>While not directly related, Big O notation can be used to analyze the performance of certain operations within a proxy server network, such as load balancing among multiple proxy servers, or routing requests through the optimal path in the network.<\/p>"},{"question":"Are there similar terms to Big O notation in algorithm analysis?","answer":"<p>Yes, there are similar terms used in algorithm analysis including Big \u03a9 (Omega) notation, which provides an asymptotic lower bound, and Big \u0398 (Theta) notation, which provides a tight bound or both upper and lower bounds.<\/p>"},{"question":"How does Big O notation relate to future technologies?","answer":"<p>As emerging technologies such as quantum computing advance and the complexity of algorithms in areas like machine learning and artificial intelligence increase, understanding computational complexity through tools like Big O notation will continue to be crucial.<\/p>"},{"question":"Where can I find more information about Big O notation?","answer":"<p>There are numerous resources online to learn more about Big O notation. Some recommended links include the Wikipedia page for Big O notation, Rob Bell's beginner's guide, and an article on Big O notation in JavaScript on Codeburst.<\/p>"}]},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki\/476013","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\/476013\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/media\/467722"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/media?parent=476013"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}