Fibonacci: O(2^N)’den O(1)’e Ge\u00e7i\u015f<\/title><br \/>\n<\/head><br \/>\n<body><\/p>\n<p>Fibonacci: O(2^N)’den O(1)’e Ge\u00e7i\u015f<\/p>\n<p>Fibonacci dizisi, matematik ve bilgisayar bilimlerinde s\u0131k\u00e7a kar\u015f\u0131la\u015ft\u0131\u011f\u0131m\u0131z, her terimin kendinden \u00f6nceki iki terimin toplam\u0131 olarak tan\u0131mlanan bir say\u0131 dizisidir. Bu diziyi hesaplaman\u0131n bir\u00e7ok yolu vard\u0131r ve bu yollar\u0131n karma\u015f\u0131kl\u0131klar\u0131 (zaman karma\u015f\u0131kl\u0131\u011f\u0131) olduk\u00e7a farkl\u0131l\u0131k g\u00f6sterir. Bu makalede, Fibonacci dizisini hesaplaman\u0131n farkl\u0131 y\u00f6ntemlerini, bunlar\u0131n zaman karma\u015f\u0131kl\u0131klar\u0131n\u0131 ve \u00f6zellikle O(2^N) karma\u015f\u0131kl\u0131\u011f\u0131ndan O(1) karma\u015f\u0131kl\u0131\u011f\u0131na nas\u0131l ula\u015fabilece\u011fimizi detayl\u0131 olarak inceleyece\u011fiz. <a href=\"https:\/\/fatihsoysal.com\">Fatih Soysal<\/a> olarak sizlere bu konuyu ad\u0131m ad\u0131m a\u00e7\u0131klayaca\u011f\u0131m.<\/p>\n<h2>Naif Yakla\u015f\u0131m: O(2^N) Karma\u015f\u0131kl\u0131\u011f\u0131<\/h2>\n<p>Fibonacci dizisini hesaplaman\u0131n en basit, ancak en verimsiz yolu, do\u011frudan rek\u00fcrsif bir fonksiyon kullanmakt\u0131r. Bu y\u00f6ntemde, her Fibonacci say\u0131s\u0131 i\u00e7in fonksiyon kendini iki kez \u00e7a\u011f\u0131r\u0131r. Sonu\u00e7 olarak, ayn\u0131 Fibonacci say\u0131s\u0131 bir\u00e7ok kez hesaplan\u0131r. Bu da, zaman karma\u015f\u0131kl\u0131\u011f\u0131 O(2^N) olan, yani N say\u0131s\u0131 artt\u0131k\u00e7a \u00fcstel olarak b\u00fcy\u00fcyen bir algoritma ortaya \u00e7\u0131kar\u0131r. Bu y\u00f6ntem, b\u00fcy\u00fck N de\u011ferleri i\u00e7in son derece yava\u015ft\u0131r. \u00d6rne\u011fin, F(35)’i hesaplamak bile uzun s\u00fcrebilir.<\/p>\n<pre><code>\nfunction fibonacciRekursif(n) {\n if (n <= 1) return n;\n return fibonacciRekursif(n - 1) + fibonacciRekursif(n - 2);\n}\n<\/code><\/pre>\n<h2>\u0130yile\u015ftirme: \u0130teratif Yakla\u015f\u0131m - O(N) Karma\u015f\u0131kl\u0131\u011f\u0131<\/h2>\n<p>Daha verimli bir yakla\u015f\u0131m, iteratif bir d\u00f6ng\u00fc kullanmakt\u0131r. Bu y\u00f6ntemde, her Fibonacci say\u0131s\u0131 yaln\u0131zca bir kez hesaplan\u0131r. Bu, zaman karma\u015f\u0131kl\u0131\u011f\u0131n\u0131 O(N)'ye d\u00fc\u015f\u00fcr\u00fcr. Yani, N say\u0131s\u0131 artt\u0131k\u00e7a lineer olarak artan bir performans elde ederiz. Bu, rek\u00fcrsif yakla\u015f\u0131ma g\u00f6re \u00e7ok daha h\u0131zl\u0131d\u0131r.<\/p>\n<pre><code>\nfunction fibonacciIteratif(n) {\n let a = 0, b = 1, temp;\n for (let i = 0; i < n; i++) {\n temp = a;\n a = b;\n b = temp + b;\n }\n return a;\n}\n<\/code><\/pre>\n<h2>Dinamik Programlama: Bellek Kullan\u0131m\u0131 ile H\u0131zland\u0131rma<\/h2>\n<p>Dinamik programlama tekni\u011fini kullanarak da Fibonacci dizisini hesaplayabiliriz. Bu y\u00f6ntemde, daha \u00f6nce hesaplanm\u0131\u015f Fibonacci say\u0131lar\u0131n\u0131 bir dizi veya s\u00f6zl\u00fckte saklar ve tekrar hesaplamaktan ka\u00e7\u0131n\u0131r\u0131z. Bu, iteratif yakla\u015f\u0131ma benzer bir zaman karma\u015f\u0131kl\u0131\u011f\u0131na (O(N)) sahip olsa da, baz\u0131 durumlarda \u00f6zellikle tekrarlanan hesaplamalar\u0131n fazla oldu\u011fu durumlarda, performans art\u0131\u015f\u0131 sa\u011flayabilir.<\/p>\n<h2>Matris \u00dcstel Alma: O(log N) Karma\u015f\u0131kl\u0131\u011f\u0131<\/h2>\n<p>Fibonacci say\u0131lar\u0131n\u0131 hesaplaman\u0131n daha da verimli bir yolu, matris \u00fcstel alma kullanmakt\u0131r. Fibonacci dizisi, bir 2x2 matrisin \u00fcss\u00fc kullan\u0131larak hesaplanabilir. Matris \u00fcstel alma algoritmalar\u0131, logaritmik zaman karma\u015f\u0131kl\u0131\u011f\u0131na (O(log N)) sahiptir. Bu y\u00f6ntem, b\u00fcy\u00fck N de\u011ferleri i\u00e7in \u00e7ok daha h\u0131zl\u0131d\u0131r. Bu y\u00f6ntemin detaylar\u0131 daha karma\u015f\u0131k olsa da, performans avantaj\u0131 nedeniyle tercih edilebilir.<\/p>\n<h2>Binet Form\u00fcl\u00fc: O(1) Karma\u015f\u0131kl\u0131\u011f\u0131<\/h2>\n<p>Son olarak, en h\u0131zl\u0131 y\u00f6ntem Binet form\u00fcl\u00fcd\u00fcr. Bu form\u00fcl, Fibonacci say\u0131s\u0131n\u0131 do\u011frudan hesaplar ve zaman karma\u015f\u0131kl\u0131\u011f\u0131 O(1)'dir. Yani, N de\u011ferinden ba\u011f\u0131ms\u0131z olarak sabit s\u00fcrede sonucu verir. Ancak, form\u00fclde karek\u00f6k ve \u00fcstel fonksiyonlar kullan\u0131ld\u0131\u011f\u0131 i\u00e7in, \u00e7ok b\u00fcy\u00fck N de\u011ferleri i\u00e7in yuvarlama hatalar\u0131 ortaya \u00e7\u0131kabilir. Bu da hassasiyet kayb\u0131na yol a\u00e7abilir. Bu nedenle, y\u00fcksek do\u011fruluk gerektiren durumlarda, di\u011fer y\u00f6ntemleri kullanmak daha uygun olabilir.<\/p>\n<p>Binet form\u00fcl\u00fc \u015fu \u015fekildedir:<\/p>\n<p>F(n) = (\u03c6<sup>n<\/sup> - \u03c8<sup>n<\/sup>) \/ \u221a5<\/p>\n<p>burada \u03c6 = (1 + \u221a5) \/ 2 (alt\u0131n oran) ve \u03c8 = (1 - \u221a5) \/ 2 dir.<\/p>\n<h2>Sonu\u00e7<\/h2>\n<p>Fibonacci dizisini hesaplaman\u0131n \u00e7e\u015fitli y\u00f6ntemleri vard\u0131r. Her y\u00f6ntemin zaman karma\u015f\u0131kl\u0131\u011f\u0131 farkl\u0131d\u0131r. En yava\u015f y\u00f6ntem O(2^N), en h\u0131zl\u0131 y\u00f6ntem ise O(1) karma\u015f\u0131kl\u0131\u011f\u0131na sahiptir. Uygulamada, ihtiya\u00e7 duyulan do\u011fruluk ve performans gereksinimlerine g\u00f6re uygun y\u00f6ntemi se\u00e7mek \u00f6nemlidir. B\u00fcy\u00fck N de\u011ferleri i\u00e7in, matris \u00fcstel alma veya Binet form\u00fcl\u00fc (do\u011fruluk kayb\u0131n\u0131 g\u00f6ze alarak) tercih edilmelidir. Daha k\u00fc\u00e7\u00fck N de\u011ferleri i\u00e7in ise iteratif yakla\u015f\u0131m yeterli olabilir. <a href=\"https:\/\/dev.to\/joseiedo\/implementando-fibonacci-de-o2n-a-o1-4jij\">Bu \u0130ngilizce makale<\/a> size daha detayl\u0131 bilgiler sa\u011flayabilir.<\/p>\n<p>Umar\u0131m bu makale size Fibonacci dizisi ve hesaplama y\u00f6ntemleri hakk\u0131nda daha fazla bilgi sa\u011flam\u0131\u015ft\u0131r. Ba\u015fka sorular\u0131n\u0131z varsa, l\u00fctfen ileti\u015fime ge\u00e7in.<\/p>\n<p>#Etiketler: Fibonacci, O(2^N), O(1), O(N), O(log N), Rek\u00fcrsif, \u0130teratif, Dinamik Programlama, Matris \u00dcstel Alma, Binet Form\u00fcl\u00fc, Algoritma, Zaman Karma\u015f\u0131kl\u0131\u011f\u0131, Performans, Optimizasyon<br \/>\n<\/body><br \/>\n<\/html><\/p>\n","protected":false},"excerpt":{"rendered":"Fibonacci: O(2^N)’den O(1)’e Ge\u00e7i\u015f Fibonacci: O(2^N)’den O(1)’e Ge\u00e7i\u015f Fibonacci dizisi, matematik ve bilgisayar bilimlerinde s\u0131k\u00e7a kar\u015f\u0131la\u015ft\u0131\u011f\u0131m\u0131z, her terimin…","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"csco_page_header_type":"","csco_page_load_nextpost":"","csco_page_subscribe_form":"","csco_page_contact_form":"","footnotes":""},"categories":[1],"tags":[],"class_list":{"0":"post-4059","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-genel","7":"cs-entry","8":"cs-video-wrap"},"yoast_head":"\n<title>Fibonacci: O(2^N)'den O(1)'e Ge\u00e7i\u015f<\/title>\n<meta name=\"description\" content=\"Fibonacci dizisi, matematik ve bilgisayar bilimlerinde s\u0131k\u00e7a kar\u015f\u0131la\u015ft\u0131\u011f\u0131m\u0131z, her terimin kendinden \u00f6nceki iki terimin toplam\u0131 olarak tan\u0131mlanan bir say\u0131 dizisidir. Bu diziyi hesaplaman\u0131n bir\u00e7ok yolu vard\u0131r ve bu yollar\u0131n karma\u015f\u0131kl\u0131klar\u0131 (zaman karma\u015f\u0131kl\u0131\u011f\u0131) olduk\u00e7a farkl\u0131l\u0131k g\u00f6sterir. Bu makalede, Fibonacci dizisini hesaplaman\u0131n farkl\u0131 y\u00f6ntemlerini, bunlar\u0131n zaman karma\u015f\u0131kl\u0131klar\u0131n\u0131 ve \u00f6zellikle O(2^N) karma\u015f\u0131kl\u0131\u011f\u0131ndan O(1) karma\u015f\u0131kl\u0131\u011f\u0131na nas\u0131l ula\u015fabilece\u011fimizi detayl\u0131 olarak inceleyece\u011fiz. 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Bu makalede, Fibonacci dizisini hesaplaman\u0131n farkl\u0131 y\u00f6ntemlerini, bunlar\u0131n zaman karma\u015f\u0131kl\u0131klar\u0131n\u0131 ve \u00f6zellikle O(2^N) karma\u015f\u0131kl\u0131\u011f\u0131ndan O(1) karma\u015f\u0131kl\u0131\u011f\u0131na nas\u0131l ula\u015fabilece\u011fimizi detayl\u0131 olarak inceleyece\u011fiz. 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Bu diziyi hesaplaman\u0131n bir\u00e7ok yolu vard\u0131r ve bu yollar\u0131n karma\u015f\u0131kl\u0131klar\u0131 (zaman karma\u015f\u0131kl\u0131\u011f\u0131) olduk\u00e7a farkl\u0131l\u0131k g\u00f6sterir. Bu makalede, Fibonacci dizisini hesaplaman\u0131n farkl\u0131 y\u00f6ntemlerini, bunlar\u0131n zaman karma\u015f\u0131kl\u0131klar\u0131n\u0131 ve \u00f6zellikle O(2^N) karma\u015f\u0131kl\u0131\u011f\u0131ndan O(1) karma\u015f\u0131kl\u0131\u011f\u0131na nas\u0131l ula\u015fabilece\u011fimizi detayl\u0131 olarak inceleyece\u011fiz. Fatih Soysal olarak sizlere bu konuyu ad\u0131m ad\u0131m a\u00e7\u0131klayaca\u011f\u0131m.\",\"breadcrumb\":{\"@id\":\"https:\/\/fatihsoysal.com\/blog\/fibonacci-o2nden-o1e-gecis\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/fatihsoysal.com\/blog\/fibonacci-o2nden-o1e-gecis\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/fatihsoysal.com\/blog\/fibonacci-o2nden-o1e-gecis\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Anasayfa\",\"item\":\"https:\/\/fatihsoysal.com\/blog\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Fibonacci: O(2^N)’den O(1)’e Ge\u00e7i\u015f\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/fatihsoysal.com\/blog\/#website\",\"url\":\"https:\/\/fatihsoysal.com\/blog\/\",\"name\":\"Fatihsoysal.com\",\"description\":\"Blog - Yaz\u0131l\u0131m D\u00fcnyas\u0131 Tecr\u00fcbelerim\",\"publisher\":{\"@id\":\"https:\/\/fatihsoysal.com\/blog\/#\/schema\/person\/002a254750921dcfd568a99e48240dd1\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/fatihsoysal.com\/blog\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"tr\"},{\"@type\":[\"Person\",\"Organization\"],\"@id\":\"https:\/\/fatihsoysal.com\/blog\/#\/schema\/person\/002a254750921dcfd568a99e48240dd1\",\"name\":\"Fatih Soysal\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"tr\",\"@id\":\"https:\/\/fatihsoysal.com\/blog\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/fatihsoysal.com\/blog\/wp-content\/uploads\/2024\/04\/cropped-replicate-prediction-3kgg1hgjn5rgp0cf0p5tr0jw7w-1.png\",\"contentUrl\":\"https:\/\/fatihsoysal.com\/blog\/wp-content\/uploads\/2024\/04\/cropped-replicate-prediction-3kgg1hgjn5rgp0cf0p5tr0jw7w-1.png\",\"width\":512,\"height\":512,\"caption\":\"Fatih Soysal\"},\"logo\":{\"@id\":\"https:\/\/fatihsoysal.com\/blog\/#\/schema\/person\/image\/\"},\"description\":\"Kullan\u0131m ve kodlama m\u00fckemmeliyetini odak alan uygulamalar olu\u015fturma deneyimine sahip, profesyonel olarak 15+ y\u0131l \u00fczeri deneyime sahip bir yaz\u0131l\u0131m m\u00fchendisi.\",\"url\":\"https:\/\/fatihsoysal.com\/blog\/author\/fatihsoysal\/\"}]}<\/script>\n","yoast_head_json":{"title":"Fibonacci: O(2^N)'den O(1)'e Ge\u00e7i\u015f","description":"Fibonacci dizisi, matematik ve bilgisayar bilimlerinde s\u0131k\u00e7a kar\u015f\u0131la\u015ft\u0131\u011f\u0131m\u0131z, her terimin kendinden \u00f6nceki iki terimin toplam\u0131 olarak tan\u0131mlanan bir say\u0131 dizisidir. Bu diziyi hesaplaman\u0131n bir\u00e7ok yolu vard\u0131r ve bu yollar\u0131n karma\u015f\u0131kl\u0131klar\u0131 (zaman karma\u015f\u0131kl\u0131\u011f\u0131) olduk\u00e7a farkl\u0131l\u0131k g\u00f6sterir. Bu makalede, Fibonacci dizisini hesaplaman\u0131n farkl\u0131 y\u00f6ntemlerini, bunlar\u0131n zaman karma\u015f\u0131kl\u0131klar\u0131n\u0131 ve \u00f6zellikle O(2^N) karma\u015f\u0131kl\u0131\u011f\u0131ndan O(1) karma\u015f\u0131kl\u0131\u011f\u0131na nas\u0131l ula\u015fabilece\u011fimizi detayl\u0131 olarak inceleyece\u011fiz. Fatih Soysal olarak sizlere bu konuyu ad\u0131m ad\u0131m a\u00e7\u0131klayaca\u011f\u0131m.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/fatihsoysal.com\/blog\/fibonacci-o2nden-o1e-gecis\/","og_locale":"tr_TR","og_type":"article","og_title":"Fibonacci: O(2^N)'den O(1)'e Ge\u00e7i\u015f","og_description":"Fibonacci dizisi, matematik ve bilgisayar bilimlerinde s\u0131k\u00e7a kar\u015f\u0131la\u015ft\u0131\u011f\u0131m\u0131z, her terimin kendinden \u00f6nceki iki terimin toplam\u0131 olarak tan\u0131mlanan bir say\u0131 dizisidir. Bu diziyi hesaplaman\u0131n bir\u00e7ok yolu vard\u0131r ve bu yollar\u0131n karma\u015f\u0131kl\u0131klar\u0131 (zaman karma\u015f\u0131kl\u0131\u011f\u0131) olduk\u00e7a farkl\u0131l\u0131k g\u00f6sterir. Bu makalede, Fibonacci dizisini hesaplaman\u0131n farkl\u0131 y\u00f6ntemlerini, bunlar\u0131n zaman karma\u015f\u0131kl\u0131klar\u0131n\u0131 ve \u00f6zellikle O(2^N) karma\u015f\u0131kl\u0131\u011f\u0131ndan O(1) karma\u015f\u0131kl\u0131\u011f\u0131na nas\u0131l ula\u015fabilece\u011fimizi detayl\u0131 olarak inceleyece\u011fiz. Fatih Soysal olarak sizlere bu konuyu ad\u0131m ad\u0131m a\u00e7\u0131klayaca\u011f\u0131m.","og_url":"https:\/\/fatihsoysal.com\/blog\/fibonacci-o2nden-o1e-gecis\/","og_site_name":"Kodlar\u0131n Gizemli D\u00fcnyas\u0131","article_published_time":"2024-11-16T17:46:32+00:00","author":"Fatih Soysal","twitter_card":"summary_large_image","twitter_misc":{"Yazan:":"Fatih Soysal","Tahmini okuma s\u00fcresi":"1 dakika"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/fatihsoysal.com\/blog\/fibonacci-o2nden-o1e-gecis\/#article","isPartOf":{"@id":"https:\/\/fatihsoysal.com\/blog\/fibonacci-o2nden-o1e-gecis\/"},"author":{"name":"Fatih Soysal","@id":"https:\/\/fatihsoysal.com\/blog\/#\/schema\/person\/002a254750921dcfd568a99e48240dd1"},"headline":"Fibonacci: O(2^N)’den O(1)’e Ge\u00e7i\u015f","datePublished":"2024-11-16T17:46:32+00:00","mainEntityOfPage":{"@id":"https:\/\/fatihsoysal.com\/blog\/fibonacci-o2nden-o1e-gecis\/"},"wordCount":720,"commentCount":0,"publisher":{"@id":"https:\/\/fatihsoysal.com\/blog\/#\/schema\/person\/002a254750921dcfd568a99e48240dd1"},"inLanguage":"tr","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/fatihsoysal.com\/blog\/fibonacci-o2nden-o1e-gecis\/#respond"]}],"copyrightYear":"2024","copyrightHolder":{"@id":"https:\/\/fatihsoysal.com\/blog\/#organization"}},{"@type":"WebPage","@id":"https:\/\/fatihsoysal.com\/blog\/fibonacci-o2nden-o1e-gecis\/","url":"https:\/\/fatihsoysal.com\/blog\/fibonacci-o2nden-o1e-gecis\/","name":"Fibonacci: O(2^N)'den O(1)'e Ge\u00e7i\u015f","isPartOf":{"@id":"https:\/\/fatihsoysal.com\/blog\/#website"},"datePublished":"2024-11-16T17:46:32+00:00","description":"Fibonacci dizisi, matematik ve bilgisayar bilimlerinde s\u0131k\u00e7a kar\u015f\u0131la\u015ft\u0131\u011f\u0131m\u0131z, her terimin kendinden \u00f6nceki iki terimin toplam\u0131 olarak tan\u0131mlanan bir say\u0131 dizisidir. Bu diziyi hesaplaman\u0131n bir\u00e7ok yolu vard\u0131r ve bu yollar\u0131n karma\u015f\u0131kl\u0131klar\u0131 (zaman karma\u015f\u0131kl\u0131\u011f\u0131) olduk\u00e7a farkl\u0131l\u0131k g\u00f6sterir. Bu makalede, Fibonacci dizisini hesaplaman\u0131n farkl\u0131 y\u00f6ntemlerini, bunlar\u0131n zaman karma\u015f\u0131kl\u0131klar\u0131n\u0131 ve \u00f6zellikle O(2^N) karma\u015f\u0131kl\u0131\u011f\u0131ndan O(1) karma\u015f\u0131kl\u0131\u011f\u0131na nas\u0131l ula\u015fabilece\u011fimizi detayl\u0131 olarak inceleyece\u011fiz. Fatih Soysal olarak sizlere bu konuyu ad\u0131m ad\u0131m a\u00e7\u0131klayaca\u011f\u0131m.","breadcrumb":{"@id":"https:\/\/fatihsoysal.com\/blog\/fibonacci-o2nden-o1e-gecis\/#breadcrumb"},"inLanguage":"tr","potentialAction":[{"@type":"ReadAction","target":["https:\/\/fatihsoysal.com\/blog\/fibonacci-o2nden-o1e-gecis\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/fatihsoysal.com\/blog\/fibonacci-o2nden-o1e-gecis\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Anasayfa","item":"https:\/\/fatihsoysal.com\/blog\/"},{"@type":"ListItem","position":2,"name":"Fibonacci: O(2^N)’den O(1)’e Ge\u00e7i\u015f"}]},{"@type":"WebSite","@id":"https:\/\/fatihsoysal.com\/blog\/#website","url":"https:\/\/fatihsoysal.com\/blog\/","name":"Fatihsoysal.com","description":"Blog - Yaz\u0131l\u0131m D\u00fcnyas\u0131 Tecr\u00fcbelerim","publisher":{"@id":"https:\/\/fatihsoysal.com\/blog\/#\/schema\/person\/002a254750921dcfd568a99e48240dd1"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/fatihsoysal.com\/blog\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"tr"},{"@type":["Person","Organization"],"@id":"https:\/\/fatihsoysal.com\/blog\/#\/schema\/person\/002a254750921dcfd568a99e48240dd1","name":"Fatih Soysal","image":{"@type":"ImageObject","inLanguage":"tr","@id":"https:\/\/fatihsoysal.com\/blog\/#\/schema\/person\/image\/","url":"https:\/\/fatihsoysal.com\/blog\/wp-content\/uploads\/2024\/04\/cropped-replicate-prediction-3kgg1hgjn5rgp0cf0p5tr0jw7w-1.png","contentUrl":"https:\/\/fatihsoysal.com\/blog\/wp-content\/uploads\/2024\/04\/cropped-replicate-prediction-3kgg1hgjn5rgp0cf0p5tr0jw7w-1.png","width":512,"height":512,"caption":"Fatih Soysal"},"logo":{"@id":"https:\/\/fatihsoysal.com\/blog\/#\/schema\/person\/image\/"},"description":"Kullan\u0131m ve kodlama m\u00fckemmeliyetini odak alan uygulamalar olu\u015fturma deneyimine sahip, profesyonel olarak 15+ y\u0131l \u00fczeri deneyime sahip bir yaz\u0131l\u0131m m\u00fchendisi.","url":"https:\/\/fatihsoysal.com\/blog\/author\/fatihsoysal\/"}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/fatihsoysal.com\/blog\/wp-json\/wp\/v2\/posts\/4059","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/fatihsoysal.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/fatihsoysal.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/fatihsoysal.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fatihsoysal.com\/blog\/wp-json\/wp\/v2\/comments?post=4059"}],"version-history":[{"count":0,"href":"https:\/\/fatihsoysal.com\/blog\/wp-json\/wp\/v2\/posts\/4059\/revisions"}],"wp:attachment":[{"href":"https:\/\/fatihsoysal.com\/blog\/wp-json\/wp\/v2\/media?parent=4059"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/fatihsoysal.com\/blog\/wp-json\/wp\/v2\/categories?post=4059"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/fatihsoysal.com\/blog\/wp-json\/wp\/v2\/tags?post=4059"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

{"id":4059,"date":"2024-11-16T20:46:32","date_gmt":"2024-11-16T17:46:32","guid":{"rendered":"https:\/\/fatihsoysal.com\/blog\/fibonacci-o2nden-o1e-gecis\/"},"modified":"2024-11-16T20:46:32","modified_gmt":"2024-11-16T17:46:32","slug":"fibonacci-o2nden-o1e-gecis","status":"publish","type":"post","link":"https:\/\/fatihsoysal.com\/blog\/fibonacci-o2nden-o1e-gecis\/","title":{"rendered":"Fibonacci: O(2^N)’den O(1)’e Ge\u00e7i\u015f"},"content":{"rendered":"

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\n Fibonacci: O(2^N)’den O(1)’e Ge\u00e7i\u015f<\/title><br \/>\n<\/head><br \/>\n<body><\/p>\n<p>Fibonacci: O(2^N)’den O(1)’e Ge\u00e7i\u015f<\/p>\n<p>Fibonacci dizisi, matematik ve bilgisayar bilimlerinde s\u0131k\u00e7a kar\u015f\u0131la\u015ft\u0131\u011f\u0131m\u0131z, her terimin kendinden \u00f6nceki iki terimin toplam\u0131 olarak tan\u0131mlanan bir say\u0131 dizisidir. Bu diziyi hesaplaman\u0131n bir\u00e7ok yolu vard\u0131r ve bu yollar\u0131n karma\u015f\u0131kl\u0131klar\u0131 (zaman karma\u015f\u0131kl\u0131\u011f\u0131) olduk\u00e7a farkl\u0131l\u0131k g\u00f6sterir. Bu makalede, Fibonacci dizisini hesaplaman\u0131n farkl\u0131 y\u00f6ntemlerini, bunlar\u0131n zaman karma\u015f\u0131kl\u0131klar\u0131n\u0131 ve \u00f6zellikle O(2^N) karma\u015f\u0131kl\u0131\u011f\u0131ndan O(1) karma\u015f\u0131kl\u0131\u011f\u0131na nas\u0131l ula\u015fabilece\u011fimizi detayl\u0131 olarak inceleyece\u011fiz. <a href=\"https:\/\/fatihsoysal.com\">Fatih Soysal<\/a> olarak sizlere bu konuyu ad\u0131m ad\u0131m a\u00e7\u0131klayaca\u011f\u0131m.<\/p>\n<h2>Naif Yakla\u015f\u0131m: O(2^N) Karma\u015f\u0131kl\u0131\u011f\u0131<\/h2>\n<p>Fibonacci dizisini hesaplaman\u0131n en basit, ancak en verimsiz yolu, do\u011frudan rek\u00fcrsif bir fonksiyon kullanmakt\u0131r. Bu y\u00f6ntemde, her Fibonacci say\u0131s\u0131 i\u00e7in fonksiyon kendini iki kez \u00e7a\u011f\u0131r\u0131r. Sonu\u00e7 olarak, ayn\u0131 Fibonacci say\u0131s\u0131 bir\u00e7ok kez hesaplan\u0131r. Bu da, zaman karma\u015f\u0131kl\u0131\u011f\u0131 O(2^N) olan, yani N say\u0131s\u0131 artt\u0131k\u00e7a \u00fcstel olarak b\u00fcy\u00fcyen bir algoritma ortaya \u00e7\u0131kar\u0131r. Bu y\u00f6ntem, b\u00fcy\u00fck N de\u011ferleri i\u00e7in son derece yava\u015ft\u0131r. \u00d6rne\u011fin, F(35)’i hesaplamak bile uzun s\u00fcrebilir.<\/p>\n<pre><code>\nfunction fibonacciRekursif(n) {\n if (n <= 1) return n;\n return fibonacciRekursif(n - 1) + fibonacciRekursif(n - 2);\n}\n<\/code><\/pre>\n<h2>\u0130yile\u015ftirme: \u0130teratif Yakla\u015f\u0131m - O(N) Karma\u015f\u0131kl\u0131\u011f\u0131<\/h2>\n<p>Daha verimli bir yakla\u015f\u0131m, iteratif bir d\u00f6ng\u00fc kullanmakt\u0131r. Bu y\u00f6ntemde, her Fibonacci say\u0131s\u0131 yaln\u0131zca bir kez hesaplan\u0131r. Bu, zaman karma\u015f\u0131kl\u0131\u011f\u0131n\u0131 O(N)'ye d\u00fc\u015f\u00fcr\u00fcr. Yani, N say\u0131s\u0131 artt\u0131k\u00e7a lineer olarak artan bir performans elde ederiz. Bu, rek\u00fcrsif yakla\u015f\u0131ma g\u00f6re \u00e7ok daha h\u0131zl\u0131d\u0131r.<\/p>\n<pre><code>\nfunction fibonacciIteratif(n) {\n let a = 0, b = 1, temp;\n for (let i = 0; i < n; i++) {\n temp = a;\n a = b;\n b = temp + b;\n }\n return a;\n}\n<\/code><\/pre>\n<h2>Dinamik Programlama: Bellek Kullan\u0131m\u0131 ile H\u0131zland\u0131rma<\/h2>\n<p>Dinamik programlama tekni\u011fini kullanarak da Fibonacci dizisini hesaplayabiliriz. Bu y\u00f6ntemde, daha \u00f6nce hesaplanm\u0131\u015f Fibonacci say\u0131lar\u0131n\u0131 bir dizi veya s\u00f6zl\u00fckte saklar ve tekrar hesaplamaktan ka\u00e7\u0131n\u0131r\u0131z. Bu, iteratif yakla\u015f\u0131ma benzer bir zaman karma\u015f\u0131kl\u0131\u011f\u0131na (O(N)) sahip olsa da, baz\u0131 durumlarda \u00f6zellikle tekrarlanan hesaplamalar\u0131n fazla oldu\u011fu durumlarda, performans art\u0131\u015f\u0131 sa\u011flayabilir.<\/p>\n<h2>Matris \u00dcstel Alma: O(log N) Karma\u015f\u0131kl\u0131\u011f\u0131<\/h2>\n<p>Fibonacci say\u0131lar\u0131n\u0131 hesaplaman\u0131n daha da verimli bir yolu, matris \u00fcstel alma kullanmakt\u0131r. Fibonacci dizisi, bir 2x2 matrisin \u00fcss\u00fc kullan\u0131larak hesaplanabilir. Matris \u00fcstel alma algoritmalar\u0131, logaritmik zaman karma\u015f\u0131kl\u0131\u011f\u0131na (O(log N)) sahiptir. Bu y\u00f6ntem, b\u00fcy\u00fck N de\u011ferleri i\u00e7in \u00e7ok daha h\u0131zl\u0131d\u0131r. Bu y\u00f6ntemin detaylar\u0131 daha karma\u015f\u0131k olsa da, performans avantaj\u0131 nedeniyle tercih edilebilir.<\/p>\n<h2>Binet Form\u00fcl\u00fc: O(1) Karma\u015f\u0131kl\u0131\u011f\u0131<\/h2>\n<p>Son olarak, en h\u0131zl\u0131 y\u00f6ntem Binet form\u00fcl\u00fcd\u00fcr. Bu form\u00fcl, Fibonacci say\u0131s\u0131n\u0131 do\u011frudan hesaplar ve zaman karma\u015f\u0131kl\u0131\u011f\u0131 O(1)'dir. Yani, N de\u011ferinden ba\u011f\u0131ms\u0131z olarak sabit s\u00fcrede sonucu verir. Ancak, form\u00fclde karek\u00f6k ve \u00fcstel fonksiyonlar kullan\u0131ld\u0131\u011f\u0131 i\u00e7in, \u00e7ok b\u00fcy\u00fck N de\u011ferleri i\u00e7in yuvarlama hatalar\u0131 ortaya \u00e7\u0131kabilir. Bu da hassasiyet kayb\u0131na yol a\u00e7abilir. Bu nedenle, y\u00fcksek do\u011fruluk gerektiren durumlarda, di\u011fer y\u00f6ntemleri kullanmak daha uygun olabilir.<\/p>\n<p>Binet form\u00fcl\u00fc \u015fu \u015fekildedir:<\/p>\n<p>F(n) = (\u03c6<sup>n<\/sup> - \u03c8<sup>n<\/sup>) \/ \u221a5<\/p>\n<p>burada \u03c6 = (1 + \u221a5) \/ 2 (alt\u0131n oran) ve \u03c8 = (1 - \u221a5) \/ 2 dir.<\/p>\n<h2>Sonu\u00e7<\/h2>\n<p>Fibonacci dizisini hesaplaman\u0131n \u00e7e\u015fitli y\u00f6ntemleri vard\u0131r. Her y\u00f6ntemin zaman karma\u015f\u0131kl\u0131\u011f\u0131 farkl\u0131d\u0131r. En yava\u015f y\u00f6ntem O(2^N), en h\u0131zl\u0131 y\u00f6ntem ise O(1) karma\u015f\u0131kl\u0131\u011f\u0131na sahiptir. Uygulamada, ihtiya\u00e7 duyulan do\u011fruluk ve performans gereksinimlerine g\u00f6re uygun y\u00f6ntemi se\u00e7mek \u00f6nemlidir. B\u00fcy\u00fck N de\u011ferleri i\u00e7in, matris \u00fcstel alma veya Binet form\u00fcl\u00fc (do\u011fruluk kayb\u0131n\u0131 g\u00f6ze alarak) tercih edilmelidir. Daha k\u00fc\u00e7\u00fck N de\u011ferleri i\u00e7in ise iteratif yakla\u015f\u0131m yeterli olabilir. <a href=\"https:\/\/dev.to\/joseiedo\/implementando-fibonacci-de-o2n-a-o1-4jij\">Bu \u0130ngilizce makale<\/a> size daha detayl\u0131 bilgiler sa\u011flayabilir.<\/p>\n<p>Umar\u0131m bu makale size Fibonacci dizisi ve hesaplama y\u00f6ntemleri hakk\u0131nda daha fazla bilgi sa\u011flam\u0131\u015ft\u0131r. Ba\u015fka sorular\u0131n\u0131z varsa, l\u00fctfen ileti\u015fime ge\u00e7in.<\/p>\n<p>#Etiketler: Fibonacci, O(2^N), O(1), O(N), O(log N), Rek\u00fcrsif, \u0130teratif, Dinamik Programlama, Matris \u00dcstel Alma, Binet Form\u00fcl\u00fc, Algoritma, Zaman Karma\u015f\u0131kl\u0131\u011f\u0131, Performans, Optimizasyon<br \/>\n<\/body><br \/>\n<\/html><\/p>\n","protected":false},"excerpt":{"rendered":"Fibonacci: O(2^N)’den O(1)’e Ge\u00e7i\u015f Fibonacci: O(2^N)’den O(1)’e Ge\u00e7i\u015f Fibonacci dizisi, matematik ve bilgisayar bilimlerinde s\u0131k\u00e7a kar\u015f\u0131la\u015ft\u0131\u011f\u0131m\u0131z, her terimin…","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"csco_page_header_type":"","csco_page_load_nextpost":"","csco_page_subscribe_form":"","csco_page_contact_form":"","footnotes":""},"categories":[1],"tags":[],"class_list":{"0":"post-4059","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-genel","7":"cs-entry","8":"cs-video-wrap"},"yoast_head":"\n<title>Fibonacci: O(2^N)'den O(1)'e Ge\u00e7i\u015f<\/title>\n<meta name=\"description\" content=\"Fibonacci dizisi, matematik ve bilgisayar bilimlerinde s\u0131k\u00e7a kar\u015f\u0131la\u015ft\u0131\u011f\u0131m\u0131z, her terimin kendinden \u00f6nceki iki terimin toplam\u0131 olarak tan\u0131mlanan bir say\u0131 dizisidir. Bu diziyi hesaplaman\u0131n bir\u00e7ok yolu vard\u0131r ve bu yollar\u0131n karma\u015f\u0131kl\u0131klar\u0131 (zaman karma\u015f\u0131kl\u0131\u011f\u0131) olduk\u00e7a farkl\u0131l\u0131k g\u00f6sterir. Bu makalede, Fibonacci dizisini hesaplaman\u0131n farkl\u0131 y\u00f6ntemlerini, bunlar\u0131n zaman karma\u015f\u0131kl\u0131klar\u0131n\u0131 ve \u00f6zellikle O(2^N) karma\u015f\u0131kl\u0131\u011f\u0131ndan O(1) karma\u015f\u0131kl\u0131\u011f\u0131na nas\u0131l ula\u015fabilece\u011fimizi detayl\u0131 olarak inceleyece\u011fiz. Fatih Soysal olarak sizlere bu konuyu ad\u0131m ad\u0131m a\u00e7\u0131klayaca\u011f\u0131m.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/fatihsoysal.com\/blog\/fibonacci-o2nden-o1e-gecis\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Fibonacci: O(2^N)'den O(1)'e Ge\u00e7i\u015f\" \/>\n<meta property=\"og:description\" content=\"Fibonacci dizisi, matematik ve bilgisayar bilimlerinde s\u0131k\u00e7a kar\u015f\u0131la\u015ft\u0131\u011f\u0131m\u0131z, her terimin kendinden \u00f6nceki iki terimin toplam\u0131 olarak tan\u0131mlanan bir say\u0131 dizisidir. Bu diziyi hesaplaman\u0131n bir\u00e7ok yolu vard\u0131r ve bu yollar\u0131n karma\u015f\u0131kl\u0131klar\u0131 (zaman karma\u015f\u0131kl\u0131\u011f\u0131) olduk\u00e7a farkl\u0131l\u0131k g\u00f6sterir. Bu makalede, Fibonacci dizisini hesaplaman\u0131n farkl\u0131 y\u00f6ntemlerini, bunlar\u0131n zaman karma\u015f\u0131kl\u0131klar\u0131n\u0131 ve \u00f6zellikle O(2^N) karma\u015f\u0131kl\u0131\u011f\u0131ndan O(1) karma\u015f\u0131kl\u0131\u011f\u0131na nas\u0131l ula\u015fabilece\u011fimizi detayl\u0131 olarak inceleyece\u011fiz. 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