{"id":43102,"date":"2026-07-05T21:06:03","date_gmt":"2026-07-05T18:06:03","guid":{"rendered":"https:\/\/fatihsoysal.com\/blog\/agac-yapilarinda-dikey-siralama-vertical-order-traversal-nedir-ve-neden-onemlidir\/"},"modified":"2026-07-05T21:06:24","modified_gmt":"2026-07-05T18:06:24","slug":"agac-yapilarinda-dikey-siralama-vertical-order-traversal-nedir-ve-neden-onemlidir","status":"publish","type":"post","link":"https:\/\/fatihsoysal.com\/blog\/agac-yapilarinda-dikey-siralama-vertical-order-traversal-nedir-ve-neden-onemlidir\/","title":{"rendered":"A\u011fa\u00e7 Yap\u0131lar\u0131nda Dikey S\u0131ralama: Vertical Order Traversal Nedir ve Neden \u00d6nemlidir?"},"content":{"rendered":"

A\u011fa\u00e7 Yap\u0131lar\u0131nda Dikey S\u0131ralama: Vertical Order Traversal Nedir ve Neden \u00d6nemlidir?<\/h2>\n

A\u011fa\u00e7 yap\u0131lar\u0131ndaki d\u00fc\u011f\u00fcmleri dikey eksende s\u0131ralama ihtiyac\u0131yla m\u0131 kar\u015f\u0131la\u015f\u0131yorsunuz? Vertical Order Traversal, bu karma\u015f\u0131k problemi \u00e7\u00f6zerek verilerinizi d\u00fczenli ve anlaml\u0131 bir \u015fekilde sunman\u0131z\u0131 sa\u011flayan g\u00fc\u00e7l\u00fc bir algoritmad\u0131r. Bu makalede, Vertical Order Traversal’\u0131n temel prensiplerinden ger\u00e7ek d\u00fcnya uygulamalar\u0131na kadar her \u015feyi ke\u015ffedin.<\/p>\n

Veri yap\u0131lar\u0131 d\u00fcnyas\u0131nda a\u011fa\u00e7lar, hiyerar\u015fik ili\u015fkileri temsil etmek i\u00e7in vazge\u00e7ilmez ara\u00e7lard\u0131r. Bir organizasyon \u015femas\u0131ndan dosya sistemlerine, genetik dizilimlerden web sayfalar\u0131n\u0131n DOM (Document Object Model) yap\u0131s\u0131na kadar pek \u00e7ok alanda kar\u015f\u0131m\u0131za \u00e7\u0131karlar. Ancak bazen, bu hiyerar\u015fik yap\u0131n\u0131n \u00f6tesine ge\u00e7erek d\u00fc\u011f\u00fcmlerin belirli bir d\u00fczene g\u00f6re s\u0131ralanmas\u0131 gerekebilir. \u0130\u015fte bu noktada Vertical Order Traversal (Dikey S\u0131ral\u0131 Ge\u00e7i\u015f) devreye girer. Bu \u00f6zel a\u011fa\u00e7 ge\u00e7i\u015f (tree traversal) y\u00f6ntemi, a\u011fa\u00e7taki t\u00fcm d\u00fc\u011f\u00fcmleri dikey s\u00fctunlar halinde d\u00fczenleyerek belirli bir s\u0131raya g\u00f6re ziyaret etmeyi ama\u00e7lar. Bu, sadece bir algoritmik problem \u00e7\u00f6z\u00fcm\u00fc de\u011fil, ayn\u0131 zamanda verilerin g\u00f6rselle\u015ftirilmesi ve analiz edilmesi i\u00e7in de kritik bir \u00f6neme sahiptir. \u00d6rne\u011fin, bir zaman \u00e7izelgesi veya bir i\u015flem ak\u0131\u015f\u0131 gibi dikeyde ilerleyen verileri, a\u011fa\u00e7 yap\u0131s\u0131nda tutsan\u0131z bile, dikey s\u0131ral\u0131 ge\u00e7i\u015f sayesinde kolayca okunabilir ve anlamland\u0131r\u0131labilir bir formata d\u00f6n\u00fc\u015ft\u00fcrebilirsiniz. Bu y\u00f6ntem, \u00f6zellikle ikili a\u011fa\u00e7lar (binary trees) ve ikili arama a\u011fa\u00e7lar\u0131 (binary search trees) gibi yayg\u0131n a\u011fa\u00e7 t\u00fcrlerinde etkili bir \u015fekilde kullan\u0131l\u0131r. Geleneksel ge\u00e7i\u015f y\u00f6ntemleri olan \u00f6ncelikli (pre-order), ortancal\u0131 (in-order) ve soncul (post-order) ge\u00e7i\u015fler genellikle d\u00fc\u011f\u00fcmlerin derinlik veya geni\u015flik baz\u0131nda s\u0131ralanmas\u0131na odaklan\u0131rken, Vertical Order Traversal tamamen farkl\u0131 bir perspektif sunar: dikey konum. Bu makalede, bu g\u00fc\u00e7l\u00fc tekni\u011fin ard\u0131ndaki mant\u0131\u011f\u0131, nas\u0131l uyguland\u0131\u011f\u0131n\u0131 ve ger\u00e7ek d\u00fcnyadaki \u00e7e\u015fitli senaryolarda nas\u0131l de\u011fer yaratt\u0131\u011f\u0131n\u0131 derinlemesine inceleyece\u011fiz. Ba\u015flang\u0131\u00e7tan ileri seviyeye kadar her ad\u0131m\u0131 kapsayarak, bu konuya hakim olman\u0131z\u0131 sa\u011flayacak kapsaml\u0131 bir rehber sunmay\u0131 hedefliyoruz. B\u00f6ylece, karma\u015f\u0131k veri yap\u0131lar\u0131yla \u00e7al\u0131\u015f\u0131rken kar\u015f\u0131la\u015fabilece\u011finiz s\u0131ralama ve d\u00fczenleme zorluklar\u0131n\u0131n \u00fcstesinden gelmek i\u00e7in g\u00fc\u00e7l\u00fc bir araca sahip olacaks\u0131n\u0131z.<\/p>\n

Vertical Order Traversal’\u0131n Temel Kavramlar\u0131 ve \u00c7al\u0131\u015fma Prensibi<\/h2>\n

Vertical Order Traversal’\u0131 anlaman\u0131n ilk ad\u0131m\u0131, a\u011fa\u00e7 d\u00fc\u011f\u00fcmlerini (nodes) sadece hiyerar\u015fik birer eleman olarak de\u011fil, ayn\u0131 zamanda iki boyutlu bir d\u00fczlemdeki noktalar olarak hayal etmektir. Bu yakla\u015f\u0131m, bu ge\u00e7i\u015f y\u00f6nteminin temelini olu\u015fturur. A\u011fac\u0131n k\u00f6k d\u00fc\u011f\u00fcm\u00fc (root node) genellikle (0,0) koordinat\u0131nda kabul edilir. Buradan hareketle, her bir d\u00fc\u011f\u00fcme dikey bir “s\u00fctun indeksi” (column index) ve bir “sat\u0131r indeksi” (row index) atan\u0131r. S\u00fctun indeksi, d\u00fc\u011f\u00fcm\u00fcn k\u00f6ke g\u00f6re yatay konumunu belirlerken, sat\u0131r indeksi d\u00fc\u011f\u00fcm\u00fcn derinli\u011fini g\u00f6sterir. \u00d6rne\u011fin, k\u00f6k\u00fcn sol \u00e7ocu\u011fu -1 s\u00fctun indeksine, sa\u011f \u00e7ocu\u011fu ise +1 s\u00fctun indeksine sahip olur. Her bir ad\u0131mda, sol \u00e7ocu\u011fa giderken s\u00fctun indeksi bir azalt\u0131l\u0131rken, sa\u011f \u00e7ocu\u011fa giderken bir art\u0131r\u0131l\u0131r. Sat\u0131r indeksi ise her bir seviyede bir artar, bu da d\u00fc\u011f\u00fcm\u00fcn k\u00f6kten ne kadar uzakta oldu\u011funu belirtir. Bu basit koordinat sistemi, a\u011fa\u00e7taki her d\u00fc\u011f\u00fcm\u00fcn benzersiz bir dikey konuma sahip olmas\u0131n\u0131 sa\u011flar.<\/p>\n

Bu koordinat atamas\u0131 tamamland\u0131ktan sonra, Vertical Order Traversal’\u0131n as\u0131l amac\u0131 devreye girer: t\u00fcm d\u00fc\u011f\u00fcmleri s\u00fctun indekslerine g\u00f6re gruplamak ve her bir s\u00fctun i\u00e7indeki d\u00fc\u011f\u00fcmleri belirli bir s\u0131raya g\u00f6re listelemek. Genellikle, ayn\u0131 s\u00fctun indeksine sahip d\u00fc\u011f\u00fcmler kendi aralar\u0131nda sat\u0131r indeksine (yani derinli\u011fe) g\u00f6re s\u0131ralan\u0131r. E\u011fer ayn\u0131 s\u00fctun ve sat\u0131r indeksine sahip birden fazla d\u00fc\u011f\u00fcm varsa (ki bu genellikle m\u00fcmk\u00fcn de\u011fildir, ancak baz\u0131 \u00f6zel a\u011fa\u00e7 yap\u0131lar\u0131nda veya ayn\u0131 seviyede farkl\u0131 yollardan eri\u015filen d\u00fc\u011f\u00fcmlerde teorik olarak d\u00fc\u015f\u00fcn\u00fclebilir), bu d\u00fc\u011f\u00fcmlerin orijinal a\u011fa\u00e7taki eklenme s\u0131ras\u0131na veya de\u011ferlerine g\u00f6re ikincil bir s\u0131ralama kriteri uygulanabilir. Bu s\u0131ralama prensibi, dikey s\u00fctunlar\u0131n soldan sa\u011fa do\u011fru, her s\u00fctun i\u00e7indeki d\u00fc\u011f\u00fcmlerin ise yukar\u0131dan a\u015fa\u011f\u0131ya do\u011fru okunmas\u0131n\u0131 sa\u011flar. Bu sayede, a\u011fa\u00e7taki t\u00fcm d\u00fc\u011f\u00fcmler, g\u00f6rsel olarak bir tabloya veya bir s\u00fctun grafi\u011fine benzer \u015fekilde d\u00fczenlenmi\u015f olur. Bu, sadece veriyi organize etmekle kalmaz, ayn\u0131 zamanda belirli bir dikey aral\u0131ktaki t\u00fcm d\u00fc\u011f\u00fcmleri h\u0131zl\u0131ca bulma veya bir a\u011fac\u0131n dikey simetrisini inceleme gibi i\u015flemlerde de b\u00fcy\u00fck kolayl\u0131k sa\u011flar. Bu temel prensipleri anlamak, Vertical Order Traversal’\u0131n karma\u015f\u0131k gibi g\u00f6r\u00fcnen yap\u0131s\u0131n\u0131 basitle\u015ftirir ve bu g\u00fc\u00e7l\u00fc algoritman\u0131n nas\u0131l \u00e7al\u0131\u015ft\u0131\u011f\u0131n\u0131 kavraman\u0131za yard\u0131mc\u0131 olur.<\/p>\n

Vertical Order Traversal Nas\u0131l Uygulan\u0131r? Ad\u0131m Ad\u0131m Yakla\u015f\u0131mlar ve Algoritmalar<\/h2>\n

Vertical Order Traversal’\u0131 uygulamak i\u00e7in genellikle iki ana yakla\u015f\u0131m kullan\u0131l\u0131r: Geni\u015flik \u00d6ncelikli Arama (BFS) ve Derinlik \u00d6ncelikli Arama (DFS). Her iki yakla\u015f\u0131m da kendi avantajlar\u0131na sahiptir ve belirli senaryolara g\u00f6re tercih edilebilir. \u00d6nemli olan, her d\u00fc\u011f\u00fcme do\u011fru dikey konum (s\u00fctun indeksi) atayabilmek ve bu konumlar\u0131 kullanarak d\u00fc\u011f\u00fcmleri gruplayabilmektir. Geni\u015flik \u00d6ncelikli Arama (BFS) genellikle bir kuyruk (queue) veri yap\u0131s\u0131 kullan\u0131larak ger\u00e7ekle\u015ftirilir. Algoritma, k\u00f6k d\u00fc\u011f\u00fcmden ba\u015flayarak t\u00fcm d\u00fc\u011f\u00fcmleri seviye seviye ziyaret eder. Her d\u00fc\u011f\u00fcm\u00fc ziyaret etti\u011finde, ona bir dikey konum (horizontal_distance<\/code> veya column_index<\/code>) atar. K\u00f6k d\u00fc\u011f\u00fcm\u00fcn dikey konumu genellikle 0’d\u0131r. Bir d\u00fc\u011f\u00fcm\u00fcn sol \u00e7ocu\u011fu, ebeveyninin dikey konumundan 1 eksik, sa\u011f \u00e7ocu\u011fu ise 1 fazla dikey konuma sahip olur. BFS ile ilerlerken, bir harita (map veya dictionary) kullanarak her dikey konum i\u00e7in bir liste tutulur. Ziyaret edilen her d\u00fc\u011f\u00fcm, kendi dikey konumuna kar\u015f\u0131l\u0131k gelen listeye eklenir. Bu y\u00f6ntem, ayn\u0131 dikey konumdaki d\u00fc\u011f\u00fcmlerin derinli\u011fe g\u00f6re otomatik olarak s\u0131ralanmas\u0131n\u0131 sa\u011flar, \u00e7\u00fcnk\u00fc BFS do\u011fas\u0131 gere\u011fi d\u00fc\u011f\u00fcmleri seviye seviye i\u015fler. Bu, \u00f6zellikle ayn\u0131 dikey s\u00fctundaki d\u00fc\u011f\u00fcmlerin yukar\u0131dan a\u015fa\u011f\u0131ya do\u011fru s\u0131ralanmas\u0131n\u0131n istendi\u011fi durumlarda olduk\u00e7a avantajl\u0131d\u0131r.<\/p>\n

Di\u011fer bir yayg\u0131n yakla\u015f\u0131m ise Derinlik \u00d6ncelikli Arama (DFS) kullanmakt\u0131r. DFS, genellikle \u00f6zyinelemeli (recursive) bir fonksiyon veya bir y\u0131\u011f\u0131n (stack) veri yap\u0131s\u0131 kullan\u0131larak uygulan\u0131r. DFS ile Vertical Order Traversal uygularken, her \u00f6zyinelemeli \u00e7a\u011fr\u0131ya d\u00fc\u011f\u00fcm\u00fcn kendisi, mevcut dikey konum ve mevcut derinlik parametre olarak ge\u00e7irilir. K\u00f6k d\u00fc\u011f\u00fcm yine 0 dikey konum ve 0 derinlikle ba\u015flar. Sol \u00e7ocu\u011fa inildi\u011finde dikey konum azal\u0131r, derinlik artar; sa\u011f \u00e7ocu\u011fa inildi\u011finde dikey konum artar, derinlik artar. DFS’de de yine bir harita veri yap\u0131s\u0131 kullan\u0131l\u0131r, ancak bu sefer her dikey konum i\u00e7in d\u00fc\u011f\u00fcmlerin bir listesi yerine, d\u00fc\u011f\u00fcmlerin (de\u011fer, derinlik) \u00e7iftleri tutulur. DFS, bir dikey s\u00fctundaki t\u00fcm d\u00fc\u011f\u00fcmleri ziyaret ettikten sonra, bu d\u00fc\u011f\u00fcmlerin derinliklerine g\u00f6re s\u0131ralanmas\u0131 gerekir, \u00e7\u00fcnk\u00fc DFS do\u011fas\u0131 gere\u011fi \u00f6nce bir dal\u0131 sonuna kadar ke\u015ffeder. Bu ek s\u0131ralama ad\u0131m\u0131, BFS’nin sundu\u011fu otomatik s\u0131ralama avantaj\u0131n\u0131 ortadan kald\u0131r\u0131r ancak DFS’nin baz\u0131 durumlarda daha az bellek kullanmas\u0131 gibi avantajlar\u0131 olabilir. Her iki y\u00f6ntemde de, son ad\u0131mda, haritada tutulan dikey konum anahtarlar\u0131na g\u00f6re (soldan sa\u011fa do\u011fru) s\u0131ralan\u0131r ve her bir dikey konum i\u00e7in tutulan d\u00fc\u011f\u00fcm listeleri (derinli\u011fe g\u00f6re s\u0131ralanm\u0131\u015f olarak) \u00e7\u0131kt\u0131 olarak verilir. A\u015fa\u011f\u0131daki Python \u00f6rne\u011fi, BFS yakla\u015f\u0131m\u0131n\u0131 kullanarak Vertical Order Traversal’\u0131 nas\u0131l uygulayabilece\u011finizi g\u00f6stermektedir. Bu \u00f6rnek, d\u00fc\u011f\u00fcmlere dikey konum ve derinlik atama mant\u0131\u011f\u0131n\u0131 ve bu bilgileri kullanarak d\u00fc\u011f\u00fcmleri nas\u0131l gruplayaca\u011f\u0131n\u0131z\u0131 net bir \u015fekilde ortaya koymaktad\u0131r.<\/p>\n

\n
\nfrom collections import deque, defaultdict\n\nclass TreeNode:\n    def __init__(self, val=0, left=None, right=None):\n        self.val = val\n        self.left = left\n        self.right = right\n\ndef verticalOrderTraversal(root: TreeNode):\n    if not root:\n        return []\n\n    # {horizontal_distance: [(node_value, depth)]}\n    node_map = defaultdict(list)\n    \n    # (node, horizontal_distance, depth)\n    queue = deque([(root, 0, 0)])\n\n    min_hd = 0\n    max_hd = 0\n\n    while queue:\n        node, hd, depth = queue.popleft()\n\n        node_map[hd].append((node.val, depth))\n        \n        min_hd = min(min_hd, hd)\n        max_hd = max(max_hd, hd)\n\n        if node.left:\n            queue.append((node.left, hd - 1, depth + 1))\n        if node.right:\n            queue.append((node.right, hd + 1, depth + 1))\n    \n    result = []\n    for hd in range(min_hd, max_hd + 1):\n        # Sort nodes in the same horizontal distance by depth, then by value\n        node_map[hd].sort(key=lambda x: (x[1], x[0]))\n        result.append([val for val, _ in node_map[hd]])\n        \n    return result\n\n# A\u011fa\u00e7 \u00f6rne\u011fi olu\u015fturma\n#       3\n#      \/ \\\n#     9  20\n#       \/  \\\n#      15   7\nroot = TreeNode(3)\nroot.left = TreeNode(9)\nroot.right = TreeNode(20)\nroot.right.left = TreeNode(15)\nroot.right.right = TreeNode(7)\n\nprint(verticalOrderTraversal(root)) \n# Beklenen \u00c7\u0131kt\u0131: [[9], [3, 15], [20], [7]]\n<\/code><\/pre>\n<\/div>\n
Yukar\u0131daki Python kodu, BFS kullanarak Vertical Order Traversal’\u0131 nas\u0131l uygulayaca\u011f\u0131n\u0131z\u0131 a\u00e7\u0131k\u00e7a g\u00f6stermektedir. deque<\/code> (\u00e7ift u\u00e7lu kuyruk) kullanarak seviye seviye ilerlenir ve her d\u00fc\u011f\u00fcme horizontal_distance<\/code> (dikey konum) ve depth<\/code> (derinlik) atan\u0131r. node_map<\/code> s\u00f6zl\u00fc\u011f\u00fc, her bir dikey konum i\u00e7in d\u00fc\u011f\u00fcm de\u011ferlerini ve derinliklerini saklar. Son olarak, dikey konumlar soldan sa\u011fa do\u011fru s\u0131ralan\u0131r ve her konumdaki d\u00fc\u011f\u00fcmler derinliklerine g\u00f6re (ve ard\u0131ndan de\u011ferlerine g\u00f6re) s\u0131ralanarak nihai sonu\u00e7 elde edilir. Bu yakla\u015f\u0131m, algoritmik d\u00fc\u015f\u00fcnme becerilerinizi geli\u015ftirirken, ayn\u0131 zamanda karma\u015f\u0131k veri yap\u0131lar\u0131n\u0131 manip\u00fcle etme yetene\u011finizi de art\u0131r\u0131r.<\/p>\n
Vertical Order Traversal’\u0131n Ger\u00e7ek D\u00fcnya Uygulamalar\u0131 ve Vaka Analizleri<\/h2>\n
Vertical Order Traversal, sadece teorik bir algoritma olman\u0131n \u00f6tesinde, \u00e7e\u015fitli ger\u00e7ek d\u00fcnya senaryolar\u0131nda somut faydalar sunar. \u00d6zellikle hiyerar\u015fik verilerin g\u00f6rselle\u015ftirilmesi ve analiz edilmesi gereken durumlarda kritik bir rol oynar. Bu y\u00f6ntem, verilerinizi daha anla\u015f\u0131l\u0131r ve d\u00fczenli bir \u015fekilde sunman\u0131za olanak tan\u0131r, b\u00f6ylece karar alma s\u00fcre\u00e7lerini destekler ve kullan\u0131c\u0131 deneyimini iyile\u015ftirir.<\/p>\n
Veri G\u00f6rselle\u015ftirme ve Kullan\u0131c\u0131 Aray\u00fczleri<\/h3>\n
En belirgin uygulama alanlar\u0131ndan biri veri g\u00f6rselle\u015ftirmedir. Bir a\u011fa\u00e7 yap\u0131s\u0131n\u0131 bir web sayfas\u0131nda veya bir masa\u00fcst\u00fc uygulamas\u0131nda kullan\u0131c\u0131ya sunarken, Vertical Order Traversal, d\u00fc\u011f\u00fcmleri dikey s\u00fctunlar halinde d\u00fczenleyerek daha okunabilir bir \u00e7\u0131kt\u0131 sa\u011flar. \u00d6rne\u011fin, bir organizasyon \u015femas\u0131n\u0131 d\u00fc\u015f\u00fcn\u00fcn. Geleneksel a\u011fa\u00e7 \u00e7izimleri bazen karma\u015f\u0131k ve anla\u015f\u0131lmas\u0131 zor olabilir. Ancak Vertical Order Traversal kullanarak, her departman veya \u00e7al\u0131\u015fan grubunu dikey bir s\u00fctun olarak g\u00f6rselle\u015ftirebilirsiniz. Bu, belirli bir departman\u0131n t\u00fcm \u00fcyelerini veya belirli bir hiyerar\u015fik seviyedeki t\u00fcm rolleri kolayca g\u00f6rmenizi sa\u011flar. Benzer \u015fekilde, bir dosya sistemini veya bir kod taban\u0131n\u0131n ba\u011f\u0131ml\u0131l\u0131k a\u011fac\u0131n\u0131 g\u00f6rselle\u015ftirirken, dikey s\u0131ralama, ilgili dosyalar\u0131 veya mod\u00fclleri yan yana getirerek yap\u0131y\u0131 daha net anlaman\u0131za yard\u0131mc\u0131 olabilir. Kullan\u0131c\u0131 aray\u00fczlerinde (UI) ise, \u00f6zellikle men\u00fc yap\u0131lar\u0131nda veya navigasyon panellerinde, dikey s\u0131ralama belirli \u00f6\u011felerin d\u00fczenini ve eri\u015filebilirli\u011fini optimize etmek i\u00e7in kullan\u0131labilir. \u00d6rne\u011fin, bir e-ticaret sitesinde \u00fcr\u00fcn kategorilerini hiyerar\u015fik bir a\u011fa\u00e7 yap\u0131s\u0131nda tutarken, Vertical Order Traversal ile bu kategorileri dikey s\u00fctunlar halinde listeleyerek kullan\u0131c\u0131lar\u0131n arad\u0131klar\u0131 \u00fcr\u00fcnlere daha h\u0131zl\u0131 ula\u015fmas\u0131n\u0131 sa\u011flayabilirsiniz. Bu, sadece estetik bir d\u00fczenleme de\u011fil, ayn\u0131 zamanda kullan\u0131c\u0131lar\u0131n bilgiye eri\u015fimini kolayla\u015ft\u0131ran fonksiyonel bir geli\u015ftirmedir.<\/p>\n
Arama ve S\u0131ralama Algoritmalar\u0131nda Kullan\u0131m<\/h3>\n
Vertical Order Traversal’\u0131n bir di\u011fer \u00f6nemli uygulama alan\u0131, arama ve s\u0131ralama algoritmalar\u0131n\u0131n performans\u0131n\u0131 art\u0131rmak veya \u00f6zel s\u0131ralama ihtiya\u00e7lar\u0131n\u0131 kar\u015f\u0131lamakt\u0131r. Bir a\u011fa\u00e7taki belirli bir dikey aral\u0131ktaki t\u00fcm d\u00fc\u011f\u00fcmleri bulmak istedi\u011finizde, bu algoritma size bu d\u00fc\u011f\u00fcmleri h\u0131zl\u0131ca sa\u011flayabilir. \u00d6rne\u011fin, bir veritaban\u0131 indeksleme sisteminde, veriler bir a\u011fa\u00e7 yap\u0131s\u0131nda d\u00fczenlenmi\u015f olabilir. Belirli bir dikey konumdaki (\u00f6rne\u011fin, belirli bir zaman dilimine veya kategoriye ait) t\u00fcm kay\u0131tlar\u0131 \u00e7ekmek istedi\u011finizde, Vertical Order Traversal do\u011frudan bu verileri hedeflemenize yard\u0131mc\u0131 olur. Bu, geleneksel a\u011fa\u00e7 ge\u00e7i\u015f y\u00f6ntemleriyle elde edilmesi daha zor veya daha maliyetli olabilecek bir sonu\u00e7tur. Ayr\u0131ca, baz\u0131 \u00f6zel s\u0131ralama algoritmalar\u0131, verileri \u00f6nce dikey konuma, sonra derinli\u011fe g\u00f6re s\u0131ralayarak daha karma\u015f\u0131k sorgulara yan\u0131t verebilir. \u00d6rne\u011fin, bir sosyal medya platformunda g\u00f6nderileri veya yorumlar\u0131 hiyerar\u015fik bir yap\u0131da tutarken, Vertical Order Traversal ile belirli bir konu ba\u015fl\u0131\u011f\u0131n\u0131n alt\u0131ndaki t\u00fcm ilgili g\u00f6nderileri, yazar\u0131n veya g\u00f6nderi zaman\u0131n\u0131n dikey konumuna g\u00f6re s\u0131ralayarak daha anlaml\u0131 bir ak\u0131\u015f olu\u015fturabilirsiniz. Bu t\u00fcr uygulamalar, b\u00fcy\u00fck veri k\u00fcmeleriyle \u00e7al\u0131\u015f\u0131rken performans ve verimlilik a\u00e7\u0131s\u0131ndan \u00f6nemli avantajlar sunar. K\u0131sacas\u0131, Vertical Order Traversal, verileri sadece hiyerar\u015fik de\u011fil, ayn\u0131 zamanda mek\u00e2nsal bir d\u00fczende de anlamland\u0131rmam\u0131z\u0131 sa\u011flayan, \u00e7ok y\u00f6nl\u00fc ve g\u00fc\u00e7l\u00fc bir ara\u00e7t\u0131r.<\/p>\n
Performans Optimizasyonu ve \u0130leri D\u00fczey \u0130pu\u00e7lar\u0131<\/h2>\n
Vertical Order Traversal algoritmas\u0131n\u0131n performans\u0131n\u0131 anlamak ve optimize etmek, b\u00fcy\u00fck veri k\u00fcmeleriyle \u00e7al\u0131\u015f\u0131rken kritik \u00f6neme sahiptir. Algoritman\u0131n verimlili\u011fi, hem zaman karma\u015f\u0131kl\u0131\u011f\u0131 (time complexity) hem de alan karma\u015f\u0131kl\u0131\u011f\u0131 (space complexity) a\u00e7\u0131s\u0131ndan de\u011ferlendirilmelidir. Bu iki fakt\u00f6r, algoritman\u0131n \u00e7al\u0131\u015fma s\u00fcresi ve bellek kullan\u0131m\u0131 hakk\u0131nda bilgi verir.<\/p>\n
Zaman ve Alan Karma\u015f\u0131kl\u0131\u011f\u0131 Analizi<\/h3>\n
Vertical Order Traversal uygulamas\u0131n\u0131n zaman karma\u015f\u0131kl\u0131\u011f\u0131, kullan\u0131lan ge\u00e7i\u015f y\u00f6ntemine (BFS veya DFS) ve d\u00fc\u011f\u00fcmleri gruplamak ve s\u0131ralamak i\u00e7in harcanan ek zamana ba\u011fl\u0131d\u0131r. Genellikle, bir a\u011fa\u00e7taki her d\u00fc\u011f\u00fcm bir kez ziyaret edildi\u011fi i\u00e7in, bu i\u015flem O(N) zaman al\u0131r, burada N a\u011fa\u00e7taki d\u00fc\u011f\u00fcm say\u0131s\u0131d\u0131r. Ancak, d\u00fc\u011f\u00fcmlerin dikey konumlar\u0131na g\u00f6re grupland\u0131\u011f\u0131 ve her dikey s\u00fctun i\u00e7indeki d\u00fc\u011f\u00fcmlerin derinli\u011fe g\u00f6re s\u0131raland\u0131\u011f\u0131 k\u0131s\u0131m ek maliyet getirir. E\u011fer bir harita (Python’daki dict<\/code> veya Java’daki HashMap<\/code>) kullan\u0131larak d\u00fc\u011f\u00fcmler gruplan\u0131yorsa, bu i\u015flemler genellikle ortalama O(1) zaman al\u0131r. Ancak, her dikey s\u00fctundaki d\u00fc\u011f\u00fcmlerin s\u0131ralanmas\u0131 gerekiyorsa (\u00f6zellikle DFS kullan\u0131ld\u0131\u011f\u0131nda veya BFS’den sonra ek bir s\u0131ralama ad\u0131m\u0131 gerekti\u011finde), bu k\u0131s\u0131m O(W * D log D) olabilir, burada W en fazla dikey s\u00fctun say\u0131s\u0131 ve D bir s\u00fctundaki en fazla d\u00fc\u011f\u00fcm say\u0131s\u0131d\u0131r. En k\u00f6t\u00fc durumda, t\u00fcm d\u00fc\u011f\u00fcmlerin tek bir dikey s\u00fctunda oldu\u011fu bir “\u00e7arp\u0131k a\u011fa\u00e7” (skewed tree) senaryosunda, bu s\u0131ralama O(N log N) olabilir. Dolay\u0131s\u0131yla, genel zaman karma\u015f\u0131kl\u0131\u011f\u0131 genellikle O(N log N) veya O(N + W * D log D) olarak ifade edilebilir. Alan karma\u015f\u0131kl\u0131\u011f\u0131na gelince, BFS yakla\u015f\u0131m\u0131nda bir kuyruk (queue) ve bir harita (map) kullan\u0131l\u0131r. Kuyruk en k\u00f6t\u00fc durumda a\u011fac\u0131n en geni\u015f seviyesindeki t\u00fcm d\u00fc\u011f\u00fcmleri saklayabilir, bu da O(N) olabilir. Harita ise t\u00fcm d\u00fc\u011f\u00fcmleri dikey konumlar\u0131na g\u00f6re saklad\u0131\u011f\u0131 i\u00e7in yine O(N) alan gerektirir. DFS yakla\u015f\u0131m\u0131nda ise \u00f6zyineleme y\u0131\u011f\u0131n\u0131 (recursion stack) en k\u00f6t\u00fc durumda a\u011fac\u0131n derinli\u011fi kadar yer kaplayabilir (O(H), H a\u011fac\u0131n y\u00fcksekli\u011fi), ancak harita yine O(N) alan gerektirir. Bu nedenle, her iki durumda da alan karma\u015f\u0131kl\u0131\u011f\u0131 genellikle O(N) olarak kabul edilir. Bu analiz, algoritman\u0131n b\u00fcy\u00fck \u00f6l\u00e7ekli veri setleri \u00fczerindeki performans\u0131n\u0131 \u00f6ng\u00f6rmek i\u00e7in \u00f6nemlidir.<\/p>\n
Verimlili\u011fi Art\u0131rma Y\u00f6ntemleri<\/h3>\n
Vertical Order Traversal’\u0131n verimlili\u011fini art\u0131rmak i\u00e7in baz\u0131 stratejiler uygulanabilir. \u00d6ncelikle, e\u011fer ayn\u0131 dikey konumdaki d\u00fc\u011f\u00fcmlerin derinli\u011fe g\u00f6re s\u0131ralanmas\u0131 kritikse ve \u00e7ok say\u0131da d\u00fc\u011f\u00fcm varsa, BFS kullanmak genellikle daha avantajl\u0131d\u0131r. \u00c7\u00fcnk\u00fc BFS, d\u00fc\u011f\u00fcmleri seviye seviye i\u015fledi\u011fi i\u00e7in ayn\u0131 dikey konumdaki d\u00fc\u011f\u00fcmler zaten derinli\u011fe g\u00f6re do\u011fal bir s\u0131raya sahip olur ve ek bir s\u0131ralama ad\u0131m\u0131na gerek kalmaz veya \u00e7ok daha az s\u0131ralama yap\u0131l\u0131r. Bu, \u00f6zellikle node_map[hd].sort()<\/code> gibi bir ad\u0131m\u0131n maliyetini azaltabilir. \u0130kinci olarak, e\u011fer a\u011fa\u00e7 \u00e7ok derin ama dar ise (yani y\u00fcksekli\u011fi fazla ama geni\u015fli\u011fi az ise), DFS tabanl\u0131 bir \u00e7\u00f6z\u00fcm bellek a\u00e7\u0131s\u0131ndan daha verimli olabilir \u00e7\u00fcnk\u00fc \u00f6zyineleme y\u0131\u011f\u0131n\u0131 daha az yer kaplar. Ancak bu durumda, ayn\u0131 dikey konumdaki d\u00fc\u011f\u00fcmlerin manuel olarak derinli\u011fe g\u00f6re s\u0131ralanmas\u0131 maliyetini g\u00f6z \u00f6n\u00fcnde bulundurmak gerekir. \u00dc\u00e7\u00fcnc\u00fc bir optimizasyon, dikey konumlar\u0131n aral\u0131\u011f\u0131n\u0131 minimumda tutmakt\u0131r. E\u011fer dikey konumlar \u00e7ok geni\u015f bir aral\u0131\u011fa yay\u0131l\u0131yorsa, harita olu\u015fturma ve \u00fczerinde gezinme i\u015flemleri daha yava\u015f olabilir. Bu genellikle a\u011fa\u00e7 yap\u0131s\u0131n\u0131n do\u011fas\u0131ndan kaynaklan\u0131r, ancak bazen a\u011fa\u00e7 dengelenerek bu durum hafifletilebilir. Son olarak, e\u011fer \u00e7\u0131kt\u0131da sadece belirli bir dikey aral\u0131ktaki d\u00fc\u011f\u00fcmler isteniyorsa, t\u00fcm a\u011fac\u0131 ge\u00e7mek yerine sadece ilgili dikey konumlar\u0131 ziyaret edecek \u015fekilde algoritmay\u0131 modifiye etmek, gereksiz hesaplamalar\u0131 \u00f6nleyerek performans\u0131 art\u0131rabilir. Bu ileri d\u00fczey ipu\u00e7lar\u0131, \u00f6zellikle b\u00fcy\u00fck ve karma\u015f\u0131k a\u011fa\u00e7 yap\u0131lar\u0131yla \u00e7al\u0131\u015f\u0131rken Vertical Order Traversal uygulaman\u0131z\u0131n daha h\u0131zl\u0131 ve daha az kaynak t\u00fcketen hale gelmesine yard\u0131mc\u0131 olacakt\u0131r.<\/p>\n
Sonu\u00e7: Vertical Order Traversal’\u0131n G\u00fcc\u00fc ve Gelece\u011fi<\/h2>\n
Vertical Order Traversal, a\u011fa\u00e7 yap\u0131lar\u0131ndaki d\u00fc\u011f\u00fcmleri dikey eksende d\u00fczenleyerek, verileri anlaml\u0131 ve g\u00f6rsel olarak \u00e7ekici bir \u015fekilde sunan g\u00fc\u00e7l\u00fc bir algoritmad\u0131r. Bu makalede, Vertical Order Traversal’\u0131n temel prensiplerini, d\u00fc\u011f\u00fcmlere dikey konumlar\u0131n nas\u0131l atand\u0131\u011f\u0131n\u0131 ve BFS ile DFS yakla\u015f\u0131mlar\u0131yla nas\u0131l uyguland\u0131\u011f\u0131n\u0131 detayl\u0131 bir \u015fekilde inceledik. Ayr\u0131ca, veri g\u00f6rselle\u015ftirmeden arama ve s\u0131ralama algoritmalar\u0131na kadar \u00e7e\u015fitli ger\u00e7ek d\u00fcnya senaryolar\u0131ndaki uygulamalar\u0131n\u0131 ve bu uygulaman\u0131n sa\u011flad\u0131\u011f\u0131 somut faydalar\u0131 ele ald\u0131k. Algoritman\u0131n zaman ve alan karma\u015f\u0131kl\u0131\u011f\u0131 analizini yaparak performans iyile\u015ftirme stratejilerine de\u011findik. G\u00f6rd\u00fc\u011f\u00fcm\u00fcz gibi, Vertical Order Traversal, hiyerar\u015fik verilerle \u00e7al\u0131\u015f\u0131rken kar\u015f\u0131la\u015f\u0131lan karma\u015f\u0131k d\u00fczenleme ve g\u00f6rselle\u015ftirme problemlerine zarif ve etkili \u00e7\u00f6z\u00fcmler sunmaktad\u0131r. Bu y\u00f6ntem, \u00f6zellikle kullan\u0131c\u0131 aray\u00fczlerinde daha iyi bir deneyim sa\u011flamak, raporlama ve analiz s\u00fcre\u00e7lerini zenginle\u015ftirmek veya \u00f6zel veri sorgular\u0131n\u0131 desteklemek i\u00e7in vazge\u00e7ilmez bir ara\u00e7 haline gelmi\u015ftir. Gelecekte, b\u00fcy\u00fck veri ve yapay zeka alanlar\u0131ndaki geli\u015fmelerle birlikte, karma\u015f\u0131k a\u011fa\u00e7 yap\u0131lar\u0131n\u0131 i\u015fleme ve g\u00f6rselle\u015ftirme ihtiyac\u0131 daha da artacakt\u0131r. Vertical Order Traversal gibi algoritmalar, bu yeni nesil uygulamalarda verilerin daha h\u0131zl\u0131 ve daha sezgisel bir \u015fekilde anla\u015f\u0131lmas\u0131na olanak tan\u0131yarak kritik bir rol oynamaya devam edecektir. Veri analistleri, yaz\u0131l\u0131m geli\u015ftiriciler ve ara\u015ft\u0131rmac\u0131lar i\u00e7in bu tekni\u011fe hakim olmak, gelece\u011fin veri odakl\u0131 d\u00fcnyas\u0131nda rekabet avantaj\u0131 sa\u011flayacakt\u0131r. Bu bilgiyle donanm\u0131\u015f olarak, a\u011fa\u00e7 yap\u0131lar\u0131yla ilgili daha karma\u015f\u0131k problemleri \u00e7\u00f6zebilir ve verilerinizden daha fazla de\u011fer elde edebilirsiniz.<\/p>\n
S\u0131k\u00e7a Sorulan Sorular (SSS)<\/h3>\n
1. Vertical Order Traversal ile di\u011fer a\u011fa\u00e7 ge\u00e7i\u015f y\u00f6ntemleri aras\u0131ndaki temel fark nedir?<\/strong><\/p>\n
Cevap: Geleneksel a\u011fa\u00e7 ge\u00e7i\u015f y\u00f6ntemleri (pre-order, in-order, post-order, level-order) d\u00fc\u011f\u00fcmleri genellikle derinlik veya seviye baz\u0131nda, yani hiyerar\u015fik yap\u0131ya g\u00f6re ziyaret eder. Vertical Order Traversal ise d\u00fc\u011f\u00fcmleri dikey s\u00fctunlar halinde gruplayarak ve her s\u00fctundaki d\u00fc\u011f\u00fcmleri derinli\u011fe g\u00f6re s\u0131ralayarak tamamen farkl\u0131 bir “mek\u00e2nsal” s\u0131ralama sunar. Bu, d\u00fc\u011f\u00fcmlerin k\u00f6ke g\u00f6re yatay konumlar\u0131na odaklan\u0131r.<\/p>\n
2. Ayn\u0131 dikey konumda birden fazla d\u00fc\u011f\u00fcm oldu\u011funda s\u0131ralama nas\u0131l yap\u0131l\u0131r?<\/strong><\/p>\n
Cevap: Ayn\u0131 dikey konumda birden fazla d\u00fc\u011f\u00fcm oldu\u011funda, bu d\u00fc\u011f\u00fcmler genellikle derinliklerine (yani k\u00f6kten uzakl\u0131klar\u0131na) g\u00f6re s\u0131ralan\u0131r. Derinli\u011fi daha az olan d\u00fc\u011f\u00fcm \u00f6nce gelir. E\u011fer hem dikey konum hem de derinlik ayn\u0131 ise (ki bu standart bir ikili a\u011fa\u00e7ta farkl\u0131 d\u00fc\u011f\u00fcmler i\u00e7in m\u00fcmk\u00fcn de\u011fildir, ancak \u00e7oklu \u00e7ocuklu a\u011fa\u00e7larda veya \u00f6zel durumlarda olabilir), o zaman d\u00fc\u011f\u00fcmlerin de\u011ferlerine g\u00f6re veya orijinal a\u011fa\u00e7taki eklenme s\u0131ras\u0131na g\u00f6re ikincil bir s\u0131ralama kriteri uygulanabilir.<\/p>\n
3. Vertical Order Traversal hangi t\u00fcr a\u011fa\u00e7 yap\u0131lar\u0131 i\u00e7in kullan\u0131labilir?<\/strong><\/p>\n
Cevap: Vertical Order Traversal en yayg\u0131n olarak ikili a\u011fa\u00e7lar (binary trees) i\u00e7in kullan\u0131l\u0131r. Ancak, \u00e7oklu \u00e7ocuklu a\u011fa\u00e7lar (N-ary trees) i\u00e7in de uyarlanabilir. Temel prensip, her d\u00fc\u011f\u00fcme bir dikey konum atamak ve bu konumlar\u0131 kullanarak d\u00fc\u011f\u00fcmleri gruplamakt\u0131r. Bu prensip, d\u00fc\u011f\u00fcmlerin \u00e7ocuk say\u0131s\u0131ndan ba\u011f\u0131ms\u0131z olarak uygulanabilir.<\/p>\n
4. Algoritman\u0131n performans\u0131n\u0131 etkileyen ana fakt\u00f6rler nelerdir?<\/strong><\/p>\n
Cevap: Performans\u0131 etkileyen ana fakt\u00f6rler, a\u011fa\u00e7taki d\u00fc\u011f\u00fcm say\u0131s\u0131 (N), a\u011fac\u0131n y\u00fcksekli\u011fi (H) ve a\u011fac\u0131n en geni\u015f dikey s\u00fctun say\u0131s\u0131 (W) ile bir s\u00fctundaki maksimum d\u00fc\u011f\u00fcm say\u0131s\u0131d\u0131r (D). D\u00fc\u011f\u00fcm say\u0131s\u0131n\u0131n yan\u0131 s\u0131ra, ayn\u0131 dikey konumdaki d\u00fc\u011f\u00fcmleri s\u0131ralama ihtiyac\u0131 (\u00f6zellikle DFS kullan\u0131ld\u0131\u011f\u0131nda) ve kullan\u0131lan harita (dictionary\/map) veri yap\u0131s\u0131n\u0131n performans\u0131 da etkilidir.<\/p>\n
5. Vertical Order Traversal uygulamalar\u0131nda kar\u015f\u0131la\u015f\u0131lan yayg\u0131n zorluklar nelerdir?<\/strong><\/p>\n
Cevap: Yayg\u0131n zorluklar aras\u0131nda, her d\u00fc\u011f\u00fcme do\u011fru dikey konum ve derinlik de\u011ferlerini atamak, bu de\u011ferleri verimli bir \u015fekilde saklamak (genellikle bir harita kullanarak), ayn\u0131 dikey konumdaki d\u00fc\u011f\u00fcmleri do\u011fru s\u0131rayla (derinli\u011fe g\u00f6re) s\u0131ralamak ve \u00f6zellikle b\u00fcy\u00fck a\u011fa\u00e7larda bellek ve zaman karma\u015f\u0131kl\u0131\u011f\u0131n\u0131 y\u00f6netmek yer al\u0131r. Ayr\u0131ca, \u00e7ok geni\u015f veya \u00e7ok derin a\u011fa\u00e7lar i\u00e7in performans optimizasyonlar\u0131 d\u00fc\u015f\u00fcnmek de \u00f6nemlidir.<\/p>\n
#Teknoloji #VeriYap\u0131lar\u0131 #Algoritmalar #A\u011fa\u00e7Yap\u0131lar\u0131 #Yaz\u0131l\u0131mGeli\u015ftirme<\/p>\n
\u00d6rnek kod:<\/strong> github.com\/fatihsoysalcom\/tree-vertical-order-traversal-example<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"A\u011fa\u00e7 yap\u0131lar\u0131ndaki d\u00fc\u011f\u00fcmleri dikey eksende s\u0131ralama ihtiyac\u0131yla m\u0131 kar\u015f\u0131la\u015f\u0131yorsunuz?","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-43102","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-genel","7":"cs-entry","8":"cs-video-wrap"},"yoast_head":"\nA\u011fa\u00e7 Yap\u0131lar\u0131nda Dikey S\u0131ralama: Vertical Order Traversal Nedir ve Neden \u00d6nemlidir? - Kodlar\u0131n Gizemli D\u00fcnyas\u0131<\/title>\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\/agac-yapilarinda-dikey-siralama-vertical-order-traversal-nedir-ve-neden-onemlidir\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A\u011fa\u00e7 Yap\u0131lar\u0131nda Dikey S\u0131ralama: Vertical Order Traversal Nedir ve Neden \u00d6nemlidir?\" \/>\n<meta property=\"og:description\" content=\"A\u011fa\u00e7 yap\u0131lar\u0131ndaki d\u00fc\u011f\u00fcmleri dikey eksende s\u0131ralama ihtiyac\u0131yla m\u0131 kar\u015f\u0131la\u015f\u0131yorsunuz?\" \/>\n<meta property=\"og:url\" content=\"https:\/\/fatihsoysal.com\/blog\/agac-yapilarinda-dikey-siralama-vertical-order-traversal-nedir-ve-neden-onemlidir\/\" \/>\n<meta property=\"og:site_name\" content=\"Kodlar\u0131n Gizemli D\u00fcnyas\u0131\" \/>\n<meta property=\"article:published_time\" content=\"2026-07-05T18:06:03+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-07-05T18:06:24+00:00\" \/>\n<meta name=\"author\" content=\"Fatih Soysal\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Yazan:\" \/>\n\t<meta name=\"twitter:data1\" content=\"Fatih Soysal\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tahmini okuma s\u00fcresi\" \/>\n\t<meta name=\"twitter:data2\" content=\"19 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/fatihsoysal.com\/blog\/agac-yapilarinda-dikey-siralama-vertical-order-traversal-nedir-ve-neden-onemlidir\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/fatihsoysal.com\/blog\/agac-yapilarinda-dikey-siralama-vertical-order-traversal-nedir-ve-neden-onemlidir\/\"},\"author\":{\"name\":\"Fatih Soysal\",\"@id\":\"https:\/\/fatihsoysal.com\/blog\/#\/schema\/person\/002a254750921dcfd568a99e48240dd1\"},\"headline\":\"A\u011fa\u00e7 Yap\u0131lar\u0131nda Dikey S\u0131ralama: Vertical Order Traversal Nedir ve Neden \u00d6nemlidir?\",\"datePublished\":\"2026-07-05T18:06:03+00:00\",\"dateModified\":\"2026-07-05T18:06:24+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/fatihsoysal.com\/blog\/agac-yapilarinda-dikey-siralama-vertical-order-traversal-nedir-ve-neden-onemlidir\/\"},\"wordCount\":3659,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/fatihsoysal.com\/blog\/#\/schema\/person\/002a254750921dcfd568a99e48240dd1\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/fatihsoysal.com\/blog\/agac-yapilarinda-dikey-siralama-vertical-order-traversal-nedir-ve-neden-onemlidir\/#respond\"]}],\"copyrightYear\":\"2026\",\"copyrightHolder\":{\"@id\":\"https:\/\/fatihsoysal.com\/blog\/#organization\"}},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/fatihsoysal.com\/blog\/agac-yapilarinda-dikey-siralama-vertical-order-traversal-nedir-ve-neden-onemlidir\/\",\"url\":\"https:\/\/fatihsoysal.com\/blog\/agac-yapilarinda-dikey-siralama-vertical-order-traversal-nedir-ve-neden-onemlidir\/\",\"name\":\"A\u011fa\u00e7 Yap\u0131lar\u0131nda Dikey S\u0131ralama: Vertical Order Traversal Nedir ve Neden \u00d6nemlidir? 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