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A Binary Search az egyik leggyakrabban alkalmazott list\u00e1ban val\u00f3 keres\u00e9sre alkalmas algoritmus.
A k\u00f3dja k\u00e9tszer lett lefuttatva, mint a k\u00e9pen l\u00e1tszik, van benne hibakezel\u00e9s, azaz az 52-es elemet megtal\u00e1lja a k\u00f3dban l\u00e9v\u0151 list\u00e1b\u00f3l, mint az a Visual Studio-ban k\u00e9sz\u00fclt k\u00f3dr\u00f3l k\u00e9sz\u00fclt k\u00e9p parancssor\u00e1ban l\u00e1tszik, a 61-es elemre pedig ki\u00edrja, hogy nem a lista r\u00e9sze, mint ahogy az igaz is.<\/p>\n
[\/et_pb_text][et_pb_toggle title=”Binary Search m\u0171k\u00f6d\u00e9se: (leny\u00edl\u00f3 tartalom – kattints a jobb sz\u00e9ls\u0151 + ikonra)” open_toggle_text_color=”#fcb03a” open_toggle_background_color=”#042f4f” closed_toggle_text_color=”#fcb03a” closed_toggle_background_color=”#042f4f” icon_color=”#fcb03a” open_icon_color=”#fcb03a” _builder_version=”4.27.4″ _module_preset=”default” title_font_size=”18px” closed_title_font_size=”18px” body_text_color=”#FFFFFF” body_font_size=”16px” body_line_height=”1.8em” hover_enabled=”0″ global_colors_info=”{}” sticky_enabled=”0″]<\/p>\n
A Binary Search (Bin\u00e1ris Keres\u00e9s) egy hat\u00e9kony algoritmus rendezett list\u00e1kban val\u00f3 keres\u00e9sre, amely az oszd meg \u00e9s uralkodj (divide and conquer) elvet alkalmazza. A m\u0171k\u00f6d\u00e9si elve a k\u00f6vetkez\u0151:<\/p>\n
1. Felt\u00e9telek:
A bin\u00e1ris keres\u00e9s m\u0171k\u00f6d\u00e9s\u00e9hez elengedhetetlen, hogy a keresett adatokat tartalmaz\u00f3 lista rendezett legyen, teh\u00e1t a lista elemei n\u00f6vekv\u0151 (vagy cs\u00f6kken\u0151) sorrendben legyenek rendezve.<\/p>\n
2. Kezd\u0151 felt\u00e9telez\u00e9s:
A keres\u00e9st a lista k\u00f6z\u00e9ps\u0151 elem\u00e9vel kezdj\u00fck. A lista eleje (left) \u00e9s v\u00e9ge (right) mutatja, hogy a keres\u00e9s melyik r\u00e9sz\u00e9n dolgozunk.<\/p>\n
3. K\u00f6z\u00e9ps\u0151 elem vizsg\u00e1lata:
Ha a k\u00f6z\u00e9ps\u0151 elem a keresett elem, akkor a keres\u00e9s sikeres, \u00e9s a keresett elem poz\u00edci\u00f3j\u00e1t adjuk vissza.
Ha a k\u00f6z\u00e9ps\u0151 elem kisebb, mint a keresett elem, akkor a keres\u00e9s a jobb oldalra (a k\u00f6z\u00e9ps\u0151 elem ut\u00e1ni r\u00e9szre) folytat\u00f3dik.
Ha a k\u00f6z\u00e9ps\u0151 elem nagyobb, mint a keresett elem, akkor a keres\u00e9s a bal oldalra (a k\u00f6z\u00e9ps\u0151 elem el\u0151tti r\u00e9szre) folytat\u00f3dik.
4. Sz\u0171k\u00edt\u00e9s:
A keres\u00e9si tartom\u00e1nyt minden egyes l\u00e9p\u00e9sn\u00e9l a k\u00f6z\u00e9ps\u0151 elem alapj\u00e1n fel\u00e9re cs\u00f6kkentj\u00fck. Ez\u00e1ltal a keres\u00e9si tartom\u00e1ny egyre kisebb lesz, \u00e9s gyorsabban el\u00e9rhetj\u00fck a keresett elemet.<\/p>\n
5. Befejez\u00e9s:
A keres\u00e9s akkor fejez\u0151dik be, ha a keresett elem meg lesz tal\u00e1lva vagy ha a bal oldali mutat\u00f3 (left) nagyobb, mint a jobb oldali mutat\u00f3 (right), ami azt jelenti, hogy az elem nincs a list\u00e1ban.<\/p>\n
P\u00e9lda:
Tegy\u00fck fel, hogy egy rendezett list\u00e1ban szeretn\u00e9nk megtal\u00e1lni a 40-et:<\/p>\n
[10, 20, 30, 40, 50, 60, 70, 80]
Els\u0151 l\u00e9p\u00e9s:
Bal oldali mutat\u00f3: left = 0
Jobb oldali mutat\u00f3: right = 7
A k\u00f6z\u00e9ps\u0151 elem: arr[3] = 40
Mivel a k\u00f6z\u00e9ps\u0151 elem megegyezik a keresett elemmel (40), a keres\u00e9s sikeres.
Id\u0151bonyolults\u00e1g:
A bin\u00e1ris keres\u00e9s minden l\u00e9p\u00e9sben a keres\u00e9si tartom\u00e1ny fel\u00e9re cs\u00f6kkenti a vizsg\u00e1land\u00f3 elemek sz\u00e1m\u00e1t, \u00edgy az algoritmus logaritmikus id\u0151bonyolults\u00e1g\u00fa, azaz O(log n), ahol n a lista elemeinek sz\u00e1ma. A legrosszabb esetben is csup\u00e1n logaritmikus sz\u00e1m\u00fa l\u00e9p\u00e9st kell v\u00e9grehajtani.<\/p>\n
El\u0151ny\u00f6k:
Nagy rendezett list\u00e1kban is gyors keres\u00e9st tesz lehet\u0151v\u00e9.
Mivel minden l\u00e9p\u00e9sben a fel\u00e9re cs\u00f6kkenti a vizsg\u00e1lt tartom\u00e1nyt, nagyon gyorsan megtal\u00e1lhatjuk a keresett elemet.
H\u00e1tr\u00e1nyok:
A lista rendezett kell, hogy legyen. Ha a lista nem rendezett, el\u0151bb rendezni kell, ami plusz id\u0151t \u00e9s k\u00f6lts\u00e9get jelenthet.<\/p>\n
[\/et_pb_toggle][et_pb_toggle title=”K\u00f3dmag: (leny\u00edl\u00f3 tartalom – kattints a jobb sz\u00e9ls\u0151 + ikonra)” open_toggle_text_color=”#fcb03a” open_toggle_background_color=”#042f4f” closed_toggle_text_color=”#fcb03a” closed_toggle_background_color=”#042f4f” icon_color=”#fcb03a” open_icon_color=”#fcb03a” _builder_version=”4.27.3″ _module_preset=”default” title_font_size=”18px” closed_title_font_size=”18px” body_text_color=”#FFFFFF” body_font_size=”16px” body_line_height=”1.8em” global_colors_info=”{}”]<\/p>\n
def binary_search(list, target):\n left, right = 0, len(list) - 1\n \n while left <= right:\n mid = (left + right) \/\/ 2\n \n # Ha a k\u00f6z\u00e9ps\u0151 elem az, amit keres\u00fcnk\n if list[mid] == target:\n return mid\n \n # Ha a k\u00f6z\u00e9ps\u0151 elem nagyobb, akkor a bal oldalra keres\u00fcnk tov\u00e1bb\n elif list[mid] > target:\n right = mid - 1\n \n # Ha a k\u00f6z\u00e9ps\u0151 elem kisebb, akkor a jobb oldalra keres\u00fcnk tov\u00e1bb\n else:\n left = mid + 1\n \n # Ha nem tal\u00e1lhat\u00f3 az elem\n return -1\n\nlist = [11, 34, 52, 76, 93, 110, 67, 47,98, 75]\ntarget = 52\n\nindex = binary_search(list, target)\nif index != -1:\n print(f\"Az elem ({target}) megtal\u00e1lhat\u00f3 az {index} indexen.\")\nelse:\n print(f\"Az elem ({target}) nem tal\u00e1lhat\u00f3 a list\u00e1ban.\")<\/pre>\n<\/code><\/p>\n[\/et_pb_toggle][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"
Bin\u00e1ris keres\u00e9si algoritmusA Binary Search az egyik leggyakrabban alkalmazott list\u00e1ban val\u00f3 keres\u00e9sre alkalmas algoritmus.A k\u00f3dja k\u00e9tszer lett lefuttatva, mint a k\u00e9pen l\u00e1tszik, van benne hibakezel\u00e9s, azaz az 52-es elemet megtal\u00e1lja a k\u00f3dban l\u00e9v\u0151 list\u00e1b\u00f3l, mint az a Visual Studio-ban k\u00e9sz\u00fclt k\u00f3dr\u00f3l k\u00e9sz\u00fclt k\u00e9p parancssor\u00e1ban l\u00e1tszik, a 61-es elemre pedig ki\u00edrja, hogy nem a lista r\u00e9sze, […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"class_list":["post-223","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/akosgombkoto.info\/en\/wp-json\/wp\/v2\/pages\/223","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/akosgombkoto.info\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/akosgombkoto.info\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/akosgombkoto.info\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/akosgombkoto.info\/en\/wp-json\/wp\/v2\/comments?post=223"}],"version-history":[{"count":14,"href":"https:\/\/akosgombkoto.info\/en\/wp-json\/wp\/v2\/pages\/223\/revisions"}],"predecessor-version":[{"id":691,"href":"https:\/\/akosgombkoto.info\/en\/wp-json\/wp\/v2\/pages\/223\/revisions\/691"}],"wp:attachment":[{"href":"https:\/\/akosgombkoto.info\/en\/wp-json\/wp\/v2\/media?parent=223"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}