Algorithms For Dummies. John Paul Mueller

Чтение книги онлайн.

СКАЧАТЬ print("Key Found!") return searchList[mid] elif key > searchList[mid]: print("searchList now contains ", searchList[mid:len(searchList)]) search(searchList[mid:len(searchList)], key) else: print("searchList now contains ", searchList[0:mid]) search(searchList[0:mid], key) aList = list(range(1, 21))search(aList, 5)

      When you run this code, you see this output:

       Searching midpoint at 11searchList now contains [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]Searching midpoint at 6searchList now contains [1, 2, 3, 4, 5]Searching midpoint at 3searchList now contains [3, 4, 5]Searching midpoint at 4searchList now contains [4, 5]Searching midpoint at 5Key Found!

      This recursive approach to the binary search begins with aList containing the numbers 1 through 20. It searches for a value of 5 in aList. Each iteration of the recursion begins by looking for the list's midpoint, mid, and then using that midpoint to determine the next step. When the key matches the midpoint, the value is found in the list and the recursion ends.

      

Note that this example makes one of two recursive calls. When key is greater than the midpoint value of the existing list, searchList[mid], the code calls search again with just the right side of the remaining list. In other words, every call to search uses just half the list found in the previous call. When key is less than or equal to searchList[mid], search receives the left half of the existing list.

      

The list may not contain a search value, so you must always provide an escape method for the recursion or the stack (a special area of memory used to store the call information; see https://www.geeksforgeeks.org/stack-vs-heap-memory-allocation/ for details) will fill, resulting in an error message. In this case, the escape occurs when mid == 0, which means that there is no more searchList to search. For example, if you change search(aList, 5) to search(aList, 22), you obtain the following output instead:

       Searching midpoint at 11searchList now contains [11, 12, 13, 14, 15, 16, 17, 18, 19, 20]Searching midpoint at 16searchList now contains [16, 17, 18, 19, 20]Searching midpoint at 18searchList now contains [18, 19, 20]Searching midpoint at 19searchList now contains [19, 20]Searching midpoint at 20searchList now contains [20]Searching midpoint at 20Key Not Found!

      Note also that the code looks for the escape condition before performing any other work to ensure that the code doesn't inadvertently cause an error because of the lack of searchList content. When working with recursion, you must remain proactive or endure the consequences later.

      Distinguishing between different possible solutions

      Recursion is part of many different algorithmic programming solutions, as you see in the upcoming chapters. In fact, it’s hard to get away from recursion in many cases because an iterative approach proves nonintuitive, cumbersome, and time consuming. However, you can create a number of different versions of the same solution, each of which has its own characteristics, flaws, and virtues.

      The solution that this chapter doesn’t consider is sequential search, because a sequential search generally takes longer than any other solution you can employ. In a best-case scenario, a sequential search requires just one comparison to complete the search, but in a worst-case scenario, you find the item you want as the last check. As an average, sequential search requires (n+1)/2 checks or O(n) time to complete. (The “Working with functions” section of Chapter 2 tells you more about big-O notation.)

      The binary search in the previous section does a much better job than a sequential search does. It works on logarithmic time or O(log n). In a best-case scenario, it takes only one check, as with a sequential search, but the output from the example shows that even a worst-case scenario, where the value doesn’t even appear in the list, takes only six checks rather than the 21 checks that a sequential search would require.

      

If you look at performance times alone, however, the data you receive can mislead you into thinking that a particular solution will work incredibly well for your application when in fact it won’t. You must also consider the kind of data you work with, the complexity of creating the solution, and a host of other factors. That’s why later examples in this book also consider the pros and cons of each approach — the hidden dangers of choosing a solution that seems to have potential and then fails to produce the desired result.

      Конец ознакомительного фрагмента.

      Текст предоставлен ООО «ЛитРес».

      Прочитайте эту книгу целиком, купив полную легальную версию на ЛитРес.

      Безопасно оплатить книгу можно банковской картой Visa, MasterCard, Maestro, со счета мобильного телефона, с платежного терминала, в салоне МТС или Связной, через PayPal, WebMoney, Яндекс.Деньги, QIWI Кошелек, бонусными картами или другим удобным Вам способом.

/9j/4AAQSkZJRgABAQEBLAEsAAD/7SsEUGhvdG9zaG9wIDMuMAA4QklNBAQAAAAAAAccAgAAAgAA ADhCSU0EJQAAAAAAEOjxXPMvwRihontnrcVk1bo4QklNBDoAAAAAAPcAAAAQAAAAAQAAAAAAC3By aW50T3V0cHV0AAAABQAAAABQc3RTYm9vbAEAAAAASW50ZWVudW0AAAAASW50ZQAAAABDbHJtAAAA D3ByaW50U2l4dGVlbkJpdGJvb2wAAAAAC3ByaW50ZXJOYW1lVEVYVAAAAAoAQQBkAG8AYgBlACAA UABEAEYAAAAAAA9wcmludFByb29mU2V0dXBPYmpjAAAADABQAHIAbwBvAGYAIABTAGUAdAB1AHAA AAAAAApwcm9vZlNldHVwAAAAAQAAAABCbHRuZW51bQAAAAxidWlsdGluUHJvb2YAAAAJcHJvb2ZD TVlLADhCSU0EOwAAAAACLQAAABAAAAABAAAAAAAScHJpbnRPdXRwdXRPcHRpb25zAAAAFwAAAABD cHRuYm9vbAAAAAAAQ2xicmJvb2wAAAAAAFJnc01ib29sAAAAAABDcm5DYm9vbAAAAAAAQ250Q2Jv b2wAAAAAAExibHNib29sAAAAAABOZ3R2Ym9vbAAAAAAARW1sRGJvb2wAAAAAAEludHJib29sAAAA AABCY2tnT2JqYwAAAAEAAAAAAABSR0JDAAAAAwAAAABSZCAgZG91YkBv4AAAAAAAAAAAAEdybiBk b3ViQG/gAAAAAAAAAAAAQmwgIGRvdWJAb+AAAAAAAAAAAABCcmRUVW50RiNSbHQAAAAAAAAAAAAA AABCbGQgVW50RiNSbHQAAAAAAAAAAAAAAABSc2x0VW50RiNQeGxAcsAAAAAAAAAAAAp2ZWN0b3JE YXRhYm9vbAEAAAAAUGdQc2VudW0AAAAAUGdQcwAAAABQZ1BDAAAAAExlZnRVbnRGI1JsdAAAAAAA AAAAAAAAAFRvcCBVbnRGI1JsdAAAAAAAAAAAAAAAAFNjbCBVbnRGI1ByY0BZAAAAAAAAAAAAEGNy b3BXaGVuUHJpbnRpbmdib29sAAAAAA5jcm9wUmVjdEJvdHRvbWxvbmcAAAAAAAAADGNyb3BSZWN0 TGVmdGxvbmcAAAAAAAAADWNyb3BSZWN0UmlnaHRsb25nAAAAAAAAAAtjcm9wUmVjdFRvcGxvbmcA AAAAADhCSU0D7QAAAAAAEAEsAAAAAQACASwAAAABAAI4QklNBCYAAAAAAA4AAAAAAAAAAAAAP4AA ADhCSU0EDQAAAAAABAAAAFo4QklNBBkAAAAAAAQAAAAeOEJJTQPzAAAAAAAJAAAAAAAAAAABADhC SU0nE

СКАЧАТЬ