In a book, the page numbers are given in form a, b, b, c, c, c,….find the alphabet written on the 100th page of the book. N
Question
In a book, the page numbers are given in form a, b, b, c, c, c,….find the alphabet written on the 100th page of the book. N
Solution
The pattern of the page numbers in the book is as follows: one page is labeled 'a', two pages are labeled 'b', three pages are labeled 'c', and so on. This pattern suggests that the nth letter of the alphabet is repeated n times.
To find the letter on the 100th page, we need to find the sum of the series 1+2+3+... until this sum is just less than or equal to 100. This is because the sum represents the total number of pages up to a certain letter.
Let's calculate:
1 + 2 = 3 (This covers the first 'a' and two 'b's)
3 + 3 = 6 (This adds the three 'c's)
6 + 4 = 10 (This adds the four 'd's)
10 + 5 = 15 (This adds the five 'e's)
15 + 6 = 21 (This adds the six 'f's)
21 + 7 = 28 (This adds the seven 'g's)
28 + 8 = 36 (This adds the eight 'h's)
36 + 9 = 45 (This adds the nine 'i's)
45 + 10 = 55 (This adds the ten 'j's)
55 + 11 = 66 (This adds the eleven 'k's)
66 + 12 = 78 (This adds the twelve 'l's)
78 + 13 = 91 (This adds the thirteen 'm's)
91 + 14 = 105 (This adds the fourteen 'n's)
We stop here because 105 is greater than 100. So, the 100th page falls in the 'n' pages. Therefore, the 100th page of the book is labeled 'n'.
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A teacher asks the class to open their books to a page number. A student can either start turning pages from the front of the book or from the back of the book. They always turn pages one at a time. When they open the book, page is always on the right side:When they flip page , they see pages and . Each page except the last page will always be printed on both sides. The last page may only be printed on the front, given the length of the book. If the book is pages long, and a student wants to turn to page , what is the minimum number of pages to turn? They can start at the beginning or the end of the book.Given and , find and print the minimum number of pages that must be turned in order to arrive at page .ExampleUsing the diagram above, if the student wants to get to page , they open the book to page , flip page and they are on the correct page. If they open the book to the last page, page , they turn page and are at the correct page. Return .Function DescriptionComplete the pageCount function in the editor below.pageCount has the following parameter(s):int n: the number of pages in the bookint p: the page number to turn toReturnsint: the minimum number of pages to turnInput FormatThe first line contains an integer , the number of pages in the book.The second line contains an integer, , the page to turn to.ConstraintsSample Input 062Sample Output 01Explanation 0If the student starts turning from page , they only need to turn page:If a student starts turning from page , they need to turn pages:Return the minimum value, .Sample Input 154Sample Output 10Explanation 1If the student starts turning from page , they need to turn pages:If they start turning from page , they do not need to turn any pages:Return the minimum value, .
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