Given an array of integers, find and print the maximum number of integers you can select from the array such that the absolute difference between any two of the chosen integers is less than or equal to 1.

For example, if your array is a = [1, 1, 2, 2, 4, 4, 5, 5, 5], you can create two subarrays meeting the criterion: [1, 1, 2, 2] and [4, 4, 5, 5, 5]. The maximum length subarray has 5 elements.

We define a magic square to be an n x m matrix of distinct positive integers from 1 to where the sum of any row, column, or diagonal of length n is always equal to the same number: the magic constant.

You will be given a 3 x 3 matrix of integers in the inclusive range [1, 9]. We can convert any digit a to any other digit b in the range [1, 9] at cost of |a - b|. Given s, convert it into a magic square at minimal cost. Print this cost on a new line.

Note: The resulting magic square must contain distinct integers in the inclusive range [1, 9].

For example, we start with the following matrix s:

1
2
3

5 3 4
1 5 8
6 4 2

We can convert it to the following magic square:

1
2
3

8 3 4
1 5 9
6 7 2

This took three replacements at a cost of |5 - 8| + |8 - 9| + |4 - 7| = 7.

Two cats and a mouse are at various positions on a line. You will be given their starting positions. Your task is to determine which cat will reach the mouse first, assuming the mouse doesn’t move and the cats travel at equal speed. If the cats arrive at the same time, the mouse will be allowed to move and it will escape while they fight.

You are given q queries in the form of x, y, and z representing the respective positions for cats A and B, and for mouse C. Complete the function catAndMouse to return the appropriate answer to each query, which will be printed on a new line.

• If cat A catches the mouse first, print Cat A.
• If cat B catches the mouse first, print Cat B.
• If both cats reach the mouse at the same time, print Mouse C as the two cats fight and mouse escapes.

For example, cat A is at position x = 2 and cat B is at y = 5. If mouse C is at position z = 4, it is 2 units from cat A and 1unit from cat B. Cat B will catch the mouse.

Monica wants to buy a keyboard and a USB drive from her favorite electronics store. The store has several models of each. Monica wants to spend as much as possible for the 2 items, given her budget.

Given the price lists for the store’s keyboards and USB drives, and Monica’s budget, find and print the amount of money Monica will spend. If she doesn’t have enough money to both a keyboard and a USB drive, print -1 instead. She will buy only the two required items.

For example, suppose she has b = 60 to spend. Three types of keyboards cost keyboard = [40, 50, 60]. Two USB drives cost drives = [5, 8, 12]. She could purchase a 40 keyboard + 12 USB drive = 52, or a 50 keyboard + 8 USB drive = 58. She chooses the latter. She can’t buy more than 2 items so she can’t spend exactly 60.

Gary is an avid hiker. He tracks his hikes meticulously, paying close attention to small details like topography. During his last hike he took exactly n steps. For every step he took, he noted if it was an uphill, U, or a downhill, D step. Gary’s hikes start and end at sea level and each step up or down represents a 1 unit change in altitude. We define the following terms:

• A mountain is a sequence of consecutive steps above sea level, starting with a step up from sea level and ending with a step down to sea level.
• A valley is a sequence of consecutive steps below sea level, starting with a step down from sea level and ending with a step up to sea level.

Given Gary’s sequence of up and down steps during his last hike, find and print the number of valleys he walked through.

For example, if Gary’s path is s = [DDUUUUDD], he first enters a valley 2 units deep. Then he climbs out an up onto a mountain 2 units high. Finally, he returns to sea level and ends his hike.

Brie’s Drawing teacher asks her class to open their books to a page number. Brie can either start turning pages from the front of the book or from the back of the book. She always turns pages one at a time. When she opens the book, page 1 is always on the right side:

When she flips page 1, she sees pages 2 and 3. 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 n pages long, and she wants to turn to page p, what is the minimum number of pages she will turn? She can start at the beginning or the end of the book.

Given n and p, find and print the minimum number of pages Brie must turn in order to arrive at page p.

John works at a clothing store. He has a large pile of socks that he must pair by color for sale. Given an array of integers representing the color of each sock, determine how many pairs of socks with matching colors there are.

For example, there are n = 7 socks with colors ar = [1, 2, 1, 2, 1, 3, 2]. There is one pair of color 1 and one of color 2. There are three odd socks left, one of each color. The number of pairs is 2.

Anna and Brian are sharing a meal at a restuarant and they agree to split the bill equally. Brian wants to order something that Anna is allergic to though, and they agree that Anna won’t pay for that item. Brian gets the check and calculates Anna’s portion. You must determine if his calculation is correct.

For example, assume the bill has the following prices: bill = [2, 4, 6]. Anna declines to eat item k = bill[2] which costs 6. If Brian calculates the bill correctly, Anna will pay (2 + 4) / 2 = 3. If he includes the cost of bill[2], he will calculate (2 + 4 + 6) / 2 = 6. In the second case, he should refund 3 to Anna.

Marie invented a Time Machine and wants to test it by time-traveling to visit Russia on the Day of the Programmer (the day of the year) during a year in the inclusive range from 1700 to 2700.

From 1700 to 1917, Russia’s official calendar was the Julian calendar; since 1919 they used the Gregorian calendar system. The transition from the Julian to Gregorian calendar system occurred in 1918, when the next day after January was February . This means that in 1918, February was the day of the year in Russia.

In both calendar systems, February is the only month with a variable amount of days; it has 29 days during a leap year, and 28days during all other years. In the Julian calendar, leap years are divisible by 4; in the Gregorian calendar, leap years are either of the following:

You have been asked to help study the population of birds migrating across the continent. Each type of bird you are interested in will be identified by an integer value. Each time a particular kind of bird is spotted, its id number will be added to your array of sightings.

You would like to be able to find out which type of bird is most common given a list of sightings. Your task is to print the type number of that bird and if two or more types of birds are equally common, choose the type with the smallest ID number.

For example, assume your bird sightings are of types ar = [1, 1, 2, 2, 3]. There are two each of types 1 and 2, and one sighting of type 3. Pick the lower of the two types seen twice: type 1.