Dan is playing a video game in which his character competes in a hurdle race. Hurdles are of varying heights, and Dan has a maximum height he can jump. There is a magic potion he can take that will increase his maximum height by 1 unit for each dose. How many doses of the potion must he take to be able to jump all of the hurdles.

Given an array of hurdle heights height, and an initial maximum height Dan can jump, k, determine the minimum number of doses Dan must take to be able to clear all the hurdles in the race.

For example, if height = [1,2,3,3,2] and Dan can jump 1 unit high naturally, he must take 3 - 1 = 2 doses of potion to be able to jump all of the hurdles.

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.

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 arr = [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.

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 1 unit 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 keyboards = [40,50,60]. Two USB drives cost drives = [5, 8, 12]. She could purchase a 40 keyboards + 12 USB drive = 52, or a 50 keyboards + 8 USB drive = 58. She chooses the latter. She can’t buy more than 2 items so she can’t spend exactly 60.

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 = [1,2,1,2,1,1,3,2]. 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.

You are given an array of n integers, ar = ar[0], ar[1], …, ar[n - 1], and a positive integer, k. Find and print the number of (i, j) pairs where i < j and ar[i] + ar[j] is divisible by k.

For example, ar = [1,2,3,4,5,6] and k = 5. Our three pairs meeting the criteria are [1,4],[2,3] and [4,6].

Lily has a chocolate bar that she wants to share it with Ron for his birthday. Each of the squares has an integer on it. She decides to share a contiguous segment of the bar selected such that the length of the segment matches Ron’s birth month and the sum of the integers on the squares is equal to his birth day. You must determine how many ways she can divide the chocolate.

Consider the chocolate bar as an array of squares, s = [2, 2, 1, 3, 2]. She wants to find segments summing to Ron’s birth day, d = 4 with a length equalling his birth month, m = 2. In this case, there are two segments meeting her criteria: [2, 2] and [1, 3].