Given a set of distinct integers, print the size of a maximal subset of S where the sum of any 2 numbers in S^‘ is not evenly divisible by k.

For example, the array S = [19,10,12,10,24,25,22] and k = 4. One of the arrays that can be created is S^‘[0] = [10,12,25]. Another is S^‘[1] = [19,22,24]. After testing all permutations, the maximum length solution array has 3 elements.

Taum is planning to celebrate the birthday of his friend, Diksha. There are two types of gifts that Diksha wants from Taum: one is black and the other is white. To make her happy, Taum has to buy b black gifts and w white gifts.

• The cost of each black gift is bc units.
• The cost of every white gift is wc units.
• The cost of converting each black gift into white gift or vice versa is units.

Help Taum by deducing the minimum amount he needs to spend on Diksha’s gifts.

For example, if Taum wants to buy b = 3 black gifts and w = 5 white gifts at a cost of bc = 3, wc = 4 and conversion cost z = 1, we see that he can buy a black gift for 3 and convert it to a white gift for 1, making the total cost of each white gift 4. That matches the cost of a white gift, so he can do that or just buy black gifts and white gifts. Either way, the overall cost is 3 * 3 + 5 * 4 = 29.

You have a string of lowercase English alphabetic letters. You can perform two types of operations on the string:

1. Append a lowercase English alphabetic letter to the end of the string.
2. Delete the last character in the string. Performing this operation on an empty string results in an empty string.

Given an integer, k, and two strings, s and t, determine whether or not you can convert s to t by performing exactly k of the above operations on s. If it’s possible, print Yes. Otherwise, print No.

For example, strings s = [a,b,c] and t = [d,e,f]. Our number of moves, k = 6. To convert s to t, we first delete all of the characters in 3 moves. Next we add each of the characters of t in order. On the 6^th move, you will have the matching string. If there had been more moves available, they could have been eliminated by performing multiple deletions on an empty string. If there were fewer than 6 moves, we would not have succeeded in creating the new string.

Sami’s spaceship crashed on Mars! She sends a series of SOS messages to Earth for help.

Letters in some of the SOS messages are altered by cosmic radiation during transmission. Given the signal received by Earth as a string, s, determine how many letters of Sami’s SOS have been changed by radiation.

For example, Earth receives SOSTOT. Sami’s original message was SOSSOS. Two of the message characters were changed in transit.

Karl has an array of integers. He wants to reduce the array until all remaining elements are equal. Determine the minimum number of elements to delete to reach his goal.

For example, if his array is arr = [1,2,2,3], we see that he can delete the 2 elements 1 and 3 leaving arr = [2,2]. He could also delete both twos and either the 1 or the 3, but that would take 3 deletions. The minimum number of deletions is 2.

Lilah has a string, s, of lowercase English letters that she repeated infinitely many times.

Given an integer, n, find and print the number of letter a’s in the first letters of Lilah’s infinite string.

For example, if the string s = ‘abcac’ and n = 10, the substring we consider is abcacabcac, the first 10 characters of her infinite string. There are 4 occurrences of a in the substring.

You are given a number of sticks of varying lengths. You will iteratively cut the sticks into smaller sticks, discarding the shortest pieces until there are none left. At each iteration you will determine the length of the shortest stick remaining, cut that length from each of the longer sticks and then discard all the pieces of that shortest length. When all the remaining sticks are the same length, they cannot be shortened so discard them.

Given the lengths of n sticks, print the number of sticks that are left before each iteration until there are none left.

For example, there are n = 3 sticks of lengths arr = [1,2,3]. The shortest stick length is 1, so we cut that length from the longer two and discard the pieces of length 1. Now our lengths are arr = [1,2]. Again, the shortest stick is of length 1, so we cut that amount from the longer stick and discard those pieces. There is only one stick left, arr = [1], so we discard that stick. Our lengths are answer = [3,2,1].

The factorial of the integer n, written n!, is defined as:

n! = n x (n - 1) x (n - 2) x … x 3 x 2 x 1

Calculate and print the factorial of a given integer.

For example, if n = 3, we calculate 30 x 29 x 28 x … x 3 x 2 x 1 and get 265252859812191058636308480000000.

Aerith is playing a cloud hopping game. In this game, there are sequentially numbered clouds that can be thunderheads or cumulus clouds. Her character must jump from cloud to cloud until it reaches the start again.

To play, Aerith is given an array of clouds, c and an energy level e = 100. She starts from c[0] and uses 1 unit of energy to make a jump of size k to cloud c[(i + k) % n]. If Aerith lands on a thundercloud, c[i] = 1, her energy (e) decreases by 2 additional units. The game ends when Aerith lands back on cloud 0.

Given the values of n, k, and the configuration of the clouds as an array c, can you determine the final value of e after the game ends?

For example, give c = [0, 0, 1, 0] and k = 2, the indices of her path are 0 -> 2 -> 0. Her energy level reduces by 1 for each jump to 98. She landed on one thunderhead at an additional cost of 2 energy units. Her final energy level is 96.

Note: Recall that % refers to the modulo operation. In this case, it serves to make the route circular. If Aerith is at c[n -1] and jumps 1, she will arrive at c[0].

Emma is playing a new mobile game that starts with consecutively numbered clouds. Some of the clouds are thunderheads and others are cumulus. She can jump on any cumulus cloud having a number that is equal to the number of the current cloud plus 1 or 2. She must avoid the thunderheads. Determine the minimum number of jumps it will take Emma to jump from her starting postion to the last cloud. It is always possible to win the game.

For each game, Emma will get an array of clouds numbered 0 if they are safe or 1 if they must be avoided. For example, c = [0,1,0,0,0,1,0] indexed from 0…6. The number on each cloud is its index in the list so she must avoid the clouds at indexes 1 and 5. She could follow the following two paths: 0 -> 2 -> 4 -> 6 or 0 -> 2 -> 3 -> 4 -> 6. The first path takes 3 jumps while the second takes 4.