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.

Little Bobby loves chocolate. He frequently goes to his favorite 5 & 10 store, Penny Auntie, to buy them. They are having a promotion at Penny Auntie. If Bobby saves enough wrappers, he can turn them in for a free chocolate.

For example, Bobby has n = 15 to spend on bars of chocolate that cost c = 3 each. He can turn in m = 2 wrappers to receive another bar. Initially, he buys 5 bars and has 5 wrappers after eating them. He turns in 4 of them, leaving him with 1, for 2 more bars. After eating those two, he has 3 wrappers, turns in 2 leaving him with 1 wrapper and his new bar. Once he eats that one, he has 2 wrappers and turns them in for another bar. After eating that one, he only has 1 wrapper, and his feast ends. Overall, he has eaten 5 + 2 + 1 + 1 = 9 bars.

John Watson knows of an operation called a right circular rotation on an array of integers. One rotation operation moves the last array element to the first position and shifts all remaining elements right one. To test Sherlock’s abilities, Watson provides Sherlock with an array of integers. Sherlock is to perform the rotation operation a number of times then determine the value of the element at a given position.

For each array, perform a number of right circular rotations and return the value of the element at a given index.

For example, array a = [3,4,5], number of rotations, k = 2 and indices to check, m = [1,2].

First we perform the two rotations:

[3,4,5] -> [5,3,4] -> [4,5,3]

Now return the values from the zero-based indices and as indicated in the array.

a[1] = 5

a[2] = 3

We define a magic square to be an n X n matrix of distinct positive integers from 1 to n² 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 s 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.

Alice is playing an arcade game and wants to climb to the top of the leaderboard and wants to track her ranking. The game uses Dense Ranking, so its leaderboard works like this:

• The player with the highest score is ranked number 1 on the leaderboard.
• Players who have equal scores receive the same ranking number, and the next player(s) receive the immediately following ranking number.

For example, the four players on the leaderboard have high scores of 100, 90, 90, and 80. Those players will have ranks 1, 2, 2, and 3, respectively. If Alice’s scores are 70, 80 and 105, her rankings after each game are 4^th, 3^rd and 1^st.

Consider an array of numeric strings where each string is a positive number with anywhere from 1 to 10⁶ digits. Sort the array’s elements in non-decreasing, or ascending order of their integer values and print each element of the sorted array on a new line.