Task 3

🎓 🎓 🎓 Task 3 состоит из трех задач. Все заготовки задач находятся в корне проекта в папке src/main/kotlin. В каждой заготовке вам дан класс с открытым методом, в который нужно написать код для решения поставленной задачи. Все - как и для Task 1 или 2.

Тесты находятся в папке src/test/kotlin. Тесты можно запускать различными способами. Например, выполнить таск Gradle: Gradle -> Tasks -> verification -> test. Тогда прогонятся все unit-тесты сразу:

Или открыть класс с тестом и нажать на зелёный треугольник рядом с объявлением класса. Если все тесты пройдены успешно 😺, они отмечаются зеленым значком ✔️, иначе 🙀 - красным ❗

❗ В последних версиях Android Studio (>= 4.2) убрали по-умолчанию построение дерева tasks Gradle. Поэтому вы можете не найти задачу test в Gradle -> Tasks -> verification -> test и тесты могут не запускаться.

Во-первых, эту несправедливость несложно поправить. Зайдите в File -> Settings -> Experimental и отключите Do not build Gradle task list during Gradle sync. Затем сделайте sync проекта с Gradle: File -> Sync Project with Gradle Files

Во-вторых, всегда можно запустить тесты в консоли, набрав ./gradlew test.

Если вы пришли к выводу, что выполнили максимум того что могли сделать, то сделайте Submit задачи через https://app.rs.school/

Условия задач

1) Combinator

You know combinations: for example, if you take 5 cards from a 52 cards deck you have 2,598,960 different combinations.

In mathematics the number of x combinations you can take from a set of n elements is called the binomial coefficient of n and x, or more often n choose x.

HINT: one of formulas(for m = n choose x) from combinatorics could help you with solution.

You are a renowned poster designer and painter. You are asked to provide 6 posters all having the same design each in 2 colors. Posters must all have a different color combination and you have the choice of 4 colors: red, blue, yellow, green. How many colors can you choose for each poster?

The answer is two since 4 choose 2 = 6. The combinations will be: {red, blue}, {red, yellow}, {red, green}, {blue, yellow}, {blue, green}, {yellow, green}.

Now same question but you have 35 posters to provide and 7 colors available. How many colors for each poster? If you take combinations 7 choose 2 you will get 21 with the above formula. But 21 schemes aren't enough for 35 posters. If you take 7 choose 5 combinations you will get 21 too. Fortunately if you take 7 choose 3 or 7 choose 4 combinations you get 35 and so each poster will have a different combination of 3 colors or 5 colors. You will take 3 colors because it's less expensive.

Hence the problem is:

knowing m (number of posters to design), knowing n (total number of available colors), let us search x (number of colors for each poster so that each poster has a unique combination of colors and the number of combinations is exactly the same as the number of posters). In other words you should create a function which takes m(Int) and n(Int) and returns x(Int). Some more conditions: m >= 0 and n > 0. If many x are solutions give as result the smallest x. It can happen that when m is given at random there are no x satisfying equation (1) then return null.

Here's the examples:

[6, 4] would return 2

[4, 4] would return 1

[4, 2] would return null

2) Square Decomposer

My younger sister came back home from school with the following task: given a squared sheet of paper she has to cut it in pieces which, when assembled, give squares the sides of which form an increasing sequence of numbers. At the beginning it was lot of fun but little by little we were tired of seeing the pile of torn paper. So we decided to write a program that could help us and protects trees.

Task

Given a positive integral number n, return a strictly increasing sequence (array) of numbers, so that the sum of the squares is equal to n².

If there are multiple solutions (and there will be), return as far as possible the result with the largest possible values:

Examples

decompose 11 must return [1, 2, 4, 10]. Note that there are actually two ways to decompose 11², 11² = 121 = 1 + 4 + 16 + 100 = 1² + 2² + 4² + 10² but don't return [2, 6, 9], since 9 is smaller than 10.

For decompose 50 don't return [1, 1, 4, 9, 49] but [1, 3, 5, 8, 49] since [1, 1, 4, 9, 49] doesn't form a strictly increasing sequence.

Note

Neither [n] nor [1, 1, 1, …, 1] are valid solutions. If no valid solution exists, return null.

The function "decompose" will take a positive Int n and return the decomposition of N = n² as [x1 ... xk]

If n is negative, return null as well.

Examples:

decompose 50 returns [1, 3, 5, 8, 49]

decompose 4 returns null

3) Telephone Finder

Started in 2008 and recently resurging in popularity, a game known as Number Neighbour or Text Door Neighbor has people sending a text message to phone numbers near their own.

Traditionally this was done for numbers ±1, so someone with the phone number 555-555-5555 has neighbors 555-555-5554 and 555- 555-5556.

We're going to take this a step further and think about neighbors based on a classic phone keypad.

First, let's take a look at the classic phone keypad:

We can consider certain numbers adjacent if they appear directly next to or above/below each other. For example, 1 is adjacent to 2 and 4 (and nothing else), while 5 is adjacent to 2, 4, 6, and 8.

Let's look for phone numbers that are "neighbors" of a given phone number by having any one (and only one) of their digits be off-by-one as a number adjacent to the original.

By this definition, 555-555-5555 has both its original neighbors but also, e.g., 554-555-5555 and 555-555-5558.

Problem

Given a phone number of string from integers length N (1 ≤ N ≤ 10) as a number string (e.g. 555-555-5555 would be passed as "5555555555"), return an array of all phone numbers as number strings that would be considered neighbors of that phone number.

Examples

Given "1" returns ["2", "4"]

Given "8675309" returns ["5675309", "7675309", "9675309", "0675309", "8375309", "8575309", "8975309", "8645309", "8685309", "8672309", "8674309", "8676309", "8678309", "8675209", "8675609", "8675389", "8675306", "8675308"]

Notes

Do not wrap around a side of the keypad when finding adjacent numbers. That is, do not consider 6 adjacent to 4 nor 0 adjacent to 2.

Do not consider numbers that are diagonal to each other adjacent. In case input number is negative return null.

Do not worry about the order of number strings in the array being returned.

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