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# Introduction | ||
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At a garage sale, you find a lovely vintage typewriter at a bargain price! | ||
Excitedly, you rush home, insert a sheet of paper, and start typing away. | ||
However, your excitement wanes when you examine the output: all words are garbled! | ||
For example, it prints "stop" instead of "post" and "least" instead of "stale." | ||
Carefully, you try again, but now it prints "spot" and "slate." | ||
After some experimentation, you find there is a random delay before each letter is printed, which messes up the order. | ||
You now understand why they sold it for so little money! | ||
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You realize this quirk allows you to generate anagrams, which are words formed by rearranging the letters of another word. | ||
Pleased with your finding, you spend the rest of the day generating hundreds of anagrams. |
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# Instructions | ||
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Given a string containing brackets `[]`, braces `{}`, parentheses `()`, or any combination thereof, verify that any and all pairs are matched and nested correctly. | ||
The string may also contain other characters, which for the purposes of this exercise should be ignored. | ||
Any other characters should be ignored. | ||
For example, `"{what is (42)}?"` is balanced and `"[text}"` is not. |
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# Introduction | ||
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You're given the opportunity to write software for the Bracketeer™, an ancient but powerful mainframe. | ||
The software that runs on it is written in a proprietary language. | ||
Much of its syntax is familiar, but you notice _lots_ of brackets, braces and parentheses. | ||
Despite the Bracketeer™ being powerful, it lacks flexibility. | ||
If the source code has any unbalanced brackets, braces or parentheses, the Bracketeer™ crashes and must be rebooted. | ||
To avoid such a scenario, you start writing code that can verify that brackets, braces, and parentheses are balanced before attempting to run it on the Bracketeer™. |
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# Instructions | ||
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Compute Pascal's triangle up to a given number of rows. | ||
Your task is to output the first N rows of Pascal's triangle. | ||
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In Pascal's Triangle each number is computed by adding the numbers to the right and left of the current position in the previous row. | ||
[Pascal's triangle][wikipedia] is a triangular array of positive integers. | ||
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In Pascal's triangle, the number of values in a row is equal to its row number (which starts at one). | ||
Therefore, the first row has one value, the second row has two values, and so on. | ||
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The first (topmost) row has a single value: `1`. | ||
Subsequent rows' values are computed by adding the numbers directly to the right and left of the current position in the previous row. | ||
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If the previous row does _not_ have a value to the left or right of the current position (which only happens for the leftmost and rightmost positions), treat that position's value as zero (effectively "ignoring" it in the summation). | ||
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## Example | ||
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Let's look at the first 5 rows of Pascal's Triangle: | ||
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```text | ||
1 | ||
1 1 | ||
1 2 1 | ||
1 3 3 1 | ||
1 4 6 4 1 | ||
# ... etc | ||
``` | ||
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The topmost row has one value, which is `1`. | ||
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The leftmost and rightmost values have only one preceding position to consider, which is the position to its right respectively to its left. | ||
With the topmost value being `1`, it follows from this that all the leftmost and rightmost values are also `1`. | ||
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The other values all have two positions to consider. | ||
For example, the fifth row's (`1 4 6 4 1`) middle value is `6`, as the values to its left and right in the preceding row are `3` and `3`: | ||
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[wikipedia]: https://en.wikipedia.org/wiki/Pascal%27s_triangle |
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# Introduction | ||
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With the weather being great, you're not looking forward to spending an hour in a classroom. | ||
Annoyed, you enter the class room, where you notice a strangely satisfying triangle shape on the blackboard. | ||
Whilst waiting for your math teacher to arrive, you can't help but notice some patterns in the triangle: the outer values are all ones, each subsequent row has one more value than its previous row and the triangle is symmetrical. | ||
Weird! | ||
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Not long after you sit down, your teacher enters the room and explains that this triangle is the famous [Pascal's triangle][wikipedia]. | ||
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Over the next hour, your teacher reveals some amazing things hidden in this triangle: | ||
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- It can be used to compute how many ways you can pick K elements from N values. | ||
- It contains the Fibonacci sequence. | ||
- If you color odd and even numbers differently, you get a beautiful pattern called the [Sierpiński triangle][wikipedia-sierpinski-triangle]. | ||
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The teacher implores you and your classmates to lookup other uses, and assures you that there are lots more! | ||
At that moment, the school bell rings. | ||
You realize that for the past hour, you were completely absorbed in learning about Pascal's triangle. | ||
You quickly grab your laptop from your bag and go outside, ready to enjoy both the sunshine _and_ the wonders of Pascal's triangle. | ||
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[wikipedia]: https://en.wikipedia.org/wiki/Pascal%27s_triangle | ||
[wikipedia-sierpinski-triangle]: https://en.wikipedia.org/wiki/Sierpi%C5%84ski_triangle |
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# Instructions | ||
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Determine if a number is perfect, abundant, or deficient based on | ||
Nicomachus' (60 - 120 CE) classification scheme for positive integers. | ||
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The Greek mathematician [Nicomachus][nicomachus] devised a classification scheme for positive integers, identifying each as belonging uniquely to the categories of **perfect**, **abundant**, or **deficient** based on their [aliquot sum][aliquot-sum]. | ||
The aliquot sum is defined as the sum of the factors of a number not including the number itself. | ||
For example, the aliquot sum of 15 is (1 + 3 + 5) = 9 | ||
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- **Perfect**: aliquot sum = number | ||
- 6 is a perfect number because (1 + 2 + 3) = 6 | ||
- 28 is a perfect number because (1 + 2 + 4 + 7 + 14) = 28 | ||
- **Abundant**: aliquot sum > number | ||
- 12 is an abundant number because (1 + 2 + 3 + 4 + 6) = 16 | ||
- 24 is an abundant number because (1 + 2 + 3 + 4 + 6 + 8 + 12) = 36 | ||
- **Deficient**: aliquot sum < number | ||
- 8 is a deficient number because (1 + 2 + 4) = 7 | ||
- Prime numbers are deficient | ||
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Implement a way to determine whether a given number is **perfect**. | ||
Depending on your language track, you may also need to implement a way to determine whether a given number is **abundant** or **deficient**. | ||
Determine if a number is perfect, abundant, or deficient based on Nicomachus' (60 - 120 CE) classification scheme for positive integers. | ||
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The Greek mathematician [Nicomachus][nicomachus] devised a classification scheme for positive integers, identifying each as belonging uniquely to the categories of [perfect](#perfect), [abundant](#abundant), or [deficient](#deficient) based on their [aliquot sum][aliquot-sum]. | ||
The _aliquot sum_ is defined as the sum of the factors of a number not including the number itself. | ||
For example, the aliquot sum of `15` is `1 + 3 + 5 = 9`. | ||
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## Perfect | ||
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A number is perfect when it equals its aliquot sum. | ||
For example: | ||
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- `6` is a perfect number because `1 + 2 + 3 = 6` | ||
- `28` is a perfect number because `1 + 2 + 4 + 7 + 14 = 28` | ||
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## Abundant | ||
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A number is abundant when it is less than its aliquot sum. | ||
For example: | ||
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- `12` is an abundant number because `1 + 2 + 3 + 4 + 6 = 16` | ||
- `24` is an abundant number because `1 + 2 + 3 + 4 + 6 + 8 + 12 = 36` | ||
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## Deficient | ||
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A number is deficient when it is greater than its aliquot sum. | ||
For example: | ||
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- `8` is a deficient number because `1 + 2 + 4 = 7` | ||
- Prime numbers are deficient | ||
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## Task | ||
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Implement a way to determine whether a given number is [perfect](#perfect). | ||
Depending on your language track, you may also need to implement a way to determine whether a given number is [abundant](#abundant) or [deficient](#deficient). | ||
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[nicomachus]: https://en.wikipedia.org/wiki/Nicomachus | ||
[aliquot-sum]: https://en.wikipedia.org/wiki/Aliquot_sum |
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