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Sync docs and a couple of tests (#2820)
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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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# This is an auto-generated file. Regular comments will be removed when this | ||
# file is regenerated. Regenerating will not touch any manually added keys, | ||
# so comments can be added in a "comment" key. | ||
# This is an auto-generated file. | ||
# | ||
# Regenerating this file via `configlet sync` will: | ||
# - Recreate every `description` key/value pair | ||
# - Recreate every `reimplements` key/value pair, where they exist in problem-specifications | ||
# - Remove any `include = true` key/value pair (an omitted `include` key implies inclusion) | ||
# - Preserve any other key/value pair | ||
# | ||
# As user-added comments (using the # character) will be removed when this file | ||
# is regenerated, comments can be added via a `comment` key. | ||
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[3ac4f735-d36c-44c4-a3e2-316f79704203] | ||
description = "queen with a valid position" | ||
description = "Test creation of Queens with valid and invalid positions -> queen with a valid position" | ||
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[4e812d5d-b974-4e38-9a6b-8e0492bfa7be] | ||
description = "queen must have positive row" | ||
description = "Test creation of Queens with valid and invalid positions -> queen must have positive row" | ||
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[f07b7536-b66b-4f08-beb9-4d70d891d5c8] | ||
description = "queen must have row on board" | ||
description = "Test creation of Queens with valid and invalid positions -> queen must have row on board" | ||
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[15a10794-36d9-4907-ae6b-e5a0d4c54ebe] | ||
description = "queen must have positive column" | ||
description = "Test creation of Queens with valid and invalid positions -> queen must have positive column" | ||
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[6907762d-0e8a-4c38-87fb-12f2f65f0ce4] | ||
description = "queen must have column on board" | ||
description = "Test creation of Queens with valid and invalid positions -> queen must have column on board" | ||
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[33ae4113-d237-42ee-bac1-e1e699c0c007] | ||
description = "can not attack" | ||
description = "Test the ability of one queen to attack another -> cannot attack" | ||
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[eaa65540-ea7c-4152-8c21-003c7a68c914] | ||
description = "can attack on same row" | ||
description = "Test the ability of one queen to attack another -> can attack on same row" | ||
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[bae6f609-2c0e-4154-af71-af82b7c31cea] | ||
description = "can attack on same column" | ||
description = "Test the ability of one queen to attack another -> can attack on same column" | ||
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[0e1b4139-b90d-4562-bd58-dfa04f1746c7] | ||
description = "can attack on first diagonal" | ||
description = "Test the ability of one queen to attack another -> can attack on first diagonal" | ||
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[ff9b7ed4-e4b6-401b-8d16-bc894d6d3dcd] | ||
description = "can attack on second diagonal" | ||
description = "Test the ability of one queen to attack another -> can attack on second diagonal" | ||
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[0a71e605-6e28-4cc2-aa47-d20a2e71037a] | ||
description = "can attack on third diagonal" | ||
description = "Test the ability of one queen to attack another -> can attack on third diagonal" | ||
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[0790b588-ae73-4f1f-a968-dd0b34f45f86] | ||
description = "can attack on fourth diagonal" | ||
description = "Test the ability of one queen to attack another -> can attack on fourth diagonal" | ||
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[543f8fd4-2597-4aad-8d77-cbdab63619f8] | ||
description = "Test the ability of one queen to attack another -> cannot attack if falling diagonals are only the same when reflected across the longest falling diagonal" |
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