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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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Given an age in seconds, calculate how old someone would be on: | ||
Given an age in seconds, calculate how old someone would be on a planet in our Solar System. | ||
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- Mercury: orbital period 0.2408467 Earth years | ||
- Venus: orbital period 0.61519726 Earth years | ||
- Earth: orbital period 1.0 Earth years, 365.25 Earth days, or 31557600 seconds | ||
- Mars: orbital period 1.8808158 Earth years | ||
- Jupiter: orbital period 11.862615 Earth years | ||
- Saturn: orbital period 29.447498 Earth years | ||
- Uranus: orbital period 84.016846 Earth years | ||
- Neptune: orbital period 164.79132 Earth years | ||
One Earth year equals 365.25 Earth days, or 31,557,600 seconds. | ||
If you were told someone was 1,000,000,000 seconds old, their age would be 31.69 Earth-years. | ||
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So if you were told someone were 1,000,000,000 seconds old, you should | ||
be able to say that they're 31.69 Earth-years old. | ||
For the other planets, you have to account for their orbital period in Earth Years: | ||
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If you're wondering why Pluto didn't make the cut, go watch [this YouTube video][pluto-video]. | ||
| Planet | Orbital period in Earth Years | | ||
| ------- | ----------------------------- | | ||
| Mercury | 0.2408467 | | ||
| Venus | 0.61519726 | | ||
| Earth | 1.0 | | ||
| Mars | 1.8808158 | | ||
| Jupiter | 11.862615 | | ||
| Saturn | 29.447498 | | ||
| Uranus | 84.016846 | | ||
| Neptune | 164.79132 | | ||
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Note: The actual length of one complete orbit of the Earth around the sun is closer to 365.256 days (1 sidereal year). | ||
~~~~exercism/note | ||
The actual length of one complete orbit of the Earth around the sun is closer to 365.256 days (1 sidereal year). | ||
The Gregorian calendar has, on average, 365.2425 days. | ||
While not entirely accurate, 365.25 is the value used in this exercise. | ||
See [Year on Wikipedia][year] for more ways to measure a year. | ||
[pluto-video]: https://www.youtube.com/watch?v=Z_2gbGXzFbs | ||
[year]: https://en.wikipedia.org/wiki/Year#Summary | ||
~~~~ |
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# Introduction | ||
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The year is 2525 and you've just embarked on a journey to visit all planets in the Solar System (Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune). | ||
The first stop is Mercury, where customs require you to fill out a form (bureaucracy is apparently _not_ Earth-specific). | ||
As you hand over the form to the customs officer, they scrutinize it and frown. | ||
"Do you _really_ expect me to believe you're just 50 years old? | ||
You must be closer to 200 years old!" | ||
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Amused, you wait for the customs officer to start laughing, but they appear to be dead serious. | ||
You realize that you've entered your age in _Earth years_, but the officer expected it in _Mercury years_! | ||
As Mercury's orbital period around the sun is significantly shorter than Earth, you're actually a lot older in Mercury years. | ||
After some quick calculations, you're able to provide your age in Mercury Years. | ||
The customs officer smiles, satisfied, and waves you through. | ||
You make a mental note to pre-calculate your planet-specific age _before_ future customs checks, to avoid such mix-ups. | ||
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~~~~exercism/note | ||
If you're wondering why Pluto didn't make the cut, go watch [this YouTube video][pluto-video]. | ||
[pluto-video]: https://www.youtube.com/watch?v=Z_2gbGXzFbs | ||
~~~~ |
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