diff --git a/exercises/practice/pascals-triangle/.docs/instructions.md b/exercises/practice/pascals-triangle/.docs/instructions.md index 7109334fb..0f58f0069 100644 --- a/exercises/practice/pascals-triangle/.docs/instructions.md +++ b/exercises/practice/pascals-triangle/.docs/instructions.md @@ -1,9 +1,20 @@ # Instructions -Compute Pascal's triangle up to a given number of rows. +Your task is to output the first N rows of Pascal's triangle. -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. + +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. + +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. + +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). + +## Example + +Let's look at the first 5 rows of Pascal's Triangle: ```text 1 @@ -11,5 +22,14 @@ the right and left of the current position in the previous row. 1 2 1 1 3 3 1 1 4 6 4 1 -# ... etc ``` + +The topmost row has one value, which is `1`. + +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`. + +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`: + +[wikipedia]: https://en.wikipedia.org/wiki/Pascal%27s_triangle diff --git a/exercises/practice/pascals-triangle/.docs/introduction.md b/exercises/practice/pascals-triangle/.docs/introduction.md new file mode 100644 index 000000000..60b8ec30d --- /dev/null +++ b/exercises/practice/pascals-triangle/.docs/introduction.md @@ -0,0 +1,22 @@ +# Introduction + +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! + +Not long after you sit down, your teacher enters the room and explains that this triangle is the famous [Pascal's triangle][wikipedia]. + +Over the next hour, your teacher reveals some amazing things hidden in this triangle: + +- 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]. + +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. + +[wikipedia]: https://en.wikipedia.org/wiki/Pascal%27s_triangle +[wikipedia-sierpinski-triangle]: https://en.wikipedia.org/wiki/Sierpi%C5%84ski_triangle diff --git a/exercises/practice/pascals-triangle/.meta/config.json b/exercises/practice/pascals-triangle/.meta/config.json index 0d61aab9d..91fe9e1e3 100644 --- a/exercises/practice/pascals-triangle/.meta/config.json +++ b/exercises/practice/pascals-triangle/.meta/config.json @@ -22,5 +22,5 @@ }, "blurb": "Compute Pascal's triangle up to a given number of rows.", "source": "Pascal's Triangle at Wolfram Math World", - "source_url": "https://mathworld.wolfram.com/PascalsTriangle.html" + "source_url": "https://www.wolframalpha.com/input/?i=Pascal%27s+triangle" } diff --git a/exercises/practice/pascals-triangle/.meta/example.php b/exercises/practice/pascals-triangle/.meta/example.php index 1a5cb38a8..da7c28253 100644 --- a/exercises/practice/pascals-triangle/.meta/example.php +++ b/exercises/practice/pascals-triangle/.meta/example.php @@ -1,27 +1,5 @@ . - * - * To disable strict typing, comment out the directive below. - */ - declare(strict_types=1); function pascalsTriangleRows($rowCount) diff --git a/exercises/practice/pascals-triangle/PascalsTriangleTest.php b/exercises/practice/pascals-triangle/PascalsTriangleTest.php index e447976be..d5aed117a 100644 --- a/exercises/practice/pascals-triangle/PascalsTriangleTest.php +++ b/exercises/practice/pascals-triangle/PascalsTriangleTest.php @@ -1,27 +1,5 @@ . - * - * To disable strict typing, comment out the directive below. - */ - declare(strict_types=1); class PascalsTriangleTest extends PHPUnit\Framework\TestCase @@ -31,33 +9,102 @@ public static function setUpBeforeClass(): void require_once 'PascalsTriangle.php'; } + /** + * uuid: 9920ce55-9629-46d5-85d6-4201f4a4234d + * @testdox Zero rows + */ public function testZeroRows(): void { $this->assertSame([], pascalsTriangleRows(0)); } + /** + * uuid: 70d643ce-a46d-4e93-af58-12d88dd01f21 + * @testdox Single row + */ public function testSingleRow(): void { $this->assertSame([[1]], pascalsTriangleRows(1)); } + + /** + * uuid: a6e5a2a2-fc9a-4b47-9f4f-ed9ad9fbe4bd + * @testdox Two rows + */ public function testTwoRows(): void { $this->assertSame([[1], [1, 1]], pascalsTriangleRows(2)); } + + /** + * uuid: 97206a99-79ba-4b04-b1c5-3c0fa1e16925 + * @testdox Three rows + */ public function testThreeRows(): void { $this->assertSame([[1], [1, 1], [1, 2, 1]], pascalsTriangleRows(3)); } + + /** + * uuid: 565a0431-c797-417c-a2c8-2935e01ce306 + * @testdox Four rows + */ public function testFourRows(): void { $this->assertSame([[1], [1, 1], [1, 2, 1], [1, 3, 3, 1]], pascalsTriangleRows(4)); } - public function testNegativeRows(): void + + /** + * uuid: 06f9ea50-9f51-4eb2-b9a9-c00975686c27 + * @testdox Five rows + */ + public function testFiveRows(): void { - $this->assertEquals(-1, pascalsTriangleRows(-1)); + $this->assertEquals( + [ + [1], + [1, 1], + [1, 2, 1], + [1, 3, 3, 1], + [1, 4, 6, 4, 1] + ], + pascalsTriangleRows(5) + ); } - public function testNullNoRows(): void + + /** + * uuid: c3912965-ddb4-46a9-848e-3363e6b00b13 + * @testdox Six rows + */ + public function testSixRows(): void + { + $this->assertEquals([ + [1], + [1, 1], + [1, 2, 1], + [1, 3, 3, 1], + [1, 4, 6, 4, 1], + [1, 5, 10, 10, 5, 1] + ], pascalsTriangleRows(6)); + } + + /** + * uuid: 6cb26c66-7b57-4161-962c-81ec8c99f16b + * @testdox Ten rows + */ + public function testTenRows(): void { - $this->assertEquals(-1, pascalsTriangleRows(null)); + $this->assertEquals([ + [1], + [1, 1], + [1, 2, 1], + [1, 3, 3, 1], + [1, 4, 6, 4, 1], + [1, 5, 10, 10, 5, 1], + [1, 6, 15, 20, 15, 6, 1], + [1, 7, 21, 35, 35, 21, 7, 1], + [1, 8, 28, 56, 70, 56, 28, 8, 1], + [1, 9, 36, 84, 126, 126, 84, 36, 9, 1] + ], pascalsTriangleRows(10)); } }