Compute Pascal's triangle up to a given number of rows.
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.
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
# ... etc
To run the tests, run the command busted
from within the exercise directory.
For more detailed information about the Lua track, including how to get help if you're having trouble, please visit the exercism.io Lua language page.
Pascal's Triangle at Wolfram Math World http://mathworld.wolfram.com/PascalsTriangle.html
It's possible to submit an incomplete solution so you can see how others have completed the exercise.
local Triangle = require('pascals-triangle')
describe('pascals-triangle', function()
it('should generate a triangle with one row', function()
assert.same({ { 1 } }, Triangle(1).rows)
end)
it('should generate a triangle with two rows', function()
assert.same({ { 1 }, { 1, 1 } }, Triangle(2).rows)
end)
it('should generate a triangle with three rows', function()
assert.same({ { 1 }, { 1, 1 }, { 1, 2, 1 } }, Triangle(3).rows)
end)
it('should allow the last row to be accessed directly', function()
assert.same({ 1, 2, 1 }, Triangle(3).last_row)
end)
it('should generate the fourth row correctly', function()
assert.same({ 1, 3, 3, 1 }, Triangle(4).last_row)
end)
it('should generate the fifth row correctly', function()
assert.same({ 1, 4, 6, 4, 1 }, Triangle(5).last_row)
end)
it('should generate the twentieth row correctly', function()
local twentieth = { 1, 19, 171, 969, 3876, 11628, 27132, 50388, 75582, 92378, 92378, 75582, 50388, 27132, 11628, 3876, 969, 171, 19, 1 }
assert.same(twentieth, Triangle(20).last_row)
end)
end)
return function (nth)
local rows = {}
for i = 1, nth do
local elements = {1}
for j = 2, i do
elements[j] = rows[i-1][j-1] + (rows[i-1][j] or 0)
end
table.insert(rows,elements)
end
return {
rows = rows,
last_row = rows[nth]
}
end
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