Programming in Lua - Homework 2

1. The chunk below fails with a syntax error. Fix it:

code = [[
  foo[bar[0]] = 2
]]
print(code)

Answer:

code = [=[
  foo[bar[0]] = 2
]=]
print(code)

2. Explain what the following mistery function does:

function mistery(a, ...)
  return ...
end

Answer:

It receives a list of arguments and returns all of them but the first one.

3. Write a function that returns the first n numbers in the Fibonacci sequence:

> print(fibs(5))
> 1    1    2    3    5

Each number in the Fibonacci sequence is the sum of the two previous numbers. Hint: use an auxiliary function that uses the same trick as the range function in the lecture notes for class 3.

Answer:

function fibs(n)
  local function fibs_list(a, b, n)
    if n > 0 then
      return a, fibs_list(b, a + b, n - 1)
    end
  end
  return fibs_list(1, 1, n)
end

4. Write a function that takes as arguments the coeficients of a polynomial, and returns a function that evaluates the polynomial for some x:

f = poly(3, 0, 1)
print(f(0)) -- 1 = 3*0^2 + 0*0^1 + 1*0^0

print(f(5)) -- 76 = 3*5^2 + 0*5^1 + 1*5^0

Answer:

function poly(...)
  local cs = { ... }
  return function(x)
           local sum = 0
           local power = #cs - 1
           for _, c in ipairs(cs) do
             sum = sum + c * (x ^ power)
             power = power - 1
           end
           return sum
         end
end

5. The triangular numbers are a famous integer sequence. The first triangular number is 1. The nth triangular number can be found by taking the previous number and adding n (1, 3, 6, 10, 15, …). Write a closure iterator for the triangular numbers:

for x in triang(5) do
  io.write(x, "\t")
end
io.write("\n")
-- prints    1    3    6    10    15

Answer:

function triang(n)
  local next = 0
  local index = 1
  return function () -- iterator

           if index > n then
             return nil
           else
             next = next + index
             index = index + 1
             return next
           end
         end
end