# Helpers

function input(prompt::AbstractString="")
    print(prompt)
    return chomp(readline())
end

function swapRows!(X, i, j)
    for k = 1:size(X,2)
        X[i,k], X[j,k] = X[j,k], X[i,k]
    end
end

function get_pivot()
  id = eye(dimension)

  for i in 1:dimension
    max = A[i, i]
    row = i

    for j in i:dimension
      if A[j,i] > max
        max = A[j,i]
        row = j
      end
    end

    swapRows!(id, row, i)
  end

  return id
end

function lu_decomposition()
  p = get_pivot()
  tmp = p * A
  u = zeros(dimension, dimension)
  l = eye(dimension)

  for i in 1:dimension
    for j in 1:dimension
      if j >= i
        sum = 0.0
        for k in 1:i
          sum = sum + u[k, j] * l[i, k]
        end

        u[i, j] = tmp[i,j] - sum
      else
        sum = 0.0
        for k in 1:j
          sum = sum + u[k, j] * l[i, k]
        end

        l[i, j] = (tmp[i,j] - sum) / u[j, j]
      end
    end
  end
  return l, u, p
end

dimension = input("Podaj stopień macierzy: ")
dimension = parse(Int, dimension)
A = eye(dimension)

for row = 1:dimension
  for column = 1:dimension
    value = input("Podaj wartość komórki A[$(row), $(column)]")
    A[row, column] = parse(Int, value)
  end
end

println("\n Wprowadzono macierz:")
display(A)
println("")

L, U, P = lu_decomposition()

println("\nMacierz trójkątna dolna:")
display(L)
println("")
println("\nMacierz trójkątna górna:")
display(U)
println("")