mzdravkov

(defn tree
  [arr]
  (if (empty? arr)
    []
    [[(tree (rest arr))]
     [(tree (reverse
              (rest
                (reverse arr))))]]))

mzdravkov

<?php

$day_start = 7;
$day_end = 19;
$positions = 4;
$people = 8;
$position_hours = 8;
$work_hours = 20;

$busy = [[[3,16,19]],

mzdravkov

quicksort :: (Ord a) => [a] -> [a]  
quicksort [] = []  
quicksort (x:xs) =   
  let smallerSorted = quicksort [a | a <- xs, a <= x]  
      biggerSorted = quicksort [a | a <- xs, a > x]  
  in  smallerSorted ++ [x] ++ biggerSorted  

mzdravkov

# our schedule is 3D array with (5 workdays, W workhours, P positions) for dimensions
day_start = 7
day_end = 19
positions = 4
people = 8
position_hours = 8
work_hours = 20

# generate random schedule of each intern's busy times
busy = ntuple(people, i -> fill((0,0,0), rand(0:7)))

mzdravkov

# our schedule is 3D array with (5 workdays, W workhours, P positions) for dimensions
day_start = 9
day_end = 17
day_hours = day_end - day_start
positions = 4
people = 8
position_hours = 8
work_hours = 20

new_schedule() = fill(0, 5, day_hours, positions)

mzdravkov

function pickrand(col)
  index = rand(1:length(col))
  col[index]
end

function isbusy(intern, busy, day_hours, day, hour)
  for i = 1:length(busy[intern])
    if busy[intern][i][1] == day && (busy[intern][i][2]-day_hours) <= hour < (busy[intern][i][3]-day_hours)
      return true
    end

mzdravkov

function pickrand(col)
  index = rand(1:length(col))
  col[index]
end

function isbusy(intern, busy, day_hours, day, hour)
  for i = 1:length(busy[intern])
    if busy[intern][i][1] == day && (busy[intern][i][2]-day_hours) <= hour < (busy[intern][i][3]-day_hours)
      return true
    end

mzdravkov

# our schedule is 3D array with (5 workdays, 8 workhours, 4 positions) for dimensions
schedule = Array(Int, 5, 8, 4)
day = hour = position = 0
while true
  schedule = Array(Int, 5, 8, 4)
  remaining_hours = fill(20, 8)
  bad_schedule = false

  for day = 1:5, hour = 1:8, position = 1:4
    intern = rand(1:8)

mzdravkov

nodes = %w[1 2 3 4 5 6 7 8]

constraints = {"1" => %w[3 6],
               "2" => %w[1],
               "4" => %w[3],
               "5" => %w[3 4],
               "6" => %w[1 3]}

edges = nodes.combination(2).to_a
nodes.map { |n| constraints[n].map { |c| edges.delete([n, c].sort) } if constraints[n] }

mzdravkov

Can one find 4004 positive integers such that the sum of any 2003 of them is
not divisible by 2003?

Proof?:

Suppose we have 4004 positive integers (lets call them the set W), so that 2002 of them (the set T1) are of the type n∙2003 + 1 (where n is different for each of them) and 2002 of them (the set T2) are of the type m∙2003 + 2 (where m is different for each of them).

When we choose 2003 numbers from W, there will be an even number of T1s and an odd number of T2s or an odd number of T1s and an even of T2s.
So the two cases are:
Case 1: