Show only the combinations of two permutated arrays that have a sum less than or equal to target number

Question

I have two arrays: teams = [1,2,3] and drivers = [4,5,6] . Using permutations I have managed to show all combinations of the two arrays, but have managed to define what number of values I'd like to use from each array. So from 'Teams' I have used 1 value and 'Drivers' I have used two. I would like to only show the combinations where the sum is less than or equal to 10 and remove any duplicates.

    teams = [1,2,3]
    drivers = [4,5,6]
    team = teams.permutation(1).to_a
    driver = drivers.permutation(2).to_a
    array = team.product(driver)
    target = 11

This is successfully outputting all combinations of the two arrays using 1 number from teams and 2 from drivers as follows:

[[1], [4, 5]], [[1], [4, 6]], [[1], [5, 4]], [[1], [5, 6]], [[1], [6, 4]], [[1], [6, 5]], [[2], [4, 5]], etc...

To only show values less than or equal to 10 my expected outcome would be: [[1], [4, 5]], [[1], [5, 4]],

and then no duplicates would leave me with just: [[1], [4, 5]]

I have tried adding the below line of code but am getting an undefined method `<=' error:

@array = array[0].product(*array[1..-1]).select { |a| a.reduce(:+) <= target }

I have also tried this with no luck:

result = array.combination(1).select{|combi| combi.sum <= target}

@array = result

I'm guessing it's something to do with the permutation?

Answer 1

teams = [1,2,3]
drivers = [2,5,4,5,6,4,5,7]
max_driver_sum = 10

I have assumed that drivers can contain duplicate elements (as in my example), but I will explain at the end how the calculations would simplify if there are no duplicates.

---

As a first step let's partition drivers between values that are repeated and those that are not.

counts = drivers.tally
  #=> {2=>1, 5=>3, 4=>2, 6=>1, 7=>1}

dup_drivers, uniq_drivers = counts.partition { |_d,n| n > 1 }
                                  .map { |arr| arr.map(&:first) }​
  #=> [[5, 4], [2, 6, 7]]

Therefore,

dup_drivers
  #=> [5, 4]

uniq_drivers    
  #=> [2, 6, 7]

See Enumerable#tally and Enumerable#partition .

Here,

counts.partition { |_d,n| n > 1 } 
 #=> [[[5, 3], [4, 2]], [[2, 1], [6, 1], [7, 1]]]

---

First compute the unique combinations in which the two drivers are equal:

dup_combos = teams.each_with_object([]) do |t,arr|
  max_driver = (max_driver_sum - t)/2
  dup_drivers.each do |d|
    arr << [[t],[d,d]] if d <= max_driver
  end
end
  #=> [[[1], [4, 4]], [[2], [4, 4]]]

---

Next, compute the unique combinations in which the two drivers are not equal:

all_uniq = uniq_drivers + dup_drivers
  #=> [2, 6, 7, 5, 4]

all_uniq_combos = all_uniq.combination(2).to_a
  #=> [[2, 6], [2, 7], [2, 5], [2, 4], [6, 7], [6, 5],
  #    [6, 4], [7, 5], [7, 4], [5, 4]]

uniq_combos = teams.each_with_object([]) do |t,arr|
  adj_driver_sum = max_driver_sum - t
  all_uniq_combos.each do |combo|
    arr << [[t],combo] if combo.sum <= adj_driver_sum
  end
end
  #=> [[[1], [2, 6]], [[1], [2, 7]], [[1], [2, 5]], [[1], [2, 4]],
  #   [[1], [5, 4]], [[2], [2, 6]], [[2], [2, 5]], [[2], [2, 4]],
  #   [[3], [2, 5]], [[3], [2, 4]]]

SeeArray#combination .

---

The final step is to combine the two groups of combinations:

a1 = dup_combos + uniq_combos
  #=> [[[1], [4, 4]], [[2], [4, 4]], [[1], [2, 6]], [[1], [2, 7]],
  #    [[1], [2, 5]], [[1], [2, 4]], [[1], [5, 4]], [[2], [2, 6]],
  #    [[2], [2, 5]], [[2], [2, 4]], [[3], [2, 5]], [[3], [2, 4]]]

Sorted, this result is as follows.

a1.sort
  #=> [[[1], [2, 4]], [[1], [2, 5]], [[1], [2, 6]], [[1], [2, 7]],
  #    [[1], [4, 4]], [[1], [5, 4]],
  #    [[2], [2, 4]], [[2], [2, 5]], [[2], [2, 6]], [[2], [4, 4]],
  #    [[3], [2, 4]], [[3], [2, 5]]]

Notice that Array#uniq was not used in the foregoing. If desired, one could of course substitute out some of the variables above.

---

If drivers contains no duplicates the desired array is given by uniq_combos where all_uniq is replaced by drivers in the calculation of all_uniq_combos . If, for example,

teams = [1,2,3]
drivers = [2,5,4,6,7]
max_driver_sum = 10

then

all_uniq_combos = drivers.combination(2).to_a
  #=> [[2, 5], [2, 4], [2, 6], [2, 7], [5, 4], [5, 6],
  #    [5, 7], [4, 6], [4, 7], [6, 7]]

combos = teams.each_with_object([]) do |t,arr|
  adj_driver_sum = max_driver_sum - t
  all_uniq_combos.each do |combo|
    arr << [[t],combo] if combo.sum <= adj_driver_sum
  end
end ​
  #=> [[[1], [2, 5]], [[1], [2, 4]], [[1], [2, 6]], [[1], [2, 7]],
  #    [[1], [5, 4]], [[2], [2, 5]], [[2], [2, 4]], [[2], [2, 6]],
  #    [[3], [2, 5]], [[3], [2, 4]]]

combos.sort
  #=> [[[1], [2, 4]], [[1], [2, 5]], [[1], [2, 6]], [[1], [2, 7]],
  #    [[1], [5, 4]],
  #    [[2], [2, 4]], [[2], [2, 5]], [[2], [2, 6]],
  #    [[3], [2, 4]], [[3], [2, 5]]]

Answer 2

Here's an approach

teams = [1, 2, 3]
drivers = [2, 6, 5, 4]
team = teams.permutation(1).to_a
driver = drivers.permutation(2).to_a
array = team.product(driver)

target = 10

res = array.select {|i| i.map(&:sum).sum <= target}.compact
==> [[[1], [2, 6]], [[1], [2, 5]], [[1], [2, 4]], [[1], [6, 2]],
     [[1], [5, 2]], [[1], [5, 4]], [[1], [4, 2]], [[1], [4, 5]],
     [[2], [2, 6]], [[2], [2, 5]], [[2], [2, 4]], [[2], [6, 2]],
     [[2], [5, 2]], [[2], [4, 2]], [[3], [2, 5]], [[3], [2, 4]],
     [[3], [5, 2]], [[3], [4, 2]]]

Getting the unique items (modified to also work for values of teams > drivers)

t1 = res.map {|i| i[0]}
d2 = res.map {|i| i[1].flatten.sort}

t1.zip(d2).uniq
==> [[[1], [2, 6]], [[1], [2, 5]], [[1], [2, 4]], [[1], [4, 5]],
     [[2], [2, 6]], [[2], [2, 5]], [[2], [2, 4]], [[3], [2, 5]],
     [[3], [2, 4]]]