Step by Step solution about How to resolve the algorithm Knapsack problem/Continuous step by step in the Ruby programming language

This Ruby code is a simple greedy algorithm that tries to maximize the value of items that can be packed into a knapsack with a given maximum weight. The code defines an array of items, each represented by a tuple of the item's name, its weight, and its price. The array is then sorted in descending order of the ratio of price to weight.

The code then iterates over the items in the sorted array, and for each item, it checks if the remaining capacity in the knapsack is sufficient to hold the item. If it is, the item is added to the knapsack and its value is added to the total value. If the remaining capacity is not sufficient, the amount of the item that can be added to the knapsack is calculated, and the corresponding value is added to the total value.

The code is implemented in a straightforward manner, and the comments provide clear explanations of what the code is doing. The time complexity of the code is O(n log n), where n is the number of items in the array, due to the sorting operation. The space complexity is O(n), due to the array of items.

Overall, the code is a good example of a simple greedy algorithm, and it provides a clear demonstration of how such algorithms can be used to solve optimization problems.

items = [ [:beef   , 3.8, 36],
          [:pork   , 5.4, 43],
          [:ham    , 3.6, 90],
          [:greaves, 2.4, 45],
          [:flitch , 4.0, 30],
          [:brawn  , 2.5, 56],
          [:welt   , 3.7, 67],
          [:salami , 3.0, 95],
          [:sausage, 5.9, 98] ].sort_by{|item, weight, price| -price / weight}
maxW, value = 15.0, 0
items.each do |item, weight, price|
  if (maxW -= weight) > 0
    puts "Take all #{item}"
    value += price
  else
    puts "Take %gkg of %s" % [t=weight+maxW, item], "",
         "Total value of swag is %g" % (value+(price/weight)*t)
    break
  end
end