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| author | sucanjan <sucanjan@fit.cvut.cz> | 2018-02-14 21:57:30 +0100 |
|---|---|---|
| committer | sucanjan <sucanjan@fit.cvut.cz> | 2018-02-14 21:57:30 +0100 |
| commit | 7b34bab6af30df9cfca7df9e0c644a0ea967ff04 (patch) | |
| tree | 8eed65392f403669b5d57f36115366266b2c50db /lib/knapsack_solver/solving_methods/dynamic_programming.rb | |
Initial commit
Diffstat (limited to 'lib/knapsack_solver/solving_methods/dynamic_programming.rb')
| -rw-r--r-- | lib/knapsack_solver/solving_methods/dynamic_programming.rb | 116 |
1 files changed, 116 insertions, 0 deletions
diff --git a/lib/knapsack_solver/solving_methods/dynamic_programming.rb b/lib/knapsack_solver/solving_methods/dynamic_programming.rb new file mode 100644 index 0000000..756a9a6 --- /dev/null +++ b/lib/knapsack_solver/solving_methods/dynamic_programming.rb @@ -0,0 +1,116 @@ +module KnapsackSolver + # This class implements methods for solving 0/1 knapsack problem using + # dynamic programming with decomposition by price. + class DynamicProgramming + # Initializes instance of 0/1 knapsack problem solver based on dynamic + # programming with decomposition by price. + # + # @param instance [Instance] 0/1 knapsack problem instance + def initialize(instance) + @instance = instance + @config = Array.new(instance.things.size) + end + + # Solve the instance of 0/1 knapsack problem. + # + # @return [Hash] resulting price and thing configuration (0 = thing is not in the knapsack, 1 = thing is there) + def run + solve + { price: @best_price, config: @best_config } + end + + protected + + # Solve the instance of 0/1 knapsack problem using dynamic programming. + def solve + # Dynamic programming table + c = all_things_price + 1 # height of array from 0 to max. price + n = @instance.things.size + 1 # width of array, from 0th thing to Nth + # Value used as infinity in the dynamic programming table + @infinity = (all_things_weight + 1).freeze + @weight_array = Array.new(n) { Array.new(c, @infinity) } + @weight_array[0][0] = 0 + fill_table + find_best_price + configuration_vector + end + + # Fill the dynamic programming table. + def fill_table + (1..@instance.things.size).each do |ni| + (0..all_things_price).each do |ci| + @weight_array[ni][ci] = minimum_weight(ni, ci) + end + end + end + + # Find the value of cell in dynamic programming table. + # + # @param ni [Integer] X axis coordinate + # @param ci [Integer] Y axis coordinate + # @return [Integer] + def minimum_weight(ni, ci) + b = weight_of(ni - 1, ci - @instance.things[ni - 1].price) + b += @instance.things[ni - 1].weight + [weight_of(ni - 1, ci), b].min + end + + # Find the best price from the filled dynamic programming table. + def find_best_price + @best_price = @weight_array.last[0] + (1..all_things_price).each do |i| + @best_price = i if @weight_array.last[i] <= @instance.weight_capacity + end + end + + # Reconstructs configuration vector from dynamic programming table. + def configuration_vector + @best_config = [] + ci = @best_price + @instance.things.size.downto(1) do |i| + ci = determine_config_variable(i, ci) + end + end + + # Determine value of one scalar for the configuration vector. + # + # return [Integer] next Y index to the dynamic programming table + def determine_config_variable(i, ci) + if @weight_array[i][ci] == @weight_array[i - 1][ci] + @best_config[i - 1] = 0 + else + @best_config[i - 1] = 1 + ci -= @instance.things[i - 1].price + end + ci + end + + # Gets weight from dynamic programming table. + # + # @param i [Integer] Y index of dynamic programming table + # @param c [Integer] X index of dynamic programming table + # @return [Integer] the value from the array + def weight_of(i, c) + return @infinity if (i < 0) || (c < 0) + @weight_array[i][c] + end + + # Computes total price of all things of the instance. + # + # @return [Integer] total price + def all_things_price + price = 0 + @instance.things.each { |t| price += t.price } + price + end + + # Computes total weight of all things of the instance. + # + # @return [Integer] total weight + def all_things_weight + weight = 0 + @instance.things.each { |t| weight += t.weight } + weight + end + end +end |
