September Morn Update
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Ingy döt Net
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6856 changed files with 141342 additions and 21127 deletions
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require "bit_array"
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struct BitArray
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def clone
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BitArray.new(size).tap { |new| new.to_slice.copy_from (to_slice) }
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end
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end
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record Item, name : String, weight : Int32, value : Int32
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record Selection, mask : BitArray, cur_index : Int32, total_value : Int32
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class Knapsack
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@threshold_value = 0
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@threshold_choice : Selection?
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getter checked_nodes = 0
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def knapsack_step(taken, items, remaining_weight)
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if taken.total_value > @threshold_value
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@threshold_value = taken.total_value
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@threshold_choice = taken
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end
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candidate_index = items.index(taken.cur_index) { |item| item.weight <= remaining_weight }
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return nil unless candidate_index
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@checked_nodes += 1
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candidate = items[candidate_index]
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# candidate is a best of available items, so if we fill remaining value with it
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# and still don't reach the threshold, the branch is wrong
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return nil if taken.total_value + 1.0 * candidate.value / candidate.weight * remaining_weight < @threshold_value
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# now recursively check both variants
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mask = taken.mask.clone
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mask[candidate_index] = true
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knapsack_step Selection.new(mask, candidate_index + 1, taken.total_value + candidate.value), items, remaining_weight - candidate.weight
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mask = taken.mask.clone
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mask[candidate_index] = false
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knapsack_step Selection.new(mask, candidate_index + 1, taken.total_value), items, remaining_weight
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end
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def select(items, max_weight)
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@checked_variants = 0
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# sort by descending relative value
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list = items.sort_by { |item| -1.0 * item.value / item.weight }
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# use heuristic of relative value as an initial estimate for branch&bounds
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w = max_weight
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heur_list = list.take_while { |item| w -= item.weight; w > 0 }
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nothing = Selection.new(BitArray.new(items.size), 0, 0)
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@threshold_value = heur_list.sum(&.value) - 1
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@threshold_choice = nothing
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knapsack_step(nothing, list, max_weight)
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selected = @threshold_choice.not_nil!
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result = [] of Item
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selected.mask.each_with_index { |v, i| result << list[i] if v }
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result
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end
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end
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possible = [
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Item.new("map", 9, 150),
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Item.new("compass", 13, 35),
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Item.new("water", 153, 200),
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Item.new("sandwich", 50, 160),
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Item.new("glucose", 15, 60),
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Item.new("tin", 68, 45),
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Item.new("banana", 27, 60),
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Item.new("apple", 39, 40),
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Item.new("cheese", 23, 30),
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Item.new("beer", 52, 10),
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Item.new("suntan cream", 11, 70),
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Item.new("camera", 32, 30),
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Item.new("T-shirt", 24, 15),
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Item.new("trousers", 48, 10),
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Item.new("umbrella", 73, 40),
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Item.new("waterproof trousers", 42, 70),
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Item.new("waterproof overclothes", 43, 75),
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Item.new("note-case", 22, 80),
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Item.new("sunglasses", 7, 20),
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Item.new("towel", 18, 12),
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Item.new("socks", 4, 50),
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Item.new("book", 30, 10),
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]
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solver = Knapsack.new
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used = solver.select(possible, 400)
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puts "optimal choice: #{used.map(&.name)}"
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puts "total weight #{used.sum(&.weight)}, total value #{used.sum(&.value)}"
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puts "checked nodes: #{solver.checked_nodes}"
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57
Task/Knapsack-problem-0-1/Perl-6/knapsack-problem-0-1-2.pl6
Normal file
57
Task/Knapsack-problem-0-1/Perl-6/knapsack-problem-0-1-2.pl6
Normal file
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my $raw = qq:to/TABLE/;
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map 9 150
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compass 13 35
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water 153 200
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sandwich 50 160
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glucose 15 60
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tin 68 45
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banana 27 60
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apple 39 40
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cheese 23 30
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beer 52 10
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suntancream 11 70
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camera 32 30
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T-shirt 24 15
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trousers 48 10
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umbrella 73 40
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waterproof trousers 42 70
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waterproof overclothes 43 75
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note-case 22 80
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sunglasses 7 20
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towel 18 12
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socks 4 50
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book 30 10
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TABLE
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my (@name, @weight, @value);
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for split(["\n", /\t+/], $raw, :skip-empty) -> $n,$w,$v {
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@name.push: $n;
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@weight.push: $w;
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@value.push: $v;
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}
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my $max_weight = 400;
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my @p = [Nil xx $max_weight+2 ] xx @name;
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sub optimal ($i, $w) {
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return [0, []] if $i < 0;
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return |@p[$i][$w] if @p[$i][$w];
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if @weight[$i] > $w {
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@p[$i][$w] = optimal($i-1, $w);
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} else {
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my @x = optimal($i-1, $w);
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my @y = optimal($i-1, $w - @weight[$i]);
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if (@x[0] > @y[0] + @value[$i] ) {
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@p[$i][$w] = @x;
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} else {
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@p[$i][$w] = @y[0] + @value[$i], [|@y[1], @name[$i]];
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}
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}
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return |@p[$i][$w]
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}
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my @solution = optimal(-1+@name, $max_weight);
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say "@solution[0]: " ~ join ' ', @solution[1];
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@ -25,41 +25,35 @@ TABLE
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my (@name, @weight, @value);
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for (split "\n", $raw) {
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for ([ split /\t+/ ]) {
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push @name, $_->[0];
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push @weight, $_->[1];
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push @value, $_->[2];
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}
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for ([ split /\t+/ ]) {
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push @name, $_->[0];
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push @weight, $_->[1];
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push @value, $_->[2];
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}
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}
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my $max_weight = 400;
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my @p = (map([[0, []], map undef, 0 .. $max_weight], 0 .. $#name),
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[ map([0, []], 0 .. $max_weight + 1)]);
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my @p = map [map undef, 0 .. 1+$max_weight], 0 .. $#name;
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sub optimal {
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my ($i, $w) = @_;
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my ($i, $w) = @_;
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return [0, []] if $i < 0;
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return $p[$i][$w] if $p[$i][$w];
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if (!defined $p[$i][$w]) {
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if ($weight[$i] > $w) {
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$p[$i][$w] = optimal($i - 1, $w)
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} else {
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my $x = optimal($i - 1, $w);
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my $y = optimal($i - 1, $w - $weight[$i]);
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if ($weight[$i] > $w) {
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$p[$i][$w] = optimal($i - 1, $w)
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} else {
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my $x = optimal($i - 1, $w);
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my $y = optimal($i - 1, $w - $weight[$i]);
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if ($x->[0] > $y->[0] + $value[$i]) {
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$p[$i][$w] = $x
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} else {
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$p[$i][$w] = [ $y->[0] + $value[$i],
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[ @{$y->[1]}, $name[$i] ]]
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}
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}
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if ($x->[0] > $y->[0] + $value[$i]) {
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$p[$i][$w] = $x
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} else {
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$p[$i][$w] = [ $y->[0] + $value[$i], [ @{$y->[1]}, $name[$i] ]]
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}
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return $p[$i][$w]
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}
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return $p[$i][$w]
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}
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my $sol = optimal($#name, $max_weight);
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print "$sol->[0]: @{$sol->[1]}\n";
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# prints:
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# 1030: map compass water sandwich glucose banana suntancream waterproof trousers
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# waterproof overclothes note-case sunglasses socks
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my $solution = optimal($#name, $max_weight);
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print "$solution->[0]: @{$solution->[1]}\n";
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60
Task/Knapsack-problem-0-1/Swift/knapsack-problem-0-1.swift
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60
Task/Knapsack-problem-0-1/Swift/knapsack-problem-0-1.swift
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struct KnapsackItem {
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var name: String
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var weight: Int
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var value: Int
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}
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func knapsack(items: [KnapsackItem], limit: Int) -> [KnapsackItem] {
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var table = Array(repeating: Array(repeating: 0, count: limit + 1), count: items.count + 1)
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for j in 1..<items.count+1 {
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let item = items[j-1]
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for w in 1..<limit+1 {
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if item.weight > w {
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table[j][w] = table[j-1][w]
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} else {
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table[j][w] = max(table[j-1][w], table[j-1][w-item.weight] + item.value)
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}
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}
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}
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var result = [KnapsackItem]()
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var w = limit
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for j in stride(from: items.count, to: 0, by: -1) where table[j][w] != table[j-1][w] {
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let item = items[j-1]
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result.append(item)
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w -= item.weight
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}
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return result
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}
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let items = [
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KnapsackItem(name: "map", weight: 9, value: 150), KnapsackItem(name: "compass", weight: 13, value: 35),
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KnapsackItem(name: "water", weight: 153, value: 200), KnapsackItem(name: "sandwich", weight: 50, value: 160),
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KnapsackItem(name: "glucose", weight: 15, value: 60), KnapsackItem(name: "tin", weight: 68, value: 45),
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KnapsackItem(name: "banana", weight: 27, value: 60), KnapsackItem(name: "apple", weight: 39, value: 40),
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KnapsackItem(name: "cheese", weight: 23, value: 30), KnapsackItem(name: "beer", weight: 52, value: 10),
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KnapsackItem(name: "suntan cream", weight: 11, value: 70), KnapsackItem(name: "camera", weight: 32, value: 30),
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KnapsackItem(name: "t-shirt", weight: 24, value: 15), KnapsackItem(name: "trousers", weight: 48, value: 10),
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KnapsackItem(name: "umbrella", weight: 73, value: 40), KnapsackItem(name: "waterproof trousers", weight: 42, value: 70),
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KnapsackItem(name: "waterproof overclothes", weight: 43, value: 75), KnapsackItem(name: "note-case", weight: 22, value: 80),
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KnapsackItem(name: "sunglasses", weight: 7, value: 20), KnapsackItem(name: "towel", weight: 18, value: 12),
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KnapsackItem(name: "socks", weight: 4, value: 50), KnapsackItem(name: "book", weight: 30, value: 10)
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]
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let kept = knapsack(items: items, limit: 400)
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print("Kept: ")
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for item in kept {
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print(" \(item.name)")
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}
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let (tValue, tWeight) = kept.reduce((0, 0), { ($0.0 + $1.value, $0.1 + $1.weight) })
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print("For a total value of \(tValue) and a total weight of \(tWeight)")
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