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58 lines
1.8 KiB
Ruby
58 lines
1.8 KiB
Ruby
# dynamic programming version
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def make_change(amount, coins)
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result = Array.new(amount + 1, 0)
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result[0] = 1
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coins.each do |coin|
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(coin..amount).each do |higher_amount|
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remainder = higher_amount - coin
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result[higher_amount] += result[remainder]
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end
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end
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result[amount]
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end
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# recursive version:
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def make_change2(target, coins = [25, 10, 5, 1])
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return [] if target == 0
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return nil if coins.none? { |coin| coin <= target }
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coins = coins.sort.reverse
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best_change = nil
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coins.each_with_index do |coin, index|
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# can't use this coin, it's too big
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next if coin > target
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# use this coin
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remainder = target - coin
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# Find the best way to make change with the remainder (recursive
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# call). Why `coins.drop(index)`? This is an optimization. Because
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# we want to avoid double counting; imagine two ways to make
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# change for 6 cents:
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# (1) first use a nickel, then a penny
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# (2) first use a penny, then a nickel
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# To avoid double counting, we should require that we use *larger
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# coins first*. This is what `coins.drop(index)` enforces; if we
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# use a smaller coin, we can never go back to using larger coins
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# later.
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best_remainder = make_change2(remainder, coins.drop(index))
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# We may not be able to make the remaining amount of change (e.g.,
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# if coins doesn't have a 1cent piece), in which case we shouldn't
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# use this coin.
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next if best_remainder.nil?
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# Otherwise, the best way to make the change **using this coin**,
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# is the best way to make the remainder, plus this one coin.
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this_change = [coin] + best_remainder
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# Is this better than anything we've seen so far?
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best_change = this_changeif best_change.nil? || this_change.count < best_change.count
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end
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best_change
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end
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