60 lines
1.6 KiB
Ruby
60 lines
1.6 KiB
Ruby
# 1. Divide n by 12. Remember the remainder (n is 8 for the eight queens
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# puzzle).
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# 2. Write a list of the even numbers from 2 to n in order.
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# 3. If the remainder is 3 or 9, move 2 to the end of the list.
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# 4. Append the odd numbers from 1 to n in order, but, if the remainder is 8,
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# switch pairs (i.e. 3, 1, 7, 5, 11, 9, …).
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# 5. If the remainder is 2, switch the places of 1 and 3, then move 5 to the
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# end of the list.
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# 6. If the remainder is 3 or 9, move 1 and 3 to the end of the list.
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# 7. Place the first-column queen in the row with the first number in the
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# list, place the second-column queen in the row with the second number in
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# the list, etc.
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def n_queens(n)
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if n == 1
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return "Q"
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elsif n < 4
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puts "no solutions for n=#{n}"
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return ""
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end
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evens = (2..n).step(2).to_a
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odds = (1..n).step(2).to_a
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rem = n % 12 # (1)
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nums = evens # (2)
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nums.push(nums.shift) if rem == 3 or rem == 9 # (3)
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# (4)
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if rem == 8
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odds = odds.each_slice(2).inject([]) {|ary, (a,b)| ary += [b,a]}
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end
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nums.concat(odds)
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# (5)
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if rem == 2
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idx = []
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[1,3,5].each {|i| idx[i] = nums.index(i)}
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nums[idx[1]], nums[idx[3]] = nums[idx[3]], nums[idx[1]]
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nums.slice!(idx[5])
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nums.push(5)
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end
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# (6)
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if rem == 3 or rem == 9
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[1,3].each do |i|
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nums.slice!( nums.index(i) )
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nums.push(i)
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end
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end
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# (7)
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board = Array.new(n) {Array.new(n) {"."}}
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n.times {|i| board[i][nums[i] - 1] = "Q"}
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board.inject("") {|str, row| str << row.join(" ") << "\n"}
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end
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(1 .. 15).each {|n| puts "n=#{n}"; puts n_queens(n); puts}
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