tasks a-s

Task/N-queens-problem/Ruby/n-queens-problem.rb

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