ggzeng
10/17/2019 - 5:50 AM

puzzel eight queen

8皇后问题

解题思路： 这是一个N*N的棋盘（矩阵），从第1行开始尝试每个列位置是否可行（第1行的任何列位置肯定是可行的），如果有可行的位置则尝试下一行，如果尝试的行数大于N，那么说明已经获得了一个解，这时打印此解，并再逆向往回推看还有没有其它解。如果当前行没有可行的位置则从上一行的下一个位置开始，重复这样的检查逻辑。

puzzel_eight_queen.lua
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N = 8 -- board size

-- check whether position (n,c) is free from attacks
function isplaceok (a, n, c)
  for i = 1, n - 1 do -- for each queen already placed
    if (a[i] == c) or -- same column?
      (a[i] - i == c - n) or -- same diagonal?
      (a[i] + i == c + n) then -- same diagonal?
      return false -- place can be attacked
    end
  end
  return true -- no attacks; place is OK
end

-- print a board
function printsolution (a)
  for i = 1, N do -- for each row
    for j = 1, N do -- and for each column
      -- write "X" or "-" plus a space
      io.write(a[i] == j and "X" or "-", " ")
    end
      io.write("\n")
  end
  io.write("\n")
end

-- add to board 'a' all queens from 'n' to 'N'
function addqueen (a, n)
  if n > N then -- all queens have been placed?
    printsolution(a)  -- 获得一个解
  else -- try to place n-th queen
    for c = 1, N do
      if isplaceok(a, n, c) then
        a[n] = c -- place n-th queen at column 'c'
        addqueen(a, n + 1)
      end
    end
  end
end

-- run the program
-- 从第1行开始直到N
addqueen({}, 1)