八皇后问题解法(Lua版)

I’m learning Lua programming through reading “Programming in Lua”(PIL).
Just show the demo code in the book and add some debug information to show the program how to run.

• 源代码
• 遍历回溯过程

源代码

local N = 8local function printsolution(a)    for i = 1, N do        for j = 1, N do            io.write(a[i] == j and "X" or "-", " ")        end        io.write("\n")    end    print("---------------")endlocal function isplace(a, n, c)    for i = 1, n - 1 do        if (a[i] == c) or            (a[i] == (c + (n - i))) or -- a[i] > c            ((a[i] + (n - i)) == c)  then -- a[i] < c            return false        end    end    return trueendlocal solution_count = 0local function addqueen(a, n)    if n > N then        solution_count = solution_count + 1        ---[[        print("solution_count: ", solution_count)        printsolution(a)        --]]        return    end    for c = 1, N do        if isplace(a, n, c) then            print("[" .. n .. "," .. c .. "]")            a[n] = c            addqueen(a, n+1)        end    end    print("stop at row", n)endaddqueen({}, 1)

遍历回溯过程

Finally, it gets 92 solutions.

>lua -e "io.stdout:setvbuf 'no'" "eight_keen.lua" [1,1][2,3][3,5][4,2][5,4]stop at row 6[5,8]stop at row 6stop at row 5[4,7][5,2][6,4][7,6]stop at row 8stop at row 7stop at row 6[5,4]stop at row 6stop at row 5[4,8][5,2][6,4][7,6]stop at row 8stop at row 7stop at row 6[5,4]stop at row 6stop at row 5stop at row 4[3,6][4,2][5,7][6,5]stop at row 7stop at row 6stop at row 5[4,8][5,2][6,4]stop at row 7[6,5]stop at row 7stop at row 6stop at row 5stop at row 4[3,7][4,2][5,4][6,8]stop at row 7stop at row 6[5,8][6,5]stop at row 7stop at row 6stop at row 5stop at row 4[3,8][4,2][5,4]stop at row 6[5,7]stop at row 6stop at row 5[4,6][5,2]stop at row 6[5,4][6,2][7,5]stop at row 8stop at row 7stop at row 6stop at row 5stop at row 4stop at row 3[2,4][3,2][4,5][5,3]stop at row 6[5,8]stop at row 6stop at row 5[4,7][5,3]stop at row 6stop at row 5[4,8][5,3][6,7]stop at row 7stop at row 6[5,6][6,3]stop at row 7stop at row 6stop at row 5stop at row 4[3,6][4,3]stop at row 5[4,8][5,2][6,5][7,3]stop at row 8stop at row 7[6,7][7,3]stop at row 8stop at row 7stop at row 6[5,3][6,5]stop at row 7[6,7]stop at row 7stop at row 6stop at row 5stop at row 4[3,7][4,3][5,6][6,2][7,5]stop at row 8stop at row 7stop at row 6[5,8][6,2][7,5]stop at row 8stop at row 7stop at row 6stop at row 5[4,5][5,2]stop at row 6[5,3]stop at row 6[5,8][6,2]stop at row 7stop at row 6stop at row 5stop at row 4[3,8][4,3]stop at row 5[4,5][5,2]stop at row 6[5,3]stop at row 6stop at row 5stop at row 4stop at row 3[2,5][3,2][4,6][5,3][6,7][7,4]stop at row 8stop at row 7stop at row 6stop at row 5[4,8][5,3][6,7][7,4]stop at row 8stop at row 7stop at row 6[5,6][6,3]stop at row 7[6,4]stop at row 7stop at row 6stop at row 5stop at row 4[3,7][4,2][5,4][6,8]stop at row 7stop at row 6[5,6][6,3]stop at row 7[6,8]stop at row 7stop at row 6stop at row 5stop at row 4[3,8][4,2][5,4][6,7][7,3]stop at row 8stop at row 7stop at row 6[5,7][6,3][7,6]stop at row 8stop at row 7stop at row 6stop at row 5[4,6][5,3][6,7][7,2][8,4]solution_count:     1X - - - - - - - - - - - X - - - - - - - - - - X - - - - - X - - - - X - - - - - - - - - - - X - - X - - - - - - - - - X - - - - --------------- ..... (中间省略90种解法)---------------stop at row 8stop at row 7stop at row 6stop at row 5[4,7][5,2][6,6]stop at row 7stop at row 6[5,5][6,2][7,6]stop at row 8stop at row 7stop at row 6stop at row 5stop at row 4[3,5][4,2]stop at row 5[4,7][5,1][6,4][7,6]stop at row 8stop at row 7[6,6]stop at row 7stop at row 6[5,2][6,4][7,6]stop at row 8stop at row 7[6,6]stop at row 7stop at row 6stop at row 5stop at row 4[3,7][4,2]stop at row 5[4,4][5,1][6,5]stop at row 7stop at row 6[5,2][6,5]stop at row 7stop at row 6stop at row 5stop at row 4stop at row 3[2,4][3,1][4,3][5,5][6,2]stop at row 7[6,7]stop at row 7stop at row 6[5,6][6,2][7,7][8,5]solution_count:     92- - - - - - - X - - - X - - - - X - - - - - - - - - X - - - - - - - - - - X - - - X - - - - - - - - - - - - X - - - - - X - - - ---------------stop at row 8stop at row 7stop at row 6stop at row 5[4,7][5,2][6,6][7,3]stop at row 8stop at row 7stop at row 6[5,5][6,2][7,6]stop at row 8stop at row 7stop at row 6stop at row 5stop at row 4[3,2][4,7][5,3][6,1]stop at row 7[6,6]stop at row 7stop at row 6[5,5][6,1]stop at row 7stop at row 6stop at row 5stop at row 4[3,7][4,1][5,3][6,5]stop at row 7[6,6]stop at row 7stop at row 6[5,6][6,2][7,5]stop at row 8stop at row 7stop at row 6stop at row 5[4,3][5,6][6,2][7,5]stop at row 8stop at row 7stop at row 6stop at row 5stop at row 4stop at row 3[2,5][3,1][4,4][5,6]stop at row 6[5,7]stop at row 6stop at row 5[4,6]stop at row 5stop at row 4[3,2][4,4][5,1][6,7]stop at row 7stop at row 6[5,6]stop at row 6[5,7]stop at row 6stop at row 5[4,6][5,1][6,7][7,4]stop at row 8stop at row 7stop at row 6[5,3][6,7][7,4]stop at row 8stop at row 7stop at row 6stop at row 5stop at row 4[3,3][4,1][5,6][6,2]stop at row 7[6,4]stop at row 7stop at row 6[5,7][6,2][7,6]stop at row 8stop at row 7[6,4][7,6]stop at row 8stop at row 7stop at row 6stop at row 5[4,6]stop at row 5stop at row 4[3,7][4,1][5,3][6,6]stop at row 7stop at row 6[5,6][6,2]stop at row 7stop at row 6stop at row 5[4,2][5,6]stop at row 6stop at row 5[4,4][5,1]stop at row 6[5,6]stop at row 6stop at row 5stop at row 4stop at row 3[2,6][3,1][4,3][5,5][6,7][7,4]stop at row 8stop at row 7stop at row 6[5,7]stop at row 6stop at row 5[4,7][5,2]stop at row 6[5,5]stop at row 6stop at row 5stop at row 4[3,2][4,7][5,1][6,4]stop at row 7stop at row 6[5,5][6,1]stop at row 7stop at row 6stop at row 5stop at row 4[3,3][4,1][5,7][6,4]stop at row 7[6,5]stop at row 7stop at row 6stop at row 5[4,7][5,2][6,4]stop at row 7stop at row 6stop at row 5stop at row 4[3,4][4,1][5,5]stop at row 6[5,7][6,5][7,3]stop at row 8stop at row 7stop at row 6stop at row 5[4,2][5,5]stop at row 6[5,7][6,5][7,3]stop at row 8stop at row 7stop at row 6stop at row 5[4,7][5,1]stop at row 6[5,5]stop at row 6stop at row 5stop at row 4stop at row 3stop at row 2stop at row 1>Exit code: 0