例外：Prelude.last：Haskell解决8皇后的空列表？

Question

I'm solving the 8-queens problem in Haskell using only basic functions nothing fancy
this is the code:

queens = [[x1,x2,x3,x4,x5,x6,x7,x8]|x1<-[1..8],x2<-[1..8],x3<-[1..8],x4<-[1..8],x5<-[1..8],x6<-[1..8],x7<-[1..8],x8<-[1..8],safeH [x2,x3,x4,x5,x6,x7,x8] x1,safeD [x2,x3,x4,x5,x6,x7,x8] x1 [x1,x2,x3,x4,x5,x6,x7,x8] 1] 
safeH l e = if elem e l then False 
            else if length (l)/=0 then safeH(tail l)(head l) 
                    else True
safeD l e xs n = if last(xs)/=e || length xs == 0 then
                if length(l)/=0 then 
                    if (head(l)+n==e || head(l)-n==e) then False 
                    else safeD(tail l)(e)(xs)(n+1) 
                else safeD(tail xs)(head xs)(tail xs)(1)
            else True

To clarify the SafeH function checks that no queens are in the same row H stands for Horizantly while the SafeD is supposed to check for diagonal conflicts
I am sure that the SafeH function is okay the problem with SafeD
and when compiling the code it gives me no problems but when calling the queens function
it gives me this error:

[1 of 1] Compiling Main             ( y.hs, interpreted )
Ok, modules loaded: Main.
*Main> queens
*** Exception: Prelude.last: empty list

can anyone please help me?? thanks in advance for every thing :)

Answer 1

You can fix the immediate problem by checking the length of xs before calling last :

safeD l e xs n = if length xs == 0 || last(xs)/=e then ...

However, you will then run into another problem because you call safeD(tail xs)(head xs)(tail xs)(1) inside the then part of this branch, and you can reach the then part of this branch when length xs == 0 .

I strongly recommend learning a little bit about pattern matching ( Gentle Intro section , Haskell Report section ) and trying to write this entire code snippet without ever calling head , tail , init , last , or length . Instead, use the two patterns [] for matching empty lists and (x:xs) (or similar) for matching lists that start as x and end with xs ; if necessary, a call to reverse once in a while would be okay.

Good luck, and let us know how you fare and where you get stuck!

Answer 2

Ever thought of solving this problem for zero queens first?

Then for one queen?

Then spot the inductive / recursive pattern?.. I am not quoting the 3-liner solution, as it looks like your homework.