Question

我几乎完成了真实世界Haskell的第3章。最后一次练习阻止了我。我的代码在运行时会崩溃。有谁能告诉我我的代码中哪个部分有问题？感谢。

问题：使用前三个练习中的代码，实现Graham的扫描算法，用于一组2D点的凸包。你可以在维基百科上找到关于凸包的详细描述，以及格雷厄姆扫描算法应该如何工作。

答案：

-- Graham Scan, get the convex hull.
-- Implement the algorithm on http://en.wikipedia.org/wiki/Graham_scan

import Data.List
import Data.Ord

data Direction = TurnLeft | TurnRight | GoStraight deriving (Eq, Show)

-- Determine if three points constitute a "left turn" or "right turn" or "go straight".
-- For three points (x1,y1), (x2,y2) and (x3,y3), simply compute the direction of the cross product of the two vectors defined by points (x1,y1), (x2,y2) and (x1,y1), (x3,y3), characterized by the sign of the expression (x2 − x1)(y3 − y1) − (y2 − y1)(x3 − x1). If the result is 0, the points are collinear; if it is positive, the three points constitute a "left turn", otherwise a "right turn".
direction a b c = case compare ((x2 - x1) * (y3 - y1)) ((y2 - y1) * (x3 - x1)) of
    EQ -> GoStraight
    GT -> TurnLeft
    LT -> TurnRight
    where   x1 = fst a
            y1 = snd a
            x2 = fst b
            y2 = snd b
            x3 = fst c
            y3 = snd c

grahamScan points = scan (sort points)
            -- For each point, it is determined whether moving from the two previously considered points to this point is a "left turn" or a "right turn". If it is a "right turn", this means that the second-to-last point is not part of the convex hull and should be removed from consideration. This process is continued for as long as the set of the last three points is a "right turn". As soon as a "left turn" is encountered, the algorithm moves on to the next point in the sorted array. (If at any stage the three points are collinear, one may opt either to discard or to report it, since in some applications it is required to find all points on the boundary of the convex hull.)
    where   scan (a : (b : (c : points)))
                | (direction a b c) == TurnRight    = scan (a : (c : points))
                | otherwise                         = a : (scan (b : (c : points)))
            scan (a : (b : []))                     = []
            -- Put prime to the head.
            sort points                             = prime : (reverse (sortBy (compareByCosine prime) rest))
                        -- Sort a list to compute. The first step is to find a point whose y-coordinate is lowest. If there are more than one points with lowest y-coordinate, take the one whose x-coordinate is lowest. I name it prime.
                where   compareByYAndX a b
                            | compareByY == EQ  = comparing fst a b
                            | otherwise         = compareByY
                            where   compareByY  = comparing snd a b 
                        prime                   = minimumBy compareByYAndX points
                        -- Delete prime from the candidate points. Sort the rest part by the cosine value of the angle between each vector from prime to each point. Reverse it and put prime to the head.
                        rest                    = delete prime points
                        compareByCosine p a b   = comparing cosine pa pb
                            where   pa          = (fst a - fst p, snd a - snd p)
                                    pb          = (fst b - fst p, snd b - snd p)
                                    cosine v    = x / sqrt (x ^ 2 + y ^ 2)
                                        where   x = fst v
                                                y = snd v

Answer 1

在对已排序的点集进行扫描时，当您完成时，您将丢弃应该在船体中的点。在这一行

scan (a : (b : [])) = []

你要删除船体的最后两个点。真的应该是

scan (a : (b : [])) = [a, b]

甚至更好，

scan ps = ps

仅涵盖一个案例。

我的格雷厄姆扫描功能出了什么问题？

1 个答案: