Initial implementation of Graham Scan in Nim

Author: berquist

contents/graham_scan/code/nim/.gitignore

@@ -0,0 +1 @@
+graham

contents/graham_scan/code/nim/graham.nim

@@ -0,0 +1,49 @@
+from algorithm import sorted
+from math import arctan2
+from sequtils import deduplicate, map
+import sugar
+
+type Point[T: SomeNumber] = tuple[x, y: T]
+
+proc tup_to_point[T](t: (T, T)): Point[T] =
+  (x: t[0], y: t[1])
+
+proc is_counter_clockwise(p1, p2, p3: Point): bool =
+  (p3.y - p1.y) * (p2.x - p1.x) >= (p2.y - p1.y) * (p3.x - p1.x)
+
+proc polar_angle(reference, point: Point): float =
+  arctan2(float(point.y - reference.y), float(point.x - reference.x))
+
+proc flipped_point_cmp(pa, pb: Point): int =
+  if (pa.y, pa.x) < (pb.y, pb.x): -1
+  elif pa == pb: 0
+  else: 1
+
+proc graham_scan(gift: seq[Point]): seq[Point] =
+  # TODO make sure input has length >= 3
+  let
+    gift_without_duplicates = sorted(deduplicate(gift), flipped_point_cmp)
+    start = gift_without_duplicates[0]
+    candidates = sorted(gift_without_duplicates[1..^1],
+                        proc (pa, pb: Point): int =
+                          if polar_angle(start, pa) < polar_angle(start, pb): -1
+                          else: 1)
+  # TODO take the approach outlined in the text where we perform rotations on
+  # the candidates, rather than add to a new sequence
+  var hull = @[start, candidates[0], candidates[1]]
+  for candidate in candidates:
+    while not is_counter_clockwise(hull[^2], hull[^1], candidate):
+      discard pop(hull)
+    add(hull, candidate)
+  hull
+
+when isMainModule:
+  let
+    test_gift = @[(-5, 2), (5, 7), (-6, -12), (-14, -14), (9, 9),
+                  (-1, -1), (-10, 11), (-6, 15), (-6, -8), (15, -9),
+                  (7, -7), (-2, -9), (6, -5), (0, 14), (2, 8)].map(t => tup_to_point(t))
+    hull = graham_scan(test_gift)
+  echo "Initial gift:"
+  echo test_gift
+  echo "Final hull:"
+  echo hull

contents/graham_scan/graham_scan.md

@@ -28,6 +28,8 @@ We can find whether a rotation is counter-clockwise with trigonometric functions
 [import:27-29, lang:"java"](code/java/GrahamScan.java)
 {% sample lang="cpp" %}
 [import:10-12, lang="cpp"](code/c++/graham_scan.cpp)
+{% sample lang="nim" %}
+[import:14-15, lang:"nim"](code/nim/graham.nim)
 {% endmethod %}
 
 If the output of this function is 0, the points are collinear.
@@ -58,6 +60,8 @@ In the end, the code should look something like this:
 [import:35-70, lang:"java"](code/java/GrahamScan.java)
 {% sample lang="cpp" %}
 [import:14-47, lang="cpp"](code/c++/graham_scan.cpp)
+{% sample lang="nim" %}
+[import, lang:"nim"](code/nim/graham.nim)
 {% endmethod %}
 
 ### Bibliography
@@ -83,6 +87,8 @@ In the end, the code should look something like this:
 [import, lang:"java"](code/java/GrahamScan.java)
 {% sample lang="cpp" %}
 [import, lang="cpp"](code/c++/graham_scan.cpp)
+{% sample lang="nim" %}
+[import, lang:"nim"](code/nim/graham.nim)
 {% endmethod %}
 
 <script>