Data commit

Task/Cut-a-rectangle/Nim/cut-a-rectangle.nim

@@ -0,0 +1,76 @@
+import strformat
+
+var
+  w, h: int
+  grid: seq[byte]
+  next: array[4, int]
+  count: int
+
+const Dirs = [[0, -1], [-1, 0], [0, 1], [1, 0]]
+
+template odd(n: int): bool = (n and 1) != 0
+
+#------------------------------------------------------------------------------
+
+proc walk(y, x: int) =
+
+  if y == 0 or y == h or x == 0 or x == w:
+    inc count, 2
+    return
+
+  let t = y * (w + 1) + x
+  inc grid[t]
+  inc grid[grid.high - t]
+
+  for i, dir in Dirs:
+    if grid[t + next[i]] == 0:
+      walk(y + dir[0], x + dir[1])
+
+  dec grid[t]
+  dec grid[grid.high - t]
+
+#------------------------------------------------------------------------------
+
+proc solve(y, x: int; recursive: bool): int =
+
+  h = y
+  w = x
+  if odd(h): swap w, h
+
+  if odd(h): return 0
+  if w == 1: return 1
+  if w == 2: return h
+  if h == 2: return w
+
+  let cy = h div 2
+  let cx = w div 2
+
+  grid = newSeq[byte]((w + 1) * (h + 1))
+
+  next[0] = -1
+  next[1] = -w - 1
+  next[2] = 1
+  next[3] = w + 1
+
+  if recursive: count = 0
+
+  for x in (cx + 1)..<w:
+    let t = cy * (w + 1) + x
+    grid[t] = 1
+    grid[grid.high - t] = 1
+    walk(cy - 1, x)
+  inc count
+
+  if h == w:
+    count *= 2
+  elif not odd(w) and recursive:
+    discard solve(w, h, false)
+
+  result = count
+
+#——————————————————————————————————————————————————————————————————————————————
+
+for y in 1..10:
+  for x in 1..y:
+    if not odd(x) or not odd(y):
+      echo &"{y:2d} x {x:2d}: {solve(y, x, true)}"