Add Grid.lua

learning-lua/algo/Grid-tests.lua

@@ -0,0 +1,42 @@
+local grid = require "algo.Grid"
+
+-- Tests west, north, east, south
+local g = grid:new(10, 10)
+local u = g:node(1, 1)
+assert(not g:west(u))
+assert(not g:north(u))
+assert(g:east(u) == g:node(1, 2))
+assert(g:east(u, 9) == g:node(1, 10))
+assert(not g:east(u, 10))
+assert(g:south(u) == g:node(2, 1))
+assert(g:south(u, 9) == g:node(10, 1))
+assert(not g:south(u, 10))
+
+local u = g:node(10, 10)
+assert(not g:east(u))
+assert(not g:south(u))
+assert(g:west(u) == g:node(10, 9))
+assert(g:west(u, 9) == g:node(10, 1))
+assert(not g:west(u, 10))
+assert(g:north(u) == g:node(9, 10))
+assert(g:north(u, 9) == g:node(1, 10))
+assert(not g:north(u, 10))
+
+-- Negative test with dy or dx is non-positive
+local u = g:node(5, 5)
+for _, f in ipairs {g.west, g.north, g.east, g.south} do
+  assert(pcall(f, g, u, 2))
+  assert(not pcall(f, g, u, 0))
+  assert(not pcall(f, g, u, -1))
+end
+
+-- Test Grid:node() and Grid:coord()
+for y = 1, g.height do
+  for x = 1, g.width do
+    local node = g:node(y, x)
+    local y1, x1 = g:coord(node)
+    assert(x == x1 and y == y1)
+  end
+end
+
+os.exit()

learning-lua/algo/Grid.lua

@@ -0,0 +1,43 @@
+local Grid = require "algo.GridBase"
+
+function Grid:manhattan_dist(u, v)
+  local y1, x1 = self:coord(u)
+  local y2, x2 = self:coord(v)
+  return self:manhattan_dist_coord(y1, x1, y2, x2)
+end
+
+--- Returns a unique node number as a function of the given (y,x) coorindate
+--- within the grid; or nil if (y, x) is outside the grid.
+---@param y (number)
+---@param x (number)
+---@return (number) or nil
+function Grid:node(y, x)
+  if y <= self.height and x <= self.width then
+    return (y << self._intern.wbits) + x
+  end
+end
+
+---Inverse of Grid:node(y, x)
+---@param node (number)
+---@return (number) y, (number) x
+function Grid:coord(node)
+  return node >> self._intern.wbits, node & self._intern.wmask
+end
+
+function Grid:new(width, height)
+  assert(width > 0 and height > 0)
+  local g = {
+    width = width,
+    height = height
+  }
+  local wbits = math.ceil(math.log(width + 1, 2))
+  g._intern = {
+    wbits = wbits,
+    wmask = (1 << wbits) - 1
+  }
+  setmetatable(g, self)
+  self.__index = self
+  return g
+end
+
+return Grid

learning-lua/algo/GridBase.lua

@@ -0,0 +1,65 @@
+local Grid = {}
+
+local function move_y(grid, y, x, dy)
+  local y1 = y + dy
+  if y1 > 0 and y1 <= grid.height then
+    return grid:node(y1, x)
+  end
+end
+
+local function move_x(grid, y, x, dx)
+  local x1 = x + dx
+  if x1 > 0 and x1 <= grid.width then
+    return grid:node(y, x1)
+  end
+end
+
+function Grid:up(y, x, dy)
+  dy = dy or 1
+  assert(dy > 0)
+  return move_y(self, y, x, -dy)
+end
+
+function Grid:north(node, dy)
+  local y, x = self:coord(node)
+  return self:up(y, x, dy)
+end
+
+function Grid:down(y, x, dy)
+  dy = dy or 1
+  assert(dy > 0)
+  return move_y(self, y, x, dy)
+end
+
+function Grid:south(node, dy)
+  local y, x = self:coord(node)
+  return self:down(y, x, dy)
+end
+
+function Grid:left(y, x, dx)
+  dx = dx or 1
+  assert(dx > 0)
+  return move_x(self, y, x, -dx)
+end
+
+function Grid:west(node, dx)
+  local y, x = self:coord(node)
+  return self:left(y, x, dx)
+end
+
+function Grid:right(y, x, dx)
+  dx = dx or 1
+  assert(dx > 0)
+  return move_x(self, y, x, dx)
+end
+
+function Grid:east(node, dx)
+  local y, x = self:coord(node)
+  return self:right(y, x, dx)
+end
+
+function Grid:manhattan_dist_coord(y1, x1, y2, x2)
+  return math.abs(y1 - y2) + math.abs(x1 - x2)
+end
+
+return Grid