How do I represent a hextile/hex grid in memory?

Question

Say I\'m building a board game with a hextile grid, like Settlers of Catan:

Note that

Answer 1

We implemented a Settlers of Catan AI for a class project, and modified code from this answer (which was buggy) to create a Board with constant time random access to vertices and edges. It was a fun problem, but the board took a lot of time, so in case anyone is still looking for a simple implementation here is our Python code:

class Board:
  # Layout is just a double list of Tiles, some will be None
  def __init__(self, layout=None):
    self.numRows = len(layout)
    self.numCols = len(layout[0])
    self.hexagons = [[None for x in xrange(self.numCols)] for x in xrange(self.numRows)] 
    self.edges = [[None for x in xrange(self.numCols*2+2)] for x in xrange(self.numRows*2+2)] 
    self.vertices = [[None for x in xrange(self.numCols*2+2)] for x in xrange(self.numRows*2+2)] 
    for row in self.hexagons:
      for hexagon in row:
        if hexagon == None: continue
        edgeLocations = self.getEdgeLocations(hexagon)
        vertexLocations = self.getVertexLocations(hexagon)
        for xLoc,yLoc in edgeLocations:
          if self.edges[xLoc][yLoc] == None:
            self.edges[xLoc][yLoc] = Edge(xLoc,yLoc)
        for xLoc,yLoc in vertexLocations:
          if self.vertices[xLoc][yLoc] == None:
            self.vertices[xLoc][yLoc] = Vertex(xLoc,yLoc)

  def getNeighborHexes(self, hex):
    neighbors = []
    x = hex.X
    y = hex.Y
    offset = 1
    if x % 2 != 0:
      offset = -1

    if (y+1) < len(self.hexagons[x]):
      hexOne = self.hexagons[x][y+1]
      if hexOne != None: neighbors.append(hexOne)
    if y > 0:
      hexTwo = self.hexagons[x][y-1]
      if hexTwo != None: neighbors.append(hexTwo)
    if (x+1) < len(self.hexagons):
      hexThree = self.hexagons[x+1][y]
      if hexThree != None: neighbors.append(hexThree)
    if x > 0:
      hexFour = self.hexagons[x-1][y]
      if hexFour != None: neighbors.append(hexFour)
    if (y+offset) >= 0 and (y+offset) < len(self.hexagons[x]):
      if (x+1) < len(self.hexagons):
        hexFive = self.hexagons[x+1][y+offset]
        if hexFive != None: neighbors.append(hexFive)
      if x > 0:
        hexSix = self.hexagons[x-1][y+offset]
        if hexSix != None: neighbors.append(hexSix)
    return neighbors

  def getNeighborVertices(self, vertex):
    neighbors = []
    x = vertex.X
    y = vertex.Y
    offset = -1
    if x % 2 == y % 2: offset = 1
    # Logic from thinking that this is saying getEdgesOfVertex
    # and then for each edge getVertexEnds, taking out the three that are ==vertex
    if (y+1) < len(self.vertices[0]):
      vertexOne = self.vertices[x][y+1]
      if vertexOne != None: neighbors.append(vertexOne)
    if y > 0:
      vertexTwo = self.vertices[x][y-1]
      if vertexTwo != None: neighbors.append(vertexTwo)
    if (x+offset) >= 0 and (x+offset) < len(self.vertices):
      vertexThree = self.vertices[x+offset][y]
      if vertexThree != None: neighbors.append(vertexThree)
    return neighbors

  # used to initially create vertices
  def getVertexLocations(self, hex):
    vertexLocations = []
    x = hex.X
    y = hex.Y
    offset = x % 2
    offset = 0-offset
    vertexLocations.append((x, 2*y+offset))
    vertexLocations.append((x, 2*y+1+offset))
    vertexLocations.append((x, 2*y+2+offset))
    vertexLocations.append((x+1, 2*y+offset))
    vertexLocations.append((x+1, 2*y+1+offset))
    vertexLocations.append((x+1, 2*y+2+offset))
    return vertexLocations

  # used to initially create edges
  def getEdgeLocations(self, hex):
    edgeLocations = []
    x = hex.X
    y = hex.Y
    offset = x % 2
    offset = 0-offset
    edgeLocations.append((2*x,2*y+offset))
    edgeLocations.append((2*x,2*y+1+offset))
    edgeLocations.append((2*x+1,2*y+offset))
    edgeLocations.append((2*x+1,2*y+2+offset))
    edgeLocations.append((2*x+2,2*y+offset))
    edgeLocations.append((2*x+2,2*y+1+offset))
    return edgeLocations

  def getVertices(self, hex):
    hexVertices = []
    x = hex.X
    y = hex.Y
    offset = x % 2
    offset = 0-offset
    hexVertices.append(self.vertices[x][2*y+offset]) # top vertex
    hexVertices.append(self.vertices[x][2*y+1+offset]) # left top vertex
    hexVertices.append(self.vertices[x][2*y+2+offset]) # left bottom vertex
    hexVertices.append(self.vertices[x+1][2*y+offset]) # right top vertex
    hexVertices.append(self.vertices[x+1][2*y+1+offset]) # right bottom vertex
    hexVertices.append(self.vertices[x+1][2*y+2+offset]) # bottom vertex
    return hexVertices

  def getEdges(self, hex):
    hexEdges = []
    x = hex.X
    y = hex.Y
    offset = x % 2
    offset = 0-offset
    hexEdges.append(self.edges[2*x][2*y+offset])
    hexEdges.append(self.edges[2*x][2*y+1+offset])
    hexEdges.append(self.edges[2*x+1][2*y+offset])
    hexEdges.append(self.edges[2*x+1][2*y+2+offset])
    hexEdges.append(self.edges[2*x+2][2*y+offset])
    hexEdges.append(self.edges[2*x+2][2*y+1+offset])
    return hexEdges

  # returns (start, end) tuple
  def getVertexEnds(self, edge):
    x = edge.X
    y = edge.Y
    vertexOne = self.vertices[(x-1)/2][y]
    vertexTwo = self.vertices[(x+1)/2][y]
    if x%2 == 0:
      vertexOne = self.vertices[x/2][y]
      vertexTwo = self.vertices[x/2][y+1]
    return (vertexOne, vertexTwo)

  def getEdgesOfVertex(self, vertex):
    vertexEdges = []
    x = vertex.X
    y = vertex.Y
    offset = -1
    if x % 2 == y % 2: offset = 1
    edgeOne = self.edges[x*2][y-1]
    edgeTwo = self.edges[x*2][y]
    edgeThree = self.edges[x*2+offset][y]
    if edgeOne != None: vertexEdges.append(edgeOne)
    if edgeTwo != None: vertexEdges.append(edgeTwo)
    if edgeThree != None: vertexEdges.append(edgeThree)
    return vertexEdges

  def getHexes(self, vertex):
    vertexHexes = []
    x = vertex.X
    y = vertex.Y
    xOffset = x % 2
    yOffset = y % 2

    if x < len(self.hexagons) and y/2 < len(self.hexagons[x]):
      hexOne = self.hexagons[x][y/2]
      if hexOne != None: vertexHexes.append(hexOne)

    weirdX = x
    if (xOffset+yOffset) == 1: weirdX = x-1
    weirdY = y/2 
    if yOffset == 1: weirdY += 1
    else: weirdY -= 1
    if weirdX >= 0 and weirdX < len(self.hexagons) and weirdY >= 0 and weirdY < len(self.hexagons):
      hexTwo = self.hexagons[weirdX][weirdY]
      if hexTwo != None: vertexHexes.append(hexTwo)

    if x > 0 and x < len(self.hexagons) and y/2 < len(self.hexagons[x]):
      hexThree = self.hexagons[x-1][y/2]
      if hexThree != None: vertexHexes.append(hexThree)

    return vertexHexes