3D Support
Elias Fleckenstein
parent
b444e278fc
commit
c077ef30fe
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@ -26,7 +26,7 @@ end
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-- (Internal) Returns a unique key for the start and end points.
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local function keyOf(start, goal)
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return string.format("%d,%d>%d,%d", start.x, start.y, goal.x, goal.y)
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return string.format("%d,%d,%d>%d,%d,%d", start.x, start.y, start.z, goal.x, goal.y, goal.z)
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end
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-- (Internal) Returns the cached path for start and end points.
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@ -47,10 +47,11 @@ end
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-- (Internal) Return the distance between two points.
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-- This method doesn't bother getting the square root of s, it is faster
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-- and it still works for our use.
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local function distance(x1, y1, x2, y2)
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local function distance(x1, y1, z1, x2, y2, z2)
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local dx = x1 - x2
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local dy = y1 - y2
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local s = dx * dx + dy * dy
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local dz = z1 - z2
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local s = dx * dx + dy * dy + dz * dz
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return s
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end
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@ -66,7 +67,7 @@ end
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local function calculateScore(previous, node, goal)
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local G = previous.score + 1
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local H = distance(node.x, node.y, goal.x, goal.y)
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local H = distance(node.x, node.y, node.z, goal.x, goal.y, goal.z)
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return G + H, G, H
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end
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@ -74,7 +75,7 @@ end
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-- (Internal) Returns true if the given list contains the specified item.
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local function listContains(list, item)
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for _, test in ipairs(list) do
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if test.x == item.x and test.y == item.y then
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if test.x == item.x and test.y == item.y and test.z == item.z then
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return true
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end
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end
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@ -84,43 +85,39 @@ end
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-- (Internal) Returns the item in the given list.
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local function listItem(list, item)
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for _, test in ipairs(list) do
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if test.x == item.x and test.y == item.y then
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if test.x == item.x and test.y == item.y and test.z == item.z then
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return test
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end
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end
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end
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-- (Internal) Requests adjacent map values around the given node.
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local function getAdjacent(width, height, node, positionIsOpenFunc, includeDiagonals)
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local function getAdjacent(width, height, depth, node, positionIsOpenFunc, includeDiagonals)
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local result = { }
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local positions = {
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{ x = 0, y = -1 }, -- top
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{ x = -1, y = 0 }, -- left
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{ x = 0, y = 1 }, -- bottom
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{ x = 1, y = 0 }, -- right
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}
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local positions = {}
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if includeDiagonals then
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local diagonalMovements = {
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{ x = -1, y = -1 }, -- top left
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{ x = 1, y = -1 }, -- top right
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{ x = -1, y = 1 }, -- bot left
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{ x = 1, y = 1 }, -- bot right
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}
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for x = -1, 1 do
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for y = -1, 1 do
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for z = -1, 1 do
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local a = math.abs(x) + math.abs(y) + math.abs(z)
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for _, value in ipairs(diagonalMovements) do
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table.insert(positions, value)
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end
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if a ~= 0 and includeDiagonals or a == 1 then
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table.insert(positions, {x = x, y = y, z = z})
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end
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end
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end
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end
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for _, point in ipairs(positions) do
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local px = clamp(node.x + point.x, 1, width)
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local py = clamp(node.y + point.y, 1, height)
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local value = positionIsOpenFunc( px, py )
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local pz = clamp(node.z + point.z, 1, depth)
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local value = positionIsOpenFunc( px, py, pz )
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if value then
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table.insert( result, { x = px, y = py } )
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table.insert( result, { x = px, y = py, z = pz } )
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end
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end
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@ -129,7 +126,7 @@ local function getAdjacent(width, height, node, positionIsOpenFunc, includeDiago
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end
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-- Returns the path from start to goal, or false if no path exists.
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function module:find(width, height, start, goal, positionIsOpenFunc, useCache, excludeDiagonalMoving)
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function module:find(width, height, depth, start, goal, positionIsOpenFunc, useCache, excludeDiagonalMoving)
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if useCache then
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local cachedPath = getCached(start, goal)
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@ -144,8 +141,8 @@ function module:find(width, height, start, goal, positionIsOpenFunc, useCache, e
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start.score = 0
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start.G = 0
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start.H = distance(start.x, start.y, goal.x, goal.y)
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start.parent = { x = 0, y = 0 }
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start.H = distance(start.x, start.y, start.z, goal.x, goal.y, goal.z)
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start.parent = { x = 0, y = 0, z = 0 }
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table.insert(open, start)
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while not success and #open > 0 do
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@ -161,7 +158,7 @@ function module:find(width, height, start, goal, positionIsOpenFunc, useCache, e
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if not success then
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local adjacentList = getAdjacent(width, height, current, positionIsOpenFunc, not excludeDiagonalMoving)
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local adjacentList = getAdjacent(width, height, depth, current, positionIsOpenFunc, not excludeDiagonalMoving)
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for _, adjacent in ipairs(adjacentList) do
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@ -193,7 +190,7 @@ function module:find(width, height, start, goal, positionIsOpenFunc, useCache, e
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while node do
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table.insert(path, 1, { x = node.x, y = node.y } )
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table.insert(path, 1, { x = node.x, y = node.y, z = node.z } )
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node = listItem(closed, node.parent)
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end
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@ -2,8 +2,8 @@ describe("Lua star", function()
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-- start is always top left (1,1)
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-- goal is always bottom right (10, 10)
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local start = { x = 1, y = 1 }
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local goal = { x = 10, y = 10 }
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local start = { x = 1, y = 1, z = 1 }
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local goal = { x = 10, y = 10, z = 1 }
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local map = nil
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-- define some test maps (10 x 10)
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@ -22,16 +22,16 @@ describe("Lua star", function()
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]]
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local openmapSolution = {
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{ x = 1, y = 1 },
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{ x = 2, y = 2 },
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{ x = 3, y = 3 },
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{ x = 4, y = 4 },
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{ x = 5, y = 5 },
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{ x = 6, y = 6 },
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{ x = 7, y = 7 },
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{ x = 8, y = 8 },
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{ x = 9, y = 9 },
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{ x = 10, y = 10 },
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{ x = 1, y = 1, z = 1 },
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{ x = 2, y = 2, z = 1 },
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{ x = 3, y = 3, z = 1 },
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{ x = 4, y = 4, z = 1 },
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{ x = 5, y = 5, z = 1 },
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{ x = 6, y = 6, z = 1 },
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{ x = 7, y = 7, z = 1 },
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{ x = 8, y = 8, z = 1 },
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{ x = 9, y = 9, z = 1 },
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{ x = 10, y = 10, z = 1 },
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}
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local simplemap = [[
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@ -48,45 +48,45 @@ describe("Lua star", function()
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]]
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local simplemapSolution = {
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{ x = 1, y = 1 },
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{ x = 2, y = 2 },
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{ x = 3, y = 3 },
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{ x = 4, y = 4 },
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{ x = 4, y = 5 },
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{ x = 3, y = 6 },
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{ x = 2, y = 7 },
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{ x = 1, y = 8 },
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{ x = 2, y = 9 },
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{ x = 3, y = 10 },
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{ x = 4, y = 10 },
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{ x = 5, y = 10 },
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{ x = 6, y = 10 },
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{ x = 7, y = 10 },
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{ x = 8, y = 10 },
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{ x = 9, y = 10 },
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{ x = 10, y = 10 },
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{ x = 1, y = 1, z = 1 },
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{ x = 2, y = 2, z = 1 },
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{ x = 3, y = 3, z = 1 },
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{ x = 4, y = 4, z = 1 },
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{ x = 4, y = 5, z = 1 },
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{ x = 3, y = 6, z = 1 },
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{ x = 2, y = 7, z = 1 },
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{ x = 1, y = 8, z = 1 },
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{ x = 2, y = 9, z = 1 },
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{ x = 3, y = 10, z = 1 },
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{ x = 4, y = 10, z = 1 },
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{ x = 5, y = 10, z = 1 },
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{ x = 6, y = 10, z = 1 },
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{ x = 7, y = 10, z = 1 },
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{ x = 8, y = 10, z = 1 },
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{ x = 9, y = 10, z = 1 },
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{ x = 10, y = 10, z = 1 },
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}
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local simplemapDiagonalSolution = {
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{ x = 1, y = 1 },
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{ x = 1, y = 2 },
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{ x = 1, y = 3 },
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{ x = 1, y = 4 },
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{ x = 1, y = 5 },
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{ x = 1, y = 6 },
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{ x = 1, y = 7 },
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{ x = 1, y = 8 },
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{ x = 1, y = 9 },
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{ x = 2, y = 9 },
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{ x = 3, y = 9 },
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{ x = 4, y = 9 },
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{ x = 5, y = 9 },
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{ x = 6, y = 9 },
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{ x = 7, y = 9 },
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{ x = 8, y = 9 },
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{ x = 9, y = 9 },
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{ x = 9, y = 10 },
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{ x = 10, y = 10 },
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{ x = 1, y = 1, z = 1 },
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{ x = 1, y = 2, z = 1 },
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{ x = 1, y = 3, z = 1 },
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{ x = 1, y = 4, z = 1 },
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{ x = 1, y = 5, z = 1 },
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{ x = 1, y = 6, z = 1 },
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{ x = 1, y = 7, z = 1 },
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{ x = 1, y = 8, z = 1 },
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{ x = 1, y = 9, z = 1 },
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{ x = 2, y = 9, z = 1 },
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{ x = 3, y = 9, z = 1 },
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{ x = 4, y = 9, z = 1 },
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{ x = 5, y = 9, z = 1 },
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{ x = 6, y = 9, z = 1 },
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{ x = 7, y = 9, z = 1 },
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{ x = 8, y = 9, z = 1 },
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{ x = 9, y = 9, z = 1 },
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{ x = 9, y = 10, z = 1 },
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{ x = 10, y = 10, z = 1 },
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}
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local complexmap = [[
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@ -103,44 +103,44 @@ describe("Lua star", function()
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]]
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local complexmapSolution = {
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{ x = 1, y = 1 },
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{ x = 2, y = 1 },
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{ x = 3, y = 1 },
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{ x = 4, y = 1 },
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{ x = 5, y = 1 },
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{ x = 6, y = 1 },
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{ x = 7, y = 1 },
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{ x = 8, y = 1 },
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{ x = 9, y = 1 },
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{ x = 10, y = 2 },
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{ x = 9, y = 3 },
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{ x = 8, y = 3 },
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{ x = 7, y = 3 },
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{ x = 6, y = 3 },
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{ x = 5, y = 3 },
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{ x = 4, y = 3 },
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{ x = 3, y = 3 },
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{ x = 2, y = 3 },
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{ x = 1, y = 4 },
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{ x = 1, y = 5 },
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{ x = 1, y = 6 },
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{ x = 2, y = 7 },
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{ x = 3, y = 6 },
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{ x = 4, y = 5 },
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{ x = 5, y = 6 },
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{ x = 5, y = 7 },
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{ x = 5, y = 8 },
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{ x = 6, y = 9 },
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{ x = 7, y = 9 },
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{ x = 8, y = 8 },
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{ x = 7, y = 7 },
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{ x = 7, y = 6 },
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{ x = 8, y = 5 },
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{ x = 9, y = 6 },
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{ x = 10, y = 7 },
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{ x = 10, y = 8 },
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{ x = 10, y = 9 },
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{ x = 10, y = 10 },
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{ x = 1, y = 1, z = 1 },
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{ x = 2, y = 1, z = 1 },
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{ x = 3, y = 1, z = 1 },
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{ x = 4, y = 1, z = 1 },
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{ x = 5, y = 1, z = 1 },
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{ x = 6, y = 1, z = 1 },
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{ x = 7, y = 1, z = 1 },
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{ x = 8, y = 1, z = 1 },
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{ x = 9, y = 1, z = 1 },
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{ x = 10, y = 2, z = 1 },
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{ x = 9, y = 3, z = 1 },
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{ x = 8, y = 3, z = 1 },
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{ x = 7, y = 3, z = 1 },
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{ x = 6, y = 3, z = 1 },
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{ x = 5, y = 3, z = 1 },
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{ x = 4, y = 3, z = 1 },
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{ x = 3, y = 3, z = 1 },
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{ x = 2, y = 3, z = 1 },
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{ x = 1, y = 4, z = 1 },
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{ x = 1, y = 5, z = 1 },
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{ x = 1, y = 6, z = 1 },
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{ x = 2, y = 7, z = 1 },
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{ x = 3, y = 6, z = 1 },
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{ x = 4, y = 5, z = 1 },
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{ x = 5, y = 6, z = 1 },
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{ x = 5, y = 7, z = 1 },
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{ x = 5, y = 8, z = 1 },
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{ x = 6, y = 9, z = 1 },
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{ x = 7, y = 9, z = 1 },
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{ x = 8, y = 8, z = 1 },
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{ x = 7, y = 7, z = 1 },
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{ x = 7, y = 6, z = 1 },
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{ x = 8, y = 5, z = 1 },
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{ x = 9, y = 6, z = 1 },
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{ x = 10, y = 7, z = 1 },
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{ x = 10, y = 8, z = 1 },
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{ x = 10, y = 9, z = 1 },
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{ x = 10, y = 10, z = 1 },
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}
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local unsolvablemap = [[
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@ -167,8 +167,8 @@ describe("Lua star", function()
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end
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-- get the value at position xy on a map
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local function mapTileIsOpen(x, y)
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return map[ ((y-1) * 10) + x ] == "0"
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local function mapTileIsOpen(x, y, z)
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return z == 1 and map[ ((y-1) * 10) + x ] == "0"
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end
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local function printSolution(path)
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@ -200,7 +200,7 @@ describe("Lua star", function()
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local luastar = require("lua-star")
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makemap(openmap)
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local path = luastar:find(mapsize, mapsize, start, goal, mapTileIsOpen)
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local path = luastar:find(mapsize, mapsize, 1, start, goal, mapTileIsOpen)
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--printSolution(path)
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assert.are.equal(10, #path)
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assert.are.same(openmapSolution, path)
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@ -211,7 +211,7 @@ describe("Lua star", function()
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local luastar = require("lua-star")
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makemap(simplemap)
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local path = luastar:find(mapsize, mapsize, start, goal, mapTileIsOpen)
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local path = luastar:find(mapsize, mapsize, 1, start, goal, mapTileIsOpen)
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--printSolution(path)
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assert.are.equal(17, #path)
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assert.are.same(simplemapSolution, path)
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@ -223,7 +223,7 @@ describe("Lua star", function()
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local luastar = require("lua-star")
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local excludeDiagonals = true
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makemap(simplemap)
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local path = luastar:find(mapsize, mapsize, start, goal, mapTileIsOpen, false, excludeDiagonals)
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local path = luastar:find(mapsize, mapsize, 1, start, goal, mapTileIsOpen, false, excludeDiagonals)
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--printSolution(path)
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assert.are.equal(19, #path)
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assert.are.same(simplemapDiagonalSolution, path)
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@ -234,7 +234,7 @@ describe("Lua star", function()
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local luastar = require("lua-star")
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makemap(complexmap)
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local path = luastar:find(mapsize, mapsize, start, goal, mapTileIsOpen)
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local path = luastar:find(mapsize, mapsize, 1, start, goal, mapTileIsOpen)
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--printSolution(path)
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assert.are.equal(38, #path)
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assert.are.same(complexmapSolution, path)
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@ -245,7 +245,7 @@ describe("Lua star", function()
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local luastar = require("lua-star")
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makemap(unsolvablemap)
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local path = luastar:find(mapsize, mapsize, start, goal, mapTileIsOpen)
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local path = luastar:find(mapsize, mapsize, 1, start, goal, mapTileIsOpen)
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assert.is_false(path)
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end)
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@ -255,7 +255,7 @@ describe("Lua star", function()
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local luastar = require("lua-star")
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local excludeDiagonals = true
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makemap(unsolvablemap)
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local path = luastar:find(mapsize, mapsize, start, goal, mapTileIsOpen, false, excludeDiagonals)
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local path = luastar:find(mapsize, mapsize, 1, start, goal, mapTileIsOpen, false, excludeDiagonals)
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assert.is_false(path)
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end)
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@ -265,7 +265,7 @@ describe("Lua star", function()
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local luastar = require("lua-star")
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local excludeDiagonals = true
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makemap(complexmap)
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local path = luastar:find(mapsize, mapsize, start, goal, mapTileIsOpen, false, excludeDiagonals)
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local path = luastar:find(mapsize, mapsize, 1, start, goal, mapTileIsOpen, false, excludeDiagonals)
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||||
assert.is_false(path)
|
||||
|
||||
end)
|
||||
|
|
@ -274,8 +274,8 @@ describe("Lua star", function()
|
|||
|
||||
local luastar = require("lua-star")
|
||||
makemap(openmap)
|
||||
local path = luastar:find(mapsize, mapsize, start, goal, mapTileIsOpen)
|
||||
local samepath = luastar:find(mapsize, mapsize, start, goal, mapTileIsOpen)
|
||||
local path = luastar:find(mapsize, mapsize, 1, start, goal, mapTileIsOpen)
|
||||
local samepath = luastar:find(mapsize, mapsize, 1, start, goal, mapTileIsOpen)
|
||||
assert.is_not.equal(path, samepath)
|
||||
|
||||
end)
|
||||
|
|
@ -284,8 +284,8 @@ describe("Lua star", function()
|
|||
|
||||
local luastar = require("lua-star")
|
||||
makemap(openmap)
|
||||
local path = luastar:find(mapsize, mapsize, start, goal, mapTileIsOpen, true)
|
||||
local samepath = luastar:find(mapsize, mapsize, start, goal, mapTileIsOpen, true)
|
||||
local path = luastar:find(mapsize, mapsize, 1, start, goal, mapTileIsOpen, true)
|
||||
local samepath = luastar:find(mapsize, mapsize, 1, start, goal, mapTileIsOpen, true)
|
||||
assert.are.equal(path, samepath)
|
||||
|
||||
end)
|
||||
|
|
@ -294,7 +294,7 @@ describe("Lua star", function()
|
|||
|
||||
local luastar = require("lua-star")
|
||||
makemap(openmap)
|
||||
local path = luastar:find(mapsize, mapsize, start, goal, mapTileIsOpen, true)
|
||||
local path = luastar:find(mapsize, mapsize, 1, start, goal, mapTileIsOpen, true)
|
||||
luastar:clearCached()
|
||||
assert.is_nil(luastar.cache)
|
||||
|
||||
|
|
|
|||
|
|
@ -10,39 +10,42 @@
|
|||
|
||||
local luastar = require("lua-star")
|
||||
local map = { }
|
||||
local mapsize = 3000
|
||||
local numberOfTests = 1000
|
||||
local mapDensity = 0.65
|
||||
local mapsize = 20
|
||||
local numberOfTests = 1
|
||||
local mapDensity = 0.1
|
||||
|
||||
local seed = os.time()
|
||||
math.randomseed(seed)
|
||||
print (string.format("Running with seed %d", seed))
|
||||
|
||||
print (string.format("Building a map of %dx%d...", mapsize, mapsize))
|
||||
print (string.format("Building a map of %dx%dx%d...", mapsize, mapsize, mapsize))
|
||||
for x=1, mapsize do
|
||||
map[x] = {}
|
||||
for y=1, mapsize do
|
||||
map[x][y] = math.random()
|
||||
map[x][y] = {}
|
||||
for z=1, mapsize do
|
||||
map[x][y][z] = math.random()
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
-- precalculate a bunch of start and goal positions
|
||||
-- doubled up for each start/goal pair
|
||||
|
||||
print (string.format("Precalculating %d random start/goal positions...", mapsize * 2))
|
||||
print (string.format("Precalculating %d random start/goal positions...", numberOfTests * 2))
|
||||
local testPoints = { }
|
||||
for i = 1, mapsize * 2 do
|
||||
table.insert (testPoints, { x = math.random(1, mapsize), y = math.random(1, mapsize)})
|
||||
for i = 1, numberOfTests * 2 do
|
||||
table.insert (testPoints, { x = math.random(1, mapsize), y = math.random(1, mapsize), z = math.random(1, mapsize)})
|
||||
end
|
||||
|
||||
print (string.format("Finding %d paths...", numberOfTests))
|
||||
function positionIsOpenFunc(x, y)
|
||||
return map[x][y] > mapDensity
|
||||
function positionIsOpenFunc(x, y, z)
|
||||
return map[x][y][z] > mapDensity
|
||||
end
|
||||
local testStart = os.clock()
|
||||
for testNumber = 1, numberOfTests do
|
||||
luastar:find(
|
||||
mapsize, mapsize, -- map size
|
||||
mapsize, mapsize, mapsize, -- map size
|
||||
table.remove (testPoints), -- start
|
||||
table.remove (testPoints), -- goal
|
||||
positionIsOpenFunc)
|
||||
|
|
@ -58,6 +61,6 @@ print (string.format([[
|
|||
totalSec, -- total seconds
|
||||
pathSec, -- seconds per path
|
||||
pathSec*1000, -- milliseconds per path
|
||||
(mapsize*mapsize)/1000000, -- number of locations
|
||||
(mapsize*mapsize*mapsize)/1000000, -- number of locations
|
||||
mapDensity*100 -- % open space on the map
|
||||
))
|
||||
|
|
|
|||
Loading…
Reference in New Issue