Notes

// javascript-astar 0.4.1
// http://github.com/bgrins/javascript-astar
// Freely distributable under the MIT License.
// Implements the astar search algorithm in javascript using a Binary Heap.
// Includes Binary Heap (with modifications) from Marijn Haverbeke.
// http://eloquentjavascript.net/appendix2.html
(function(definition) {
/* global module, define */
if (typeof module === 'object' && typeof module.exports === 'object') {
module.exports = definition();
} else if (typeof define === 'function' && define.amd) {
define([], definition);
} else {
var exports = definition();
window.astar = exports.astar;
window.Graph = exports.Graph;
}
})(function() {

function pathTo(node) {
var curr = node;
var path = [];
while (curr.parent) {
path.unshift(curr);
curr = curr.parent;
}
return path;
}

function getHeap() {
return new BinaryHeap(function(node) {
return node.f;
});
}

var astar = {
/**
* Perform an A* Search on a graph given a start and end node.
* @param {Graph} graph
* @param {GridNode} start
* @param {GridNode} end
* @param {Object} [options]
* @param {bool} [options.closest] Specifies whether to return the
path to the closest node if the target is unreachable.
* @param {Function} [options.heuristic] Heuristic function (see
* astar.heuristics).
*/
search: function(graph, start, end, options) {
graph.cleanDirty();
options = options || {};
var heuristic = options.heuristic || astar.heuristics.manhattan;
var closest = options.closest || false;

var openHeap = getHeap();
var closestNode = start; // set the start node to be the closest if required

start.h = heuristic(start, end);
graph.markDirty(start);

openHeap.push(start);

while (openHeap.size() > 0) {

// Grab the lowest f(x) to process next. Heap keeps this sorted for us.
var currentNode = openHeap.pop();

// End case -- result has been found, return the traced path.
if (currentNode === end) {
return pathTo(currentNode);
}

// Normal case -- move currentNode from open to closed, process each of its neighbors.
currentNode.closed = true;

// Find all neighbors for the current node.
var neighbors = graph.neighbors(currentNode);

for (var i = 0, il = neighbors.length; i < il; ++i) {
var neighbor = neighbors[i];

if (neighbor.closed || neighbor.isWall()) {
// Not a valid node to process, skip to next neighbor.
continue;
}

// The g score is the shortest distance from start to current node.
// We need to check if the path we have arrived at this neighbor is the shortest one we have seen yet.
var gScore = currentNode.g + neighbor.getCost(currentNode);
var beenVisited = neighbor.visited;

if (!beenVisited || gScore < neighbor.g) {

// Found an optimal (so far) path to this node. Take score for node to see how good it is.
neighbor.visited = true;
neighbor.parent = currentNode;
neighbor.h = neighbor.h || heuristic(neighbor, end);
neighbor.g = gScore;
neighbor.f = neighbor.g + neighbor.h;
graph.markDirty(neighbor);
if (closest) {
// If the neighbour is closer than the current closestNode or if it's equally close but has
// a cheaper path than the current closest node then it becomes the closest node
if (neighbor.h < closestNode.h || (neighbor.h === closestNode.h && neighbor.g < closestNode.g)) {
closestNode = neighbor;
}
}

if (!beenVisited) {
// Pushing to heap will put it in proper place based on the 'f' value.
openHeap.push(neighbor);
} else {
// Already seen the node, but since it has been rescored we need to reorder it in the heap
openHeap.rescoreElement(neighbor);
}
}
}
}

if (closest) {
return pathTo(closestNode);
}

// No result was found - empty array signifies failure to find path.
return [];
},
// See list of heuristics: http://theory.stanford.edu/~amitp/GameProgramming/Heuristics.html
heuristics: {
manhattan: function(pos0, pos1) {
var d1 = Math.abs(pos1.x - pos0.x);
var d2 = Math.abs(pos1.y - pos0.y);
return d1 + d2;
},
diagonal: function(pos0, pos1) {
var D = 1;
var D2 = Math.sqrt(2);
var d1 = Math.abs(pos1.x - pos0.x);
var d2 = Math.abs(pos1.y - pos0.y);
return (D * (d1 + d2)) + ((D2 - (2 * D)) * Math.min(d1, d2));
}
},
cleanNode: function(node) {
node.f = 0;
node.g = 0;
node.h = 0;
node.visited = false;
node.closed = false;
node.parent = null;
}
};

/**
* A graph memory structure
* @param {Array} gridIn 2D array of input weights
* @param {Object} [options]
* @param {bool} [options.diagonal] Specifies whether diagonal moves are allowed
*/
function Graph(gridIn, options) {
options = options || {};
this.nodes = [];
this.diagonal = !!options.diagonal;
this.grid = [];
for (var x = 0; x < gridIn.length; x++) {
this.grid[x] = [];

for (var y = 0, row = gridIn[x]; y < row.length; y++) {
var node = new GridNode(x, y, row[y]);
this.grid[x][y] = node;
this.nodes.push(node);
}
}
this.init();
}

Graph.prototype.init = function() {
this.dirtyNodes = [];
for (var i = 0; i < this.nodes.length; i++) {
astar.cleanNode(this.nodes[i]);
}
};

Graph.prototype.cleanDirty = function() {
for (var i = 0; i < this.dirtyNodes.length; i++) {
astar.cleanNode(this.dirtyNodes[i]);
}
this.dirtyNodes = [];
};

Graph.prototype.markDirty = function(node) {
this.dirtyNodes.push(node);
};

Graph.prototype.neighbors = function(node) {
var ret = [];
var x = node.x;
var y = node.y;
var grid = this.grid;

// West
if (grid[x - 1] && grid[x - 1][y]) {
ret.push(grid[x - 1][y]);
}

// East
if (grid[x + 1] && grid[x + 1][y]) {
ret.push(grid[x + 1][y]);
}

// South
if (grid[x] && grid[x][y - 1]) {
ret.push(grid[x][y - 1]);
}

// North
if (grid[x] && grid[x][y + 1]) {
ret.push(grid[x][y + 1]);
}

if (this.diagonal) {
// Southwest
if (grid[x - 1] && grid[x - 1][y - 1]) {
ret.push(grid[x - 1][y - 1]);
}

// Southeast
if (grid[x + 1] && grid[x + 1][y - 1]) {
ret.push(grid[x + 1][y - 1]);
}

// Northwest
if (grid[x - 1] && grid[x - 1][y + 1]) {
ret.push(grid[x - 1][y + 1]);
}

// Northeast
if (grid[x + 1] && grid[x + 1][y + 1]) {
ret.push(grid[x + 1][y + 1]);
}
}

return ret;
};

Graph.prototype.toString = function() {
var graphString = [];
var nodes = this.grid;
for (var x = 0; x < nodes.length; x++) {
var rowDebug = [];
var row = nodes[x];
for (var y = 0; y < row.length; y++) {
rowDebug.push(row[y].weight);
}
graphString.push(rowDebug.join(" "));
}
return graphString.join("n");
};

function GridNode(x, y, weight) {
this.x = x;
this.y = y;
this.weight = weight;
}

GridNode.prototype.toString = function() {
return "[" + this.x + " " + this.y + "]";
};

GridNode.prototype.getCost = function(fromNeighbor) {
// Take diagonal weight into consideration.
if (fromNeighbor && fromNeighbor.x != this.x && fromNeighbor.y != this.y) {
return this.weight * 1.41421;
}
return this.weight;
};

GridNode.prototype.isWall = function() {
return this.weight === 0;
};

function BinaryHeap(scoreFunction) {
this.content = [];
this.scoreFunction = scoreFunction;
}

BinaryHeap.prototype = {
push: function(element) {
// Add the new element to the end of the array.
this.content.push(element);

// Allow it to sink down.
this.sinkDown(this.content.length - 1);
},
pop: function() {
// Store the first element so we can return it later.
var result = this.content[0];
// Get the element at the end of the array.
var end = this.content.pop();
// If there are any elements left, put the end element at the
// start, and let it bubble up.
if (this.content.length > 0) {
this.content[0] = end;
this.bubbleUp(0);
}
return result;
},
remove: function(node) {
var i = this.content.indexOf(node);

// When it is found, the process seen in 'pop' is repeated
// to fill up the hole.
var end = this.content.pop();

if (i !== this.content.length - 1) {
this.content[i] = end;

if (this.scoreFunction(end) < this.scoreFunction(node)) {
this.sinkDown(i);
} else {
this.bubbleUp(i);
}
}
},
size: function() {
return this.content.length;
},
rescoreElement: function(node) {
this.sinkDown(this.content.indexOf(node));
},
sinkDown: function(n) {
// Fetch the element that has to be sunk.
var element = this.content[n];

// When at 0, an element can not sink any further.
while (n > 0) {

// Compute the parent element's index, and fetch it.
var parentN = ((n + 1) >> 1) - 1;
var parent = this.content[parentN];
// Swap the elements if the parent is greater.
if (this.scoreFunction(element) < this.scoreFunction(parent)) {
this.content[parentN] = element;
this.content[n] = parent;
// Update 'n' to continue at the new position.
n = parentN;
}
// Found a parent that is less, no need to sink any further.
else {
break;
}
}
},
bubbleUp: function(n) {
// Look up the target element and its score.
var length = this.content.length;
var element = this.content[n];
var elemScore = this.scoreFunction(element);

while (true) {
// Compute the indices of the child elements.
var child2N = (n + 1) << 1;
var child1N = child2N - 1;
// This is used to store the new position of the element, if any.
var swap = null;
var child1Score;
// If the first child exists (is inside the array)...
if (child1N < length) {
// Look it up and compute its score.
var child1 = this.content[child1N];
child1Score = this.scoreFunction(child1);

// If the score is less than our element's, we need to swap.
if (child1Score < elemScore) {
swap = child1N;
}
}

// Do the same checks for the other child.
if (child2N < length) {
var child2 = this.content[child2N];
var child2Score = this.scoreFunction(child2);
if (child2Score < (swap === null ? elemScore : child1Score)) {
swap = child2N;
}
}

// If the element needs to be moved, swap it, and continue.
if (swap !== null) {
this.content[n] = this.content[swap];
this.content[swap] = element;
n = swap;
}
// Otherwise, we are done.
else {
break;
}
}
}
};

return {
astar: astar,
Graph: Graph
};

});