Note that this code has been updated. I have an updated blog post detailing what changed. The new source code is available at https://github.com/bgrins/javascript-astar, and the code as of the original post is still available here: https://github.com/bgrins/javascript-astar/tree/0.0.1/original-implementation

View the online demo

I first implemented the A* algorithm for a research group I was in through school (Computer Graphics and Image Understanding). A* is a best-first, graph search algorithm. Some basic information can be found on the [Wikipedia page for A](http://en.wikipedia.org/wiki/A_search_algorithm) and the external links contained in it. Please refer to that page for general reference about the algorithm, I will simply explain in my own words how it works and how I got it working.

Why JavaScript?

Because it was easy to deploy!

Since I know JavaScript pretty well, and most of the examples you can find are in C, Java or a similar language that you cannot run without downloading source code or executables, I thought it would be a good idea to program it on an html page. This way, people could see what was going on and view the source very easily by using the online demo.

My hope was to build a page that could be extended with other search algorithms by separating the UI code (that generates a graph with walls and animates the path that is determined by an algorithm), and the algorithm that finds the path. Maybe I will get around to plugging in some more algorithms sometime and making it into a little resource for graph search algorithms.

How?

search.html

Just a basic html file that includes jQuery, the excellent JavaScript library, main.css, graph.js, and astar.js. Also, I have a JavaScript block that initializes the page.

graph.js

The point of this file is to build the graph, call the search function, and animate the results after the search has returned. It also has an option to show the debugging information created by the search algorithm. I won’t get too into the code here, since it distracts from the search algorithm.

Please take a look at it, be aware that there are some improvements I would make if I was to rewrite this today. There are some performance issues that could be addressed, and It modifies the Array.prototype to add on specific methods (findGraphNode and removeGraphNode) for search algorithms, which may not be ideal for bigger projects. For this little page, I’m not too worried about it, but if I do get around to adding in more algorithms, I will probably improve this code.

astar.js

This is the actual implementation of the algorithm. I will do my best to explain what is going on, but feel free to just look at the source of the example, or just download astar.js.

There are three functions that we keep track of for nodes that we look at:

g(x): The total cost of getting to that node (pretty straightforward). If we reach a node for the first time or reach a node in less time than it currently took, then update the g(x) to the cost to reach this node.

h(x): The estimated time to reach the finish from the current node. This is also called a heuristic. We online need to update this if it is not set already, since the distance to the finish will not change even if the path we took to arrive at a node changes. Note: There are many different ways to guess how far you are from the end, I use the Manhattan distance in this implementation.

f(x): Simply g(x) + h(x). The lower the f(x), the better. Think about it like this: the best node is one that takes the least total amount of time to arrive at and to get to the end. So, a node that took only 1 step to arrive at and 5 to get to the end is more ideal than one that took 10 to arrive and and only 1 to get to the end.

Here is some high level pseudocode of what is happening in the algorithm. Also see the Wikipedia pseudocode for another example.

push startNode onto openList while ( openList is not empty ) { currentNode = find lowest f in openList if currentNode is final , return the successful path push currentNode onto closedList and remove from openList foreach neighbor of currentNode { if neighbor is not in openList { save g , h , and f then save the current parent add neighbor to openList } if neighbor is in openList but the current g is better than previous g { save g and f , then save the current parent } }

Here is the JavaScript for the list implementation:

var astar = { init : function ( grid ) { for ( var x = ; x < grid . length ; x ++ ) { for ( var y = ; y < grid [ x ]. length ; y ++ ) { grid [ x ][ y ]. f = ; grid [ x ][ y ]. g = ; grid [ x ][ y ]. h = ; grid [ x ][ y ]. debug = "" ; grid [ x ][ y ]. parent = null ; } } }, search : function ( grid , start , end ) { astar . init ( grid ); var openList = []; var closedList = []; openList . push ( start ); while ( openList . length > ) { // Grab the lowest f(x) to process next var lowInd = ; for ( var i = ; i < openList . length ; i ++ ) { if ( openList [ i ]. f < openList [ lowInd ]. f ) { lowInd = i ; } } var currentNode = openList [ lowInd ]; // End case -- result has been found, return the traced path if ( currentNode . pos == end . pos ) { var curr = currentNode ; var ret = []; while ( curr . parent ) { ret . push ( curr ); curr = curr . parent ; } return ret . reverse (); } // Normal case -- move currentNode from open to closed, process each of its neighbors openList . removeGraphNode ( currentNode ); closedList . push ( currentNode ); var neighbors = astar . neighbors ( grid , currentNode ); for ( var i = ; i < neighbors . length ; i ++ ) { var neighbor = neighbors [ i ]; if ( closedList . findGraphNode ( neighbor ) || neighbor . isWall ()) { // not a valid node to process, skip to next neighbor continue ; } // 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 + 1 ; // 1 is the distance from a node to it's neighbor var gScoreIsBest = false ; if ( ! openList . findGraphNode ( neighbor )) { // This the the first time we have arrived at this node, it must be the best // Also, we need to take the h (heuristic) score since we haven't done so yet gScoreIsBest = true ; neighbor . h = astar . heuristic ( neighbor . pos , end . pos ); openList . push ( neighbor ); } else if ( gScore < neighbor . g ) { // We have already seen the node, but last time it had a worse g (distance from start) gScoreIsBest = true ; } if ( gScoreIsBest ) { // Found an optimal (so far) path to this node. Store info on how we got here and // just how good it really is... neighbor . parent = currentNode ; neighbor . g = gScore ; neighbor . f = neighbor . g + neighbor . h ; neighbor . debug = "F: " + neighbor . f + "<br />G: " + neighbor . g + "<br />H: " + neighbor . h ; } } } // No result was found -- empty array signifies failure to find path return []; }, heuristic : function ( pos0 , pos1 ) { // This is the Manhattan distance var d1 = Math . abs ( pos1 . x - pos0 . x ); var d2 = Math . abs ( pos1 . y - pos0 . y ); return d1 + d2 ; }, neighbors : function ( grid , node ) { var ret = []; var x = node . pos . x ; var y = node . pos . y ; if ( grid [ x - 1 ] && grid [ x - 1 ][ y ]) { ret . push ( grid [ x - 1 ][ y ]); } if ( grid [ x + 1 ] && grid [ x + 1 ][ y ]) { ret . push ( grid [ x + 1 ][ y ]); } if ( grid [ x ][ y - 1 ] && grid [ x ][ y - 1 ]) { ret . push ( grid [ x ][ y - 1 ]); } if ( grid [ x ][ y + 1 ] && grid [ x ][ y + 1 ]) { ret . push ( grid [ x ][ y + 1 ]); } return ret ; } };

And here is a faster implementation, using a Binary Heap instead of a list. This is a lot faster and also includes the option to search diagonally - 8 directional movement. Head over to the astar graph search project page to get the latest version of the code!

var astar = { init : function ( grid ) { for ( var x = , xl = grid . length ; x < xl ; x ++ ) { for ( var y = , yl = grid [ x ]. length ; y < yl ; y ++ ) { var node = grid [ x ][ y ]; node . f = ; node . g = ; node . h = ; node . cost = 1 ; node . visited = false ; node . closed = false ; node . parent = null ; } } }, heap : function () { return new BinaryHeap ( function ( node ) { return node . f ; }); }, search : function ( grid , start , end , diagonal , heuristic ) { astar . init ( grid ); heuristic = heuristic || astar . manhattan ; diagonal = !! diagonal ; var openHeap = astar . heap (); openHeap . push ( start ); while ( openHeap . size () > ) { // 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 ) { var curr = currentNode ; var ret = []; while ( curr . parent ) { ret . push ( curr ); curr = curr . parent ; } return ret . reverse (); } // Normal case -- move currentNode from open to closed, process each of its neighbors. currentNode . closed = true ; // Find all neighbors for the current node. Optionally find diagonal neighbors as well (false by default). var neighbors = astar . neighbors ( grid , currentNode , diagonal ); for ( var i = , 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 . cost ; 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 . pos , end . pos ); neighbor . g = gScore ; neighbor . f = neighbor . g + neighbor . h ; 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 ); } } } } // No result was found - empty array signifies failure to find path. return []; }, manhattan : function ( pos0 , pos1 ) { // See list of heuristics: http://theory.stanford.edu/~amitp/GameProgramming/Heuristics.html var d1 = Math . abs ( pos1 . x - pos0 . x ); var d2 = Math . abs ( pos1 . y - pos0 . y ); return d1 + d2 ; }, neighbors : function ( grid , node , diagonals ) { var ret = []; var x = node . x ; var y = node . y ; // 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 ( diagonals ) { // 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 ; } };

Conclusion

This A* search implementation could be used as a component to larger system (like a game - maybe tower defense or puzzle), or just for learning purposes. I have done my best to make the code understandable and to present the concepts in a way that would help someone who has never seen the algorithm before, or someone who is not very familiar with JavaScript.

Feel free to view the demo, or download the latest version of the astar.js file to mess around with it. Check out the javascript-astar project page on Github for the latest code and documentation.

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