A星算法

var list = [
              [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0],
              [0,1,1,0,1,1,0,1,0,1,1,1,1,0,0],
              [0,0,1,1,1,0,0,1,1,1,1,0,1,0,1],
              [0,0,0,1,1,0,0,1,1,0,1,0,1,1,1],
              [0,0,0,1,0,0,1,1,1,0,1,0,1,1,1],
              [0,0,1,1,1,1,1,1,0,0,0,0,1,0,1],
              [0,0,1,1,1,0,0,1,0,1,1,0,1,0,1],
            ];
var graph = new AStar.Graph(list,{});
var start = graph.grid[0][0];
var end = graph.grid[3][14];
var result = AStar.astar.search(graph, start, end,{closest:true, heuristic:AStar.astar.heuristics.diagonal});

module AStar {
    export class AStar {
        public constructor() {
        }
    }

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

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

    export 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
     */
    export 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;
        }
        }
    }
    };
}