優先度つきキューを使用したダイクストラ法をJavaScriptで実装した。

■実装

/**
 * Vertex
 * @param int value
 */
var Vertex = function(value){
    var self = this;
    self.value    = value;
    self.state    = 0;
    self.dist     = Number.POSITIVE_INFINITY;// もしくは十分に大きい値とか
    self.neighbor = [];
    self.appendNeighbor = function(){
        for(var i = 0; i < arguments.length; i++){
            self.neighbor.push(arguments[i]);
        }
    }
}

// set up a graph
var s  = new Vertex(0);
var v1 = new Vertex(1);
var v2 = new Vertex(2);
var v3 = new Vertex(3);
var v4 = new Vertex(4);
var g  = new Vertex(5);

// set up connections
// 単純化のためループや往路を除去した
s.appendNeighbor(
    {"weight" : 1, "vertex" : v1},
    {"weight" : 3, "vertex" : v2}
);
v1.appendNeighbor(
    {"weight" : 1, "vertex" : v2},
    {"weight" : 4, "vertex" : v3}
);
v2.appendNeighbor(
    {"weight" : 1, "vertex" : v3}
);
v3.appendNeighbor(
    {"weight" : 1, "vertex" : v4},
    {"weight" : 10, "vertex" : g}
);
v4.appendNeighbor(
    {"weight" : 1, "vertex" : g}
);
g.appendNeighbor(
);

// initialize
var vertexes = [s, v1, v2, v3, v4, g];
var pred     = [];
var pq       = new BinaryHeap();// sからの距離が短い頂点順の優先度つきキュー
s.dist = 0;
for(var i = 0; i < vertexes.length; i++){// キューの生成
    pred[i] = -1;
    pq.insert(vertexes[i], vertexes[i].dist);
}

// search
var dijkstraPQ = function(){
    while(pq.getList().length > 0){
        var u = pq.getPrior();// スタートからの距離が近い頂点を取得しcurrent頂点とする
        for(var i = 0; i < u.neighbor.length; i++){
            var neighbor  = u.neighbor[i].vertex;
            var weight    = u.neighbor[i].weight;// 隣接点の距離...(a)
            var newLength = u.dist + weight;// current頂点のsからの距離と(a)を加算...(b)
            // (b) < visitした時の距離の場合
            // キューを更新し、最短経路も更新する
            if(newLength < neighbor.dist){
                pq.changePriority(neighbor, newLength);
                neighbor.dist = newLength;
                pred[neighbor.value] = u.value;
            }
        }
    }
}
dijkstraPQ();

// 最短経路
console.log(pred);// [-1, 0, 1, 2, 3, 4]
// g<-v4<-v3-<v2<-v1<-s

// 最短距離
console.log(g.dist);// 5

任意の頂点に対して一つ前の頂点とその時の距離が分かる。

■特性

• 辺の重みは0より大きい値
• 重みの和が0より小さい閉路が存在すると無限ループする可能性がある

/**
 * BinaryHeap
 */
var BinaryHeap = function(){
    var self = this;
    self._ary  = [];
}
BinaryHeap.prototype._build = function(){
    var self = this;
    /**
     * heapify
     * 3要素を比較し最も小さい要素を親とする
     * @param {array} ary
     * @param {int} i
     * @param {max} max
     */
    var heapify = function(ary, i, max){
        /**
         * swap
         * @param {array} ary
         * @param {int} x
         * @param {int} y
         */
        var swap = function(ary, x, y){
            var a = ary[x];
            var b = ary[y];
            ary[x] = b;
            ary[y] = a;
            return true;
        }
        
        var l = 2 * i + 1;
        var r = 2 * i + 2;
        var li = 0;
        if(l < max && ary[l].priority < ary[i].priority){
            li = l;
        }
        else{
            li = i;
        }
        if(r < max && ary[r].priority < ary[li].priority){
            li = r;
        }
        if(li !== i){
            swap(ary, i, li);
            heapify(ary, li, max);
        }
    }
    var ary = self._ary;
    for(var i = ary.length - 1; i >= 0; i--){
        heapify(ary, i, self._ary.length);
    }
}
/**
 * BinaryHeap::insert
 * @param {Object} elm
 * @param {int} priority
 */
BinaryHeap.prototype.insert = function(elm, priority){
    var self = this;
    self._ary.push({
        "priority" : priority,
        "elm"      : elm
    });
    self._build();
}
/**
 * BinaryHeap::changePriority
 * @param {Object} elm
 * @param {int} priority
 */
BinaryHeap.prototype.changePriority = function(elm, priority){
    var self = this;
    var ary  = self._ary;
    for(var i = 0; i < ary.length; i++){
        if(elm === ary[i]["elm"]){
            ary[i]["priority"] = priority;
            self._build();
            return true;
        }
    }
    return false;
}
/**
 * BinaryHeap::getPrior
 */
BinaryHeap.prototype.getPrior = function(){
    var self = this;
    var elm  = self._ary.shift();
    self._build();
    return elm["elm"];
}
/**
 * BinaryHeap::getList
 */
BinaryHeap.prototype.getList = function(){
    var self = this;
    return self._ary;
}