首先让我们指出，如果图未加权，广度优先搜索 (BFS) 会计算来自给定源顶点的最短路径。换句话说，我们将路径的长度视为路径中边的数量。
这是构建未加权图的简单方法：
function Graph() {
var neighbors = this.neighbors = {}; // Key = vertex, value = array of neighbors.
this.addEdge = function (u, v) {
if (neighbors[u] === undefined) { // Add the edge u -> v.
neighbors[u] = [];
}
neighbors[u].push(v);
if (neighbors[v] === undefined) { // Also add the edge v -> u so as
neighbors[v] = []; // to implement an undirected graph.
} // For a directed graph, delete
neighbors[v].push(u); // these four lines.
};
return this;
}
请注意，我们已经实现了无向图。正如内联注释中提到的，您可以修改代码以通过删除四行来构造有向图addEdge功能。
BFS 的这种实现在有向图上同样可以很好地工作：
function bfs(graph, source) {
var queue = [ { vertex: source, count: 0 } ],
visited = { [source]: true },
tail = 0;
while (tail < queue.length) {
var u = queue[tail].vertex,
count = queue[tail++].count; // Pop a vertex off the queue.
print('distance from ' + source + ' to ' + u + ': ' + count);
graph.neighbors[u].forEach(function (v) {
if (!visited[v]) {
visited[v] = true;
queue.push({ vertex: v, count: count + 1 });
}
});
}
}
为了找到两个给定顶点之间的最短路径并沿路径显示顶点，我们在探索图形时必须记住每个顶点的前趋：
function shortestPath(graph, source, target) {
if (source == target) { // Delete these four lines if
print(source); // you want to look for a cycle
return; // when the source is equal to
} // the target.
var queue = [ source ],
visited = { [source]: true },
predecessor = {},
tail = 0;
while (tail < queue.length) {
var u = queue[tail++], // Pop a vertex off the queue.
neighbors = graph.neighbors[u];
for (var i = 0; i < neighbors.length; ++i) {
var v = neighbors[i];
if (visited[v]) {
continue;
}
visited[v] = true;
if (v === target) { // Check if the path is complete.
var path = [ v ]; // If so, backtrack through the path.
while (u !== source) {
path.push(u);
u = predecessor[u];
}
path.push(u);
path.reverse();
print(path.join(' → '));
return;
}
predecessor[v] = u;
queue.push(v);
}
}
print('there is no path from ' + source + ' to ' + target);
}
以下代码片段在您在问题中给出的图表上演示了这些操作。首先，我们找到从 到所有可到达的顶点的最短路径A。然后我们找到最短路径B to G和来自G to A.
function Graph() {
var neighbors = this.neighbors = {}; // Key = vertex, value = array of neighbors.
this.addEdge = function (u, v) {
if (neighbors[u] === undefined) { // Add the edge u -> v.
neighbors[u] = [];
}
neighbors[u].push(v);
if (neighbors[v] === undefined) { // Also add the edge v -> u in order
neighbors[v] = []; // to implement an undirected graph.
} // For a directed graph, delete
neighbors[v].push(u); // these four lines.
};
return this;
}
function bfs(graph, source) {
var queue = [ { vertex: source, count: 0 } ],
visited = { [source]: true },
tail = 0;
while (tail < queue.length) {
var u = queue[tail].vertex,
count = queue[tail++].count; // Pop a vertex off the queue.
print('distance from ' + source + ' to ' + u + ': ' + count);
graph.neighbors[u].forEach(function (v) {
if (!visited[v]) {
visited[v] = true;
queue.push({ vertex: v, count: count + 1 });
}
});
}
}
function shortestPath(graph, source, target) {
if (source == target) { // Delete these four lines if
print(source); // you want to look for a cycle
return; // when the source is equal to
} // the target.
var queue = [ source ],
visited = { [source]: true },
predecessor = {},
tail = 0;
while (tail < queue.length) {
var u = queue[tail++], // Pop a vertex off the queue.
neighbors = graph.neighbors[u];
for (var i = 0; i < neighbors.length; ++i) {
var v = neighbors[i];
if (visited[v]) {
continue;
}
visited[v] = true;
if (v === target) { // Check if the path is complete.
var path = [ v ]; // If so, backtrack through the path.
while (u !== source) {
path.push(u);
u = predecessor[u];
}
path.push(u);
path.reverse();
print(path.join(' → '));
return;
}
predecessor[v] = u;
queue.push(v);
}
}
print('there is no path from ' + source + ' to ' + target);
}
function print(s) { // A quick and dirty way to display output.
s = s || '';
document.getElementById('display').innerHTML += s + '<br>';
}
window.onload = function () {
var graph = new Graph();
graph.addEdge('A', 'B');
graph.addEdge('B', 'C');
graph.addEdge('B', 'E');
graph.addEdge('C', 'D');
graph.addEdge('C', 'E');
graph.addEdge('C', 'G');
graph.addEdge('D', 'E');
graph.addEdge('E', 'F');
bfs(graph, 'A');
print();
shortestPath(graph, 'B', 'G');
print();
shortestPath(graph, 'G', 'A');
};
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