假设您想递归地实现一个二叉树的宽度优先搜索。你会怎么做?
是否可以只使用调用堆栈作为辅助存储?
假设您想递归地实现一个二叉树的宽度优先搜索。你会怎么做?
是否可以只使用调用堆栈作为辅助存储?
当前回答
二进制(或n-ary)树的BFS可以在没有队列的情况下递归完成,如下所示(在Java中):
public class BreathFirst {
static class Node {
Node(int value) {
this(value, 0);
}
Node(int value, int nChildren) {
this.value = value;
this.children = new Node[nChildren];
}
int value;
Node[] children;
}
static void breathFirst(Node root, Consumer<? super Node> printer) {
boolean keepGoing = true;
for (int level = 0; keepGoing; level++) {
keepGoing = breathFirst(root, printer, level);
}
}
static boolean breathFirst(Node node, Consumer<? super Node> printer, int depth) {
if (depth < 0 || node == null) return false;
if (depth == 0) {
printer.accept(node);
return true;
}
boolean any = false;
for (final Node child : node.children) {
any |= breathFirst(child, printer, depth - 1);
}
return any;
}
}
按升序遍历打印数字1-12的示例:
public static void main(String... args) {
// 1
// / | \
// 2 3 4
// / | | \
// 5 6 7 8
// / | | \
// 9 10 11 12
Node root = new Node(1, 3);
root.children[0] = new Node(2, 2);
root.children[1] = new Node(3);
root.children[2] = new Node(4, 2);
root.children[0].children[0] = new Node(5, 2);
root.children[0].children[1] = new Node(6);
root.children[2].children[0] = new Node(7, 2);
root.children[2].children[1] = new Node(8);
root.children[0].children[0].children[0] = new Node(9);
root.children[0].children[0].children[1] = new Node(10);
root.children[2].children[0].children[0] = new Node(11);
root.children[2].children[0].children[1] = new Node(12);
breathFirst(root, n -> System.out.println(n.value));
}
其他回答
我必须实现以BFS顺序输出的堆遍历。它实际上不是BFS,但完成了相同的任务。
private void getNodeValue(Node node, int index, int[] array) {
array[index] = node.value;
index = (index*2)+1;
Node left = node.leftNode;
if (left!=null) getNodeValue(left,index,array);
Node right = node.rightNode;
if (right!=null) getNodeValue(right,index+1,array);
}
public int[] getHeap() {
int[] nodes = new int[size];
getNodeValue(root,0,nodes);
return nodes;
}
我发现了一个非常漂亮的递归(甚至函数)宽度优先遍历相关算法。不是我的想法,但我认为在这个话题中应该提到它。
Chris Okasaki在http://okasaki.blogspot.de/2008/07/breadth-first-numbering-algorithm-in.html上用3张图片非常清楚地解释了他的ICFP 2000的宽度优先编号算法。
Debasish Ghosh的Scala实现,我在http://debasishg.blogspot.de/2008/09/breadth-first-numbering-okasakis.html找到的,是:
trait Tree[+T]
case class Node[+T](data: T, left: Tree[T], right: Tree[T]) extends Tree[T]
case object E extends Tree[Nothing]
def bfsNumForest[T](i: Int, trees: Queue[Tree[T]]): Queue[Tree[Int]] = {
if (trees.isEmpty) Queue.Empty
else {
trees.dequeue match {
case (E, ts) =>
bfsNumForest(i, ts).enqueue[Tree[Int]](E)
case (Node(d, l, r), ts) =>
val q = ts.enqueue(l, r)
val qq = bfsNumForest(i+1, q)
val (bb, qqq) = qq.dequeue
val (aa, tss) = qqq.dequeue
tss.enqueue[org.dg.collection.BFSNumber.Tree[Int]](Node(i, aa, bb))
}
}
}
def bfsNumTree[T](t: Tree[T]): Tree[Int] = {
val q = Queue.Empty.enqueue[Tree[T]](t)
val qq = bfsNumForest(1, q)
qq.dequeue._1
}
下面是一个BFS递归遍历Python实现,用于没有周期的图。
def bfs_recursive(level):
'''
@params level: List<Node> containing the node for a specific level.
'''
next_level = []
for node in level:
print(node.value)
for child_node in node.adjency_list:
next_level.append(child_node)
if len(next_level) != 0:
bfs_recursive(next_level)
class Node:
def __init__(self, value):
self.value = value
self.adjency_list = []
c#实现的递归宽度优先搜索二叉树算法。
二叉树数据可视化
IDictionary<string, string[]> graph = new Dictionary<string, string[]> {
{"A", new [] {"B", "C"}},
{"B", new [] {"D", "E"}},
{"C", new [] {"F", "G"}},
{"E", new [] {"H"}}
};
void Main()
{
var pathFound = BreadthFirstSearch("A", "H", new string[0]);
Console.WriteLine(pathFound); // [A, B, E, H]
var pathNotFound = BreadthFirstSearch("A", "Z", new string[0]);
Console.WriteLine(pathNotFound); // []
}
IEnumerable<string> BreadthFirstSearch(string start, string end, IEnumerable<string> path)
{
if (start == end)
{
return path.Concat(new[] { end });
}
if (!graph.ContainsKey(start)) { return new string[0]; }
return graph[start].SelectMany(letter => BreadthFirstSearch(letter, end, path.Concat(new[] { start })));
}
如果你想让算法不仅适用于二叉树,而且适用于有两个或两个以上节点指向同一个节点的图,你必须通过持有已经访问过的节点列表来避免自循环。实现可能是这样的。
图形数据可视化
IDictionary<string, string[]> graph = new Dictionary<string, string[]> {
{"A", new [] {"B", "C"}},
{"B", new [] {"D", "E"}},
{"C", new [] {"F", "G", "E"}},
{"E", new [] {"H"}}
};
void Main()
{
var pathFound = BreadthFirstSearch("A", "H", new string[0], new List<string>());
Console.WriteLine(pathFound); // [A, B, E, H]
var pathNotFound = BreadthFirstSearch("A", "Z", new string[0], new List<string>());
Console.WriteLine(pathNotFound); // []
}
IEnumerable<string> BreadthFirstSearch(string start, string end, IEnumerable<string> path, IList<string> visited)
{
if (start == end)
{
return path.Concat(new[] { end });
}
if (!graph.ContainsKey(start)) { return new string[0]; }
return graph[start].Aggregate(new string[0], (acc, letter) =>
{
if (visited.Contains(letter))
{
return acc;
}
visited.Add(letter);
var result = BreadthFirstSearch(letter, end, path.Concat(new[] { start }), visited);
return acc.Concat(result).ToArray();
});
}
在学习AlgoExpert时,对这个问题进行了改编。提示符中已经提供了以下Class。这里是python中的迭代和递归解决方案。这个问题的目标是返回一个输出数组,其中列出了按访问顺序排列的节点名称。如果遍历顺序为A -> B -> D -> F,则输出为['A','B','D','F']
class Node:
def __init__(self, name):
self.children = []
self.name = name
def addChild(self, name):
self.children.append(Node(name))
return self
递归
def breadthFirstSearch(self, array):
return self._bfs(array, [self])
def _bfs(self, array, visited):
# Base case - no more nodes to visit
if len(visited) == 0:
return array
node = visited.pop(0)
array.append(node.name)
visited.extend(node.children)
return self._bfs(array, visited)
迭代
def breadthFirstSearch(self, array):
array.append(self.name)
queue = [self]
while len(queue) > 0:
node = queue.pop(0)
for child in node.children:
array.append(child.name)
queue.append(child)
return array