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
Here is a JavaScript Implementation that fakes Breadth First Traversal with Depth First recursion. I'm storing the node values at each depth inside an array, inside of a hash. If a level already exists(we have a collision), so we just push to the array at that level. You could use an array instead of a JavaScript object as well since our levels are numeric and can serve as array indices. You can return nodes, values, convert to a Linked List, or whatever you want. I'm just returning values for the sake of simplicity.
BinarySearchTree.prototype.breadthFirstRec = function() {
var levels = {};
var traverse = function(current, depth) {
if (!current) return null;
if (!levels[depth]) levels[depth] = [current.value];
else levels[depth].push(current.value);
traverse(current.left, depth + 1);
traverse(current.right, depth + 1);
};
traverse(this.root, 0);
return levels;
};
var bst = new BinarySearchTree();
bst.add(20, 22, 8, 4, 12, 10, 14, 24);
console.log('Recursive Breadth First: ', bst.breadthFirstRec());
/*Recursive Breadth First:
{ '0': [ 20 ],
'1': [ 8, 22 ],
'2': [ 4, 12, 24 ],
'3': [ 10, 14 ] } */
下面是一个使用迭代方法的实际广度优先遍历的示例。
BinarySearchTree.prototype.breadthFirst = function() {
var result = '',
queue = [],
current = this.root;
if (!current) return null;
queue.push(current);
while (current = queue.shift()) {
result += current.value + ' ';
current.left && queue.push(current.left);
current.right && queue.push(current.right);
}
return result;
};
console.log('Breadth First: ', bst.breadthFirst());
//Breadth First: 20 8 22 4 12 24 10 14
其他回答
我已经用c++做了一个程序，它是在联合和不联合图工作。
#include <queue>
#include "iostream"
#include "vector"
#include "queue"
using namespace std;
struct Edge {
int source,destination;
};
class Graph{
int V;
vector<vector<int>> adjList;
public:
Graph(vector<Edge> edges,int V){
this->V = V;
adjList.resize(V);
for(auto i : edges){
adjList[i.source].push_back(i.destination);
// adjList[i.destination].push_back(i.source);
}
}
void BFSRecursivelyJoinandDisjointtGraphUtil(vector<bool> &discovered, queue<int> &q);
void BFSRecursivelyJointandDisjointGraph(int s);
void printGraph();
};
void Graph :: printGraph()
{
for (int i = 0; i < this->adjList.size(); i++)
{
cout << i << " -- ";
for (int v : this->adjList[i])
cout <<"->"<< v << " ";
cout << endl;
}
}
void Graph ::BFSRecursivelyJoinandDisjointtGraphUtil(vector<bool> &discovered, queue<int> &q) {
if (q.empty())
return;
int v = q.front();
q.pop();
cout << v <<" ";
for (int u : this->adjList[v])
{
if (!discovered[u])
{
discovered[u] = true;
q.push(u);
}
}
BFSRecursivelyJoinandDisjointtGraphUtil(discovered, q);
}
void Graph ::BFSRecursivelyJointandDisjointGraph(int s) {
vector<bool> discovered(V, false);
queue<int> q;
for (int i = s; i < V; i++) {
if (discovered[i] == false)
{
discovered[i] = true;
q.push(i);
BFSRecursivelyJoinandDisjointtGraphUtil(discovered, q);
}
}
}
int main()
{
vector<Edge> edges =
{
{0, 1}, {0, 2}, {1, 2}, {2, 0}, {2,3},{3,3}
};
int V = 4;
Graph graph(edges, V);
// graph.printGraph();
graph.BFSRecursivelyJointandDisjointGraph(2);
cout << "\n";
edges = {
{0,4},{1,2},{1,3},{1,4},{2,3},{3,4}
};
Graph graph2(edges,5);
graph2.BFSRecursivelyJointandDisjointGraph(0);
return 0;
}
下面是简短的Scala解决方案:
def bfs(nodes: List[Node]): List[Node] = {
if (nodes.nonEmpty) {
nodes ++ bfs(nodes.flatMap(_.children))
} else {
List.empty
}
}
使用返回值作为累加器的想法是很适合的。 可以在其他语言中以类似的方式实现，只需确保您的递归函数处理的节点列表。
测试代码清单(使用@marco测试树):
import org.scalatest.FlatSpec
import scala.collection.mutable
class Node(val value: Int) {
private val _children: mutable.ArrayBuffer[Node] = mutable.ArrayBuffer.empty
def add(child: Node): Unit = _children += child
def children = _children.toList
override def toString: String = s"$value"
}
class BfsTestScala extends FlatSpec {
// 1
// / | \
// 2 3 4
// / | | \
// 5 6 7 8
// / | | \
// 9 10 11 12
def tree(): Node = {
val root = new Node(1)
root.add(new Node(2))
root.add(new Node(3))
root.add(new Node(4))
root.children(0).add(new Node(5))
root.children(0).add(new Node(6))
root.children(2).add(new Node(7))
root.children(2).add(new Node(8))
root.children(0).children(0).add(new Node(9))
root.children(0).children(0).add(new Node(10))
root.children(2).children(0).add(new Node(11))
root.children(2).children(0).add(new Node(12))
root
}
def bfs(nodes: List[Node]): List[Node] = {
if (nodes.nonEmpty) {
nodes ++ bfs(nodes.flatMap(_.children))
} else {
List.empty
}
}
"BFS" should "work" in {
println(bfs(List(tree())))
}
}
输出:
List(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
我找不到一种完全递归的方法(没有任何辅助数据结构)。但是如果队列Q是通过引用传递的，那么你可以得到下面这个愚蠢的尾部递归函数:
BFS(Q)
{
if (|Q| > 0)
v <- Dequeue(Q)
Traverse(v)
foreach w in children(v)
Enqueue(Q, w)
BFS(Q)
}
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();
});
}
Here is a JavaScript Implementation that fakes Breadth First Traversal with Depth First recursion. I'm storing the node values at each depth inside an array, inside of a hash. If a level already exists(we have a collision), so we just push to the array at that level. You could use an array instead of a JavaScript object as well since our levels are numeric and can serve as array indices. You can return nodes, values, convert to a Linked List, or whatever you want. I'm just returning values for the sake of simplicity.
BinarySearchTree.prototype.breadthFirstRec = function() {
var levels = {};
var traverse = function(current, depth) {
if (!current) return null;
if (!levels[depth]) levels[depth] = [current.value];
else levels[depth].push(current.value);
traverse(current.left, depth + 1);
traverse(current.right, depth + 1);
};
traverse(this.root, 0);
return levels;
};
var bst = new BinarySearchTree();
bst.add(20, 22, 8, 4, 12, 10, 14, 24);
console.log('Recursive Breadth First: ', bst.breadthFirstRec());
/*Recursive Breadth First:
{ '0': [ 20 ],
'1': [ 8, 22 ],
'2': [ 4, 12, 24 ],
'3': [ 10, 14 ] } */
下面是一个使用迭代方法的实际广度优先遍历的示例。
BinarySearchTree.prototype.breadthFirst = function() {
var result = '',
queue = [],
current = this.root;
if (!current) return null;
queue.push(current);
while (current = queue.shift()) {
result += current.value + ' ';
current.left && queue.push(current.left);
current.right && queue.push(current.right);
}
return result;
};
console.log('Breadth First: ', bst.breadthFirst());
//Breadth First: 20 8 22 4 12 24 10 14
