Breadth-First Search (BFS)

Datenstrukturen und Algorithmen in Python

Miriam Antona

Software engineer

Breadth-First Search – Binärbäume

Startet an der Wurzel
Besucht alle Knoten jeder Ebene

Grafische Darstellung von Breadth-First Search auf einem binären Suchbaum.

Breadth-First Search – Binärbäume

  def bfs(self):

    if self.root:

      visited_nodes = []

      bfs_queue = queue.SimpleQueue()

Grafische Darstellung eines binären Suchbaums.

visited_nodes:
bfs_queue:

Breadth-First Search – Binärbäume

  def bfs(self):
    if self.root:
      visited_nodes = []
      bfs_queue = queue.SimpleQueue()
      bfs_queue.put(self.root)

      while not bfs_queue.empty():

Grafische Darstellung eines binären Suchbaums.

visited_nodes:
bfs_queue: 65

Breadth-First Search – Binärbäume

  def bfs(self):
    if self.root:
      visited_nodes = []
      bfs_queue = queue.SimpleQueue()
      bfs_queue.put(self.root)
      while not bfs_queue.empty():
        current_node = bfs_queue.get()

Grafische Darstellung eines binären Suchbaums.

visited_nodes:
bfs_queue:
current_node: 65

Breadth-First Search – Binärbäume

  def bfs(self):

    if self.root:
      visited_nodes = []
      bfs_queue = queue.SimpleQueue()
      bfs_queue.put(self.root)
      while not bfs_queue.empty():
        current_node = bfs_queue.get()
        visited_nodes.append(current_node.data)

        if current_node.left:

Grafische Darstellung eines binären Suchbaums.

visited_nodes: 65
bfs_queue:
current_node: 65

Breadth-First Search – Binärbäume

  def bfs(self):

    if self.root:
      visited_nodes = []
      bfs_queue = queue.SimpleQueue()
      bfs_queue.put(self.root)
      while not bfs_queue.empty():
        current_node = bfs_queue.get()
        visited_nodes.append(current_node.data)
        if current_node.left:
          bfs_queue.put(current_node.left)

Grafische Darstellung eines binären Suchbaums.

visited_nodes: 65
bfs_queue: 20
current_node: 65

Breadth-First Search – Binärbäume

  def bfs(self):
    if self.root:
      visited_nodes = []
      bfs_queue = queue.SimpleQueue()
      bfs_queue.put(self.root)
      while not bfs_queue.empty():
        current_node = bfs_queue.get()
        visited_nodes.append(current_node.data)
        if current_node.left:
          bfs_queue.put(current_node.left)
        if current_node.right:
          bfs_queue.put(current_node.right)

Grafische Darstellung eines binären Suchbaums.

visited_nodes: 65
bfs_queue: 20, 70
current_node: 65

Breadth-First Search – Binärbäume

  def bfs(self):
    if self.root:
      visited_nodes = []
      bfs_queue = queue.SimpleQueue()
      bfs_queue.put(self.root)
      while not bfs_queue.empty():
        current_node = bfs_queue.get()
        visited_nodes.append(current_node.data)
        if current_node.left:
          bfs_queue.put(current_node.left)
        if current_node.right:
          bfs_queue.put(current_node.right)

Grafische Darstellung eines binären Suchbaums.

visited_nodes: 65
bfs_queue: 70
current_node: 20

Breadth-First Search – Binärbäume

  def bfs(self):
    if self.root:
      visited_nodes = []
      bfs_queue = queue.SimpleQueue()
      bfs_queue.put(self.root)
      while not bfs_queue.empty():
        current_node = bfs_queue.get()
        visited_nodes.append(current_node.data)
        if current_node.left:
          bfs_queue.put(current_node.left)
        if current_node.right:
          bfs_queue.put(current_node.right)

Grafische Darstellung eines binären Suchbaums.

visited_nodes: 65, 20
bfs_queue: 70
current_node: 20

Breadth-First Search – Binärbäume

  def bfs(self):
    if self.root:
      visited_nodes = []
      bfs_queue = queue.SimpleQueue()
      bfs_queue.put(self.root)
      while not bfs_queue.empty():
        current_node = bfs_queue.get()
        visited_nodes.append(current_node.data)
        if current_node.left:
          bfs_queue.put(current_node.left)
        if current_node.right:
          bfs_queue.put(current_node.right)

Grafische Darstellung eines binären Suchbaums.

visited_nodes: 65, 20
bfs_queue: 70, 10
current_node: 20

Breadth-First Search – Binärbäume

  def bfs(self):
    if self.root:
      visited_nodes = []
      bfs_queue = queue.SimpleQueue()
      bfs_queue.put(self.root)
      while not bfs_queue.empty():
        current_node = bfs_queue.get()
        visited_nodes.append(current_node.data)
        if current_node.left:
          bfs_queue.put(current_node.left)
        if current_node.right:
          bfs_queue.put(current_node.right)

Grafische Darstellung eines binären Suchbaums.

visited_nodes: 65, 20
bfs_queue: 70, 10, 22
current_node: 20

Breadth-First Search – Binärbäume

  def bfs(self):
    if self.root:
      visited_nodes = []
      bfs_queue = queue.SimpleQueue()
      bfs_queue.put(self.root)
      while not bfs_queue.empty():
        current_node = bfs_queue.get()
        visited_nodes.append(current_node.data)
        if current_node.left:
          bfs_queue.put(current_node.left)
        if current_node.right:
          bfs_queue.put(current_node.right)

Grafische Darstellung eines binären Suchbaums.

visited_nodes: 65, 20
bfs_queue: 10, 22
current_node: 70

Breadth-First Search – Binärbäume

  def bfs(self):
    if self.root:
      visited_nodes = []
      bfs_queue = queue.SimpleQueue()
      bfs_queue.put(self.root)
      while not bfs_queue.empty():
        current_node = bfs_queue.get()
        visited_nodes.append(current_node.data)
        if current_node.left:
          bfs_queue.put(current_node.left)
        if current_node.right:
          bfs_queue.put(current_node.right)

Grafische Darstellung eines binären Suchbaums.

visited_nodes: 65, 20, 70
bfs_queue: 10, 22
current_node: 70

Breadth-First Search – Binärbäume

  def bfs(self):
    if self.root:
      visited_nodes = []
      bfs_queue = queue.SimpleQueue()
      bfs_queue.put(self.root)
      while not bfs_queue.empty():
        current_node = bfs_queue.get()
        visited_nodes.append(current_node.data)
        if current_node.left:
          bfs_queue.put(current_node.left)
        if current_node.right:
          bfs_queue.put(current_node.right)

Grafische Darstellung eines binären Suchbaums.

visited_nodes: 65, 20, 70
bfs_queue: 10, 22, 68
current_node: 70

Breadth-First Search – Binärbäume

  def bfs(self):
    if self.root:
      visited_nodes = []
      bfs_queue = queue.SimpleQueue()
      bfs_queue.put(self.root)
      while not bfs_queue.empty():
        current_node = bfs_queue.get()
        visited_nodes.append(current_node.data)
        if current_node.left:
          bfs_queue.put(current_node.left)
        if current_node.right:
          bfs_queue.put(current_node.right)

Grafische Darstellung eines binären Suchbaums.

visited_nodes: 65, 20, 70
bfs_queue: 10, 22, 68, 75
current_node: 70

Breadth-First Search – Binärbäume

  def bfs(self):
    if self.root:
      visited_nodes = []
      bfs_queue = queue.SimpleQueue()
      bfs_queue.put(self.root)
      while not bfs_queue.empty():
        current_node = bfs_queue.get()
        visited_nodes.append(current_node.data)
        if current_node.left:
          bfs_queue.put(current_node.left)
        if current_node.right:
          bfs_queue.put(current_node.right)

Grafische Darstellung eines binären Suchbaums.

visited_nodes: 65, 20, 70, 10
bfs_queue: 22, 68, 75
current_node: 10

Breadth-First Search – Binärbäume

  def bfs(self):
    if self.root:
      visited_nodes = []
      bfs_queue = queue.SimpleQueue()
      bfs_queue.put(self.root)
      while not bfs_queue.empty():
        current_node = bfs_queue.get()
        visited_nodes.append(current_node.data)
        if current_node.left:
          bfs_queue.put(current_node.left)
        if current_node.right:
          bfs_queue.put(current_node.right)

Grafische Darstellung eines binären Suchbaums.

visited_nodes: 65, 20, 70, 10
bfs_queue: 68, 75
current_node: 22

Breadth-First Search – Binärbäume

  def bfs(self):
    if self.root:
      visited_nodes = []
      bfs_queue = queue.SimpleQueue()
      bfs_queue.put(self.root)
      while not bfs_queue.empty():
        current_node = bfs_queue.get()
        visited_nodes.append(current_node.data)
        if current_node.left:
          bfs_queue.put(current_node.left)
        if current_node.right:
          bfs_queue.put(current_node.right)

Grafische Darstellung eines binären Suchbaums.

visited_nodes: 65, 20, 70, 10, 22
bfs_queue: 68, 75
current_node: 22

Breadth-First Search – Binärbäume

  def bfs(self):
    if self.root:
      visited_nodes = []
      bfs_queue = queue.SimpleQueue()
      bfs_queue.put(self.root)
      while not bfs_queue.empty():
        current_node = bfs_queue.get()
        visited_nodes.append(current_node.data)
        if current_node.left:
          bfs_queue.put(current_node.left)
        if current_node.right:
          bfs_queue.put(current_node.right)

Grafische Darstellung eines binären Suchbaums.

visited_nodes: 65, 20, 70, 10, 22, 68
bfs_queue: 75
current_node: 68

Breadth-First Search – Binärbäume

  def bfs(self):
    if self.root:
      visited_nodes = []
      bfs_queue = queue.SimpleQueue()
      bfs_queue.put(self.root)
      while not bfs_queue.empty():
        current_node = bfs_queue.get()
        visited_nodes.append(current_node.data)
        if current_node.left:
          bfs_queue.put(current_node.left)
        if current_node.right:
          bfs_queue.put(current_node.right)

Grafische Darstellung eines binären Suchbaums.

visited_nodes: 65, 20, 70, 10, 22, 68
bfs_queue:
current_node: 75

Breadth-First Search – Binärbäume

  def bfs(self):
    if self.root:
      visited_nodes = []
      bfs_queue = queue.SimpleQueue()
      bfs_queue.put(self.root)
      while not bfs_queue.empty():
        current_node = bfs_queue.get()
        visited_nodes.append(current_node.data)
        if current_node.left:
          bfs_queue.put(current_node.left)
        if current_node.right:
          bfs_queue.put(current_node.right)

Grafische Darstellung eines binären Suchbaums.

visited_nodes: 65, 20, 70, 10, 22, 68, 75
bfs_queue:
current_node: 75

Breadth-First Search – Binärbäume

  def bfs(self):
    if self.root:
      visited_nodes = []
      bfs_queue = queue.SimpleQueue()
      bfs_queue.put(self.root)
      while not bfs_queue.empty():
        current_node = bfs_queue.get()
        visited_nodes.append(current_node.data)
        if current_node.left:
          bfs_queue.put(current_node.left)
        if current_node.right:
          bfs_queue.put(current_node.right)
    return visited_nodes

Komplexität: $O(n)$

Grafische Darstellung eines binären Suchbaums.

visited_nodes: 65, 20, 70, 10, 22, 68, 75
bfs_queue:
current_node: 75

Breadth-First Search – Graphen

Graphen können Zyklen haben
- Prüfen, ob Knoten schon besucht wurden

Breadth-First Search – Graphen

def bfs(graph, initial_vertex):

  visited_vertices = []

  bfs_queue = queue.SimpleQueue()

  bfs_queue.put(initial_vertex)

  visited_vertices.append(initial_vertex)

  while not bfs_queue.empty():

    current_vertex = bfs_queue.get()

    for adjacent_vertex in graph[current_vertex]:

      if adjacent_vertex not in visited_vertices:

        visited_vertices.append(adjacent_vertex)

        bfs_queue.put(adjacent_vertex)

  return visited_vertices

Komplexität: $O(V+E)$
- $V$ -> Anzahl der Knoten
- $E$ -> Anzahl der Kanten

Breadth-First Search – Graphen

Grafische Darstellung von Breadth-First Search auf einem Graphen.

BFS vs. DFS

BFS

Ziel liegt nah am Startknoten
Anwendungen:
- Webcrawling
- Kürzester Weg in ungewichteten Graphen
- Verbundene Orte per GPS finden
- Baustein komplexerer Algorithmen

DFS

Ziel liegt weit vom Startknoten entfernt
Anwendungen:
- Rätsel mit nur einer Lösung (z. B. Labyrinthe)
- Zyklen in Graphen erkennen
- Kürzester Weg in gewichteten Graphen
- Baustein komplexerer Algorithmen

Lass uns üben!

Datenstrukturen und Algorithmen in Python