Breadth-first search (BFS)

Datastructuren en algoritmen in Python

Miriam Antona

Software engineer

Breadth-first search - binaire bomen

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  • Bezoekt elk knooppunt van elk niveau

Grafische weergave van breadth-first search op een binaire zoekboom.

Datastructuren en algoritmen in Python

Breadth-first search - binaire bomen

  def bfs(self):

    if self.root:

      visited_nodes = []

      bfs_queue = queue.SimpleQueue()

Grafische weergave van een binaire zoekboom.

  • visited_nodes:
  • bfs_queue:
Datastructuren en algoritmen in Python

Breadth-first search - binaire bomen

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

      while not bfs_queue.empty():

Grafische weergave van een binaire zoekboom.

  • visited_nodes:
  • bfs_queue: 65
Datastructuren en algoritmen in Python

Breadth-first search - binaire bomen

  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 weergave van een binaire zoekboom.

  • visited_nodes:
  • bfs_queue:
  • current_node: 65
Datastructuren en algoritmen in Python

Breadth-first search - binaire bomen

  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 weergave van een binaire zoekboom.

  • visited_nodes: 65
  • bfs_queue:
  • current_node: 65
Datastructuren en algoritmen in Python

Breadth-first search - binaire bomen

  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 weergave van een binaire zoekboom.

  • visited_nodes: 65
  • bfs_queue: 20
  • current_node: 65
Datastructuren en algoritmen in Python

Breadth-first search - binaire bomen

  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 weergave van een binaire zoekboom.

  • visited_nodes: 65
  • bfs_queue: 20, 70
  • current_node: 65
Datastructuren en algoritmen in Python

Breadth-first search - binaire bomen

  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 weergave van een binaire zoekboom.

  • visited_nodes: 65
  • bfs_queue: 70
  • current_node: 20
Datastructuren en algoritmen in Python

Breadth-first search - binaire bomen

  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 weergave van een binaire zoekboom.

  • visited_nodes: 65, 20
  • bfs_queue: 70
  • current_node: 20
Datastructuren en algoritmen in Python

Breadth-first search - binaire bomen

  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 weergave van een binaire zoekboom.

  • visited_nodes: 65, 20
  • bfs_queue: 70, 10
  • current_node: 20
Datastructuren en algoritmen in Python

Breadth-first search - binaire bomen

  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 weergave van een binaire zoekboom.

  • visited_nodes: 65, 20
  • bfs_queue: 70, 10, 22
  • current_node: 20
Datastructuren en algoritmen in Python

Breadth-first search - binaire bomen

  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 weergave van een binaire zoekboom.

  • visited_nodes: 65, 20
  • bfs_queue: 10, 22
  • current_node: 70
Datastructuren en algoritmen in Python

Breadth-first search - binaire bomen

  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 weergave van een binaire zoekboom.

  • visited_nodes: 65, 20, 70
  • bfs_queue: 10, 22
  • current_node: 70
Datastructuren en algoritmen in Python

Breadth-first search - binaire bomen

  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 weergave van een binaire zoekboom.

  • visited_nodes: 65, 20, 70
  • bfs_queue: 10, 22, 68
  • current_node: 70
Datastructuren en algoritmen in Python

Breadth-first search - binaire bomen

  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 weergave van een binaire zoekboom.

  • visited_nodes: 65, 20, 70
  • bfs_queue: 10, 22, 68, 75
  • current_node: 70
Datastructuren en algoritmen in Python

Breadth-first search - binaire bomen

  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 weergave van een binaire zoekboom.

  • visited_nodes: 65, 20, 70, 10
  • bfs_queue: 22, 68, 75
  • current_node: 10
Datastructuren en algoritmen in Python

Breadth-first search - binaire bomen

  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 weergave van een binaire zoekboom.

  • visited_nodes: 65, 20, 70, 10
  • bfs_queue: 68, 75
  • current_node: 22
Datastructuren en algoritmen in Python

Breadth-first search - binaire bomen

  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 weergave van een binaire zoekboom.

  • visited_nodes: 65, 20, 70, 10, 22
  • bfs_queue: 68, 75
  • current_node: 22
Datastructuren en algoritmen in Python

Breadth-first search - binaire bomen

  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 weergave van een binaire zoekboom.

  • visited_nodes: 65, 20, 70, 10, 22, 68
  • bfs_queue: 75
  • current_node: 68
Datastructuren en algoritmen in Python

Breadth-first search - binaire bomen

  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 weergave van een binaire zoekboom.

  • visited_nodes: 65, 20, 70, 10, 22, 68
  • bfs_queue:
  • current_node: 75
Datastructuren en algoritmen in Python

Breadth-first search - binaire bomen

  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 weergave van een binaire zoekboom.

  • visited_nodes: 65, 20, 70, 10, 22, 68, 75
  • bfs_queue:
  • current_node: 75
Datastructuren en algoritmen in Python

Breadth-first search - binaire bomen

  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
  • Complexiteit: $O(n)$

Grafische weergave van een binaire zoekboom.

  • visited_nodes: 65, 20, 70, 10, 22, 68, 75
  • bfs_queue:
  • current_node: 75
Datastructuren en algoritmen in Python

Breadth-first search - grafen

  • Grafen kunnen cycli hebben
    • Controleer of de knopen al bezocht zijn
Datastructuren en algoritmen in Python

Breadth-first search - grafen

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
  • Complexiteit: $O(V+E)$
    • $V$ -> aantal knopen
    • $E$ -> aantal randen
Datastructuren en algoritmen in Python

Breadth-first search - grafen

Grafische weergave van breadth-first search op een graaf.

Datastructuren en algoritmen in Python

BFS vs DFS

BFS

  • Doelwit dicht bij de startknoop
  • Toepassingen:
    • Webcrawlen
    • Kortste pad in ongewogen grafen
    • Verbonden locaties vinden met GPS
    • Onderdeel van complexere algoritmen

DFS

  • Doelwit ver van de startknoop
  • Toepassingen:
    • Puzzels met één oplossing (bv. doolhoven)
    • Cycli detecteren in grafen
    • Kortste pad in een gewogen graaf
    • Onderdeel van complexere algoritmen
Datastructuren en algoritmen in Python

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Datastructuren en algoritmen in Python

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