Breadth First Search (BFS)

Data Structures and Algorithms in Python

Miriam Antona

Software engineer

Breadth first search - binary trees

  • Starts from the root
  • Visits every node of every level

Graphical representation of bread first search over a binary search tree.

Data Structures and Algorithms in Python

Breadth first search - binary trees

  def bfs(self):

    if self.root:

      visited_nodes = []

      bfs_queue = queue.SimpleQueue()

Graphical representation of a binary search tree.

  • visited_nodes:
  • bfs_queue:
Data Structures and Algorithms in Python

Breadth first search - binary trees

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

      while not bfs_queue.empty():

Graphical representation of a binary search tree.

  • visited_nodes:
  • bfs_queue: 65
Data Structures and Algorithms in Python

Breadth first search - binary trees

  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()

Graphical representation of a binary search tree.

  • visited_nodes:
  • bfs_queue:
  • current_node: 65
Data Structures and Algorithms in Python

Breadth first search - binary trees

  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:

Graphical representation of a binary search tree.

  • visited_nodes: 65
  • bfs_queue:
  • current_node: 65
Data Structures and Algorithms in Python

Breadth first search - binary trees

  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)

Graphical representation of a binary search tree.

  • visited_nodes: 65
  • bfs_queue: 20
  • current_node: 65
Data Structures and Algorithms in Python

Breadth first search - binary trees

  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)

Graphical representation of a binary search tree.

  • visited_nodes: 65
  • bfs_queue: 20, 70
  • current_node: 65
Data Structures and Algorithms in Python

Breadth first search - binary trees

  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)

Graphical representation of a binary search tree.

  • visited_nodes: 65
  • bfs_queue: 70
  • current_node: 20
Data Structures and Algorithms in Python

Breadth first search - binary trees

  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)

Graphical representation of a binary search tree.

  • visited_nodes: 65, 20
  • bfs_queue: 70
  • current_node: 20
Data Structures and Algorithms in Python

Breadth first search - binary trees

  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)

Graphical representation of a binary search tree.

  • visited_nodes: 65, 20
  • bfs_queue: 70, 10
  • current_node: 20
Data Structures and Algorithms in Python

Breadth first search - binary trees

  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)

Graphical representation of a binary search tree.

  • visited_nodes: 65, 20
  • bfs_queue: 70, 10, 22
  • current_node: 20
Data Structures and Algorithms in Python

Breadth first search - binary trees

  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)

Graphical representation of a binary search tree.

  • visited_nodes: 65, 20
  • bfs_queue: 10, 22
  • current_node: 70
Data Structures and Algorithms in Python

Breadth first search - binary trees

  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)

Graphical representation of a binary search tree.

  • visited_nodes: 65, 20, 70
  • bfs_queue: 10, 22
  • current_node: 70
Data Structures and Algorithms in Python

Breadth first search - binary trees

  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)

Graphical representation of a binary search tree.

  • visited_nodes: 65, 20, 70
  • bfs_queue: 10, 22, 68
  • current_node: 70
Data Structures and Algorithms in Python

Breadth first search - binary trees

  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)

Graphical representation of a binary search tree.

  • visited_nodes: 65, 20, 70
  • bfs_queue: 10, 22, 68, 75
  • current_node: 70
Data Structures and Algorithms in Python

Breadth first search - binary trees

  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)

Graphical representation of a binary search tree.

  • visited_nodes: 65, 20, 70, 10
  • bfs_queue: 22, 68, 75
  • current_node: 10
Data Structures and Algorithms in Python

Breadth first search - binary trees

  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)

Graphical representation of a binary search tree.

  • visited_nodes: 65, 20, 70, 10
  • bfs_queue: 68, 75
  • current_node: 22
Data Structures and Algorithms in Python

Breadth first search - binary trees

  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)

Graphical representation of a binary search tree.

  • visited_nodes: 65, 20, 70, 10, 22
  • bfs_queue: 68, 75
  • current_node: 22
Data Structures and Algorithms in Python

Breadth first search - binary trees

  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)

Graphical representation of a binary search tree.

  • visited_nodes: 65, 20, 70, 10, 22, 68
  • bfs_queue: 75
  • current_node: 68
Data Structures and Algorithms in Python

Breadth first search - binary trees

  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)

Graphical representation of a binary search tree.

  • visited_nodes: 65, 20, 70, 10, 22, 68
  • bfs_queue:
  • current_node: 75
Data Structures and Algorithms in Python

Breadth first search - binary trees

  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)

Graphical representation of a binary search tree.

  • visited_nodes: 65, 20, 70, 10, 22, 68, 75
  • bfs_queue:
  • current_node: 75
Data Structures and Algorithms in Python

Breadth first search - binary trees

  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
  • Complexity: $O(n)$

Graphical representation of a binary search tree.

  • visited_nodes: 65, 20, 70, 10, 22, 68, 75
  • bfs_queue:
  • current_node: 75
Data Structures and Algorithms in Python

Breadth first search - graphs

  • Graphs can have cycles
    • Need to check if the vertices have already been visited
Data Structures and Algorithms in Python

Breadth first search - graphs

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
  • Complexity: $O(V+E)$
    • $V$ -> number of vertices
    • $E$ -> number of edges
Data Structures and Algorithms in Python

Breadth first search - graphs

Graphical representation of bread first search over a graph.

Data Structures and Algorithms in Python

BFS vs DFS

BFS

  • Target close to the starting vertex
  • Applications:
    • Web crawling
    • Finding shortest path in unweighted graphs
    • Finding connected locations using GPS
    • Used as part of other more complex algorithms

DFS

  • Target far away from the starting vertex
  • Applications:
    • Solving puzzles with only one solution (e.g. mazes)
    • Detecting cycles in graphs
    • Finding shortest path in a weighted graph
    • Used as part of other more complex algorithms
Data Structures and Algorithms in Python

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Data Structures and Algorithms in Python

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