Breadth First Search (BFS)

Cấu trúc dữ liệu và Thuật toán với 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.

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:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Breadth first search - graphs

Graphs can have cycles
- Need to check if the vertices have already been visited

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

Breadth first search - graphs

Graphical representation of bread first search over a graph.

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

Let's practice!

Cấu trúc dữ liệu và Thuật toán với Python