Pencarian Lebar Dulu (BFS)

Struktur Data dan Algoritma di Python

Miriam Antona

Software engineer

Breadth first search - pohon biner

  • Mulai dari root
  • Kunjungi semua node di tiap level

Representasi grafis BFS pada pohon pencarian biner.

Struktur Data dan Algoritma di Python

Breadth first search - pohon biner

  def bfs(self):

    if self.root:

      visited_nodes = []

      bfs_queue = queue.SimpleQueue()

Representasi grafis pohon pencarian biner.

  • visited_nodes:
  • bfs_queue:
Struktur Data dan Algoritma di Python

Breadth first search - pohon biner

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

      while not bfs_queue.empty():

Representasi grafis pohon pencarian biner.

  • visited_nodes:
  • bfs_queue: 65
Struktur Data dan Algoritma di Python

Breadth first search - pohon biner

  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()

Representasi grafis pohon pencarian biner.

  • visited_nodes:
  • bfs_queue:
  • current_node: 65
Struktur Data dan Algoritma di Python

Breadth first search - pohon biner

  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:

Representasi grafis pohon pencarian biner.

  • visited_nodes: 65
  • bfs_queue:
  • current_node: 65
Struktur Data dan Algoritma di Python

Breadth first search - pohon biner

  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)

Representasi grafis pohon pencarian biner.

  • visited_nodes: 65
  • bfs_queue: 20
  • current_node: 65
Struktur Data dan Algoritma di Python

Breadth first search - pohon biner

  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)

Representasi grafis pohon pencarian biner.

  • visited_nodes: 65
  • bfs_queue: 20, 70
  • current_node: 65
Struktur Data dan Algoritma di Python

Breadth first search - pohon biner

  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)

Representasi grafis pohon pencarian biner.

  • visited_nodes: 65
  • bfs_queue: 70
  • current_node: 20
Struktur Data dan Algoritma di Python

Breadth first search - pohon biner

  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)

Representasi grafis pohon pencarian biner.

  • visited_nodes: 65, 20
  • bfs_queue: 70
  • current_node: 20
Struktur Data dan Algoritma di Python

Breadth first search - pohon biner

  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)

Representasi grafis pohon pencarian biner.

  • visited_nodes: 65, 20
  • bfs_queue: 70, 10
  • current_node: 20
Struktur Data dan Algoritma di Python

Breadth first search - pohon biner

  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)

Representasi grafis pohon pencarian biner.

  • visited_nodes: 65, 20
  • bfs_queue: 70, 10, 22
  • current_node: 20
Struktur Data dan Algoritma di Python

Breadth first search - pohon biner

  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)

Representasi grafis pohon pencarian biner.

  • visited_nodes: 65, 20
  • bfs_queue: 10, 22
  • current_node: 70
Struktur Data dan Algoritma di Python

Breadth first search - pohon biner

  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)

Representasi grafis pohon pencarian biner.

  • visited_nodes: 65, 20, 70
  • bfs_queue: 10, 22
  • current_node: 70
Struktur Data dan Algoritma di Python

Breadth first search - pohon biner

  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)

Representasi grafis pohon pencarian biner.

  • visited_nodes: 65, 20, 70
  • bfs_queue: 10, 22, 68
  • current_node: 70
Struktur Data dan Algoritma di Python

Breadth first search - pohon biner

  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)

Representasi grafis pohon pencarian biner.

  • visited_nodes: 65, 20, 70
  • bfs_queue: 10, 22, 68, 75
  • current_node: 70
Struktur Data dan Algoritma di Python

Breadth first search - pohon biner

  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)

Representasi grafis pohon pencarian biner.

  • visited_nodes: 65, 20, 70, 10
  • bfs_queue: 22, 68, 75
  • current_node: 10
Struktur Data dan Algoritma di Python

Breadth first search - pohon biner

  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)

Representasi grafis pohon pencarian biner.

  • visited_nodes: 65, 20, 70, 10
  • bfs_queue: 68, 75
  • current_node: 22
Struktur Data dan Algoritma di Python

Breadth first search - pohon biner

  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)

Representasi grafis pohon pencarian biner.

  • visited_nodes: 65, 20, 70, 10, 22
  • bfs_queue: 68, 75
  • current_node: 22
Struktur Data dan Algoritma di Python

Breadth first search - pohon biner

  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)

Representasi grafis pohon pencarian biner.

  • visited_nodes: 65, 20, 70, 10, 22, 68
  • bfs_queue: 75
  • current_node: 68
Struktur Data dan Algoritma di Python

Breadth first search - pohon biner

  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)

Representasi grafis pohon pencarian biner.

  • visited_nodes: 65, 20, 70, 10, 22, 68
  • bfs_queue:
  • current_node: 75
Struktur Data dan Algoritma di Python

Breadth first search - pohon biner

  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)

Representasi grafis pohon pencarian biner.

  • visited_nodes: 65, 20, 70, 10, 22, 68, 75
  • bfs_queue:
  • current_node: 75
Struktur Data dan Algoritma di Python

Breadth first search - pohon biner

  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
  • Kompleksitas: $O(n)$

Representasi grafis pohon pencarian biner.

  • visited_nodes: 65, 20, 70, 10, 22, 68, 75
  • bfs_queue:
  • current_node: 75
Struktur Data dan Algoritma di Python

Breadth first search - graf

  • Graf bisa memiliki siklus
    • Perlu memeriksa apakah simpul sudah dikunjungi
Struktur Data dan Algoritma di Python

Breadth first search - graf

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
  • Kompleksitas: $O(V+E)$
    • $V$ -> jumlah simpul
    • $E$ -> jumlah sisi
Struktur Data dan Algoritma di Python

Breadth first search - graf

Representasi grafis BFS pada graf.

Struktur Data dan Algoritma di Python

BFS vs DFS

BFS

  • Sasaran dekat dengan simpul awal
  • Aplikasi:
    • Perayapan web
    • Mencari jalur terpendek pada graf tak berbobot
    • Menemukan lokasi terhubung dengan GPS
    • Digunakan dalam algoritme lain yang lebih kompleks

DFS

  • Sasaran jauh dari simpul awal
  • Aplikasi:
    • Memecahkan teka-teki dengan satu solusi (mis. labirin)
    • Mendeteksi siklus pada graf
    • Mencari jalur terpendek pada graf berbobot
    • Digunakan dalam algoritme lain yang lebih kompleks
Struktur Data dan Algoritma di Python

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Struktur Data dan Algoritma di Python

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