The Breadth-First Search

Report
報告者:李慧娟
教授:徐熊健
Contents
The Breadth-First Search
Depth-First Search
Hill Climbing
Best-First Search Strategy
The Breadth-First Search
The Breadth-First Search
The Breadth-First Search
Step 1
• Form a one-element queue consisting of the root node.
Step 2
• Test to see if the first element in the queue is a goal node.
If it is, stop. Otherwise, go to step 3.
Step 3
• Remove the first element from the queue. Add the first
element’s descendants, if any, to the end of the queue.
Step 4
• If the queue is empty, then failure. Otherwise, go to Step 2.
The Breadth-First Search
The Breadth-First Search
寬度優先搜尋(BFS)演算法
 Breadth-first search (BFS) is a general
technique for traversing a graph
 BFS on a graph with n vertices and m edges
takesO(n + m ) time
 依序走訪同一層的所有節點,走訪完畢後,才繼續走
訪下一層的節點
 BFS 會使用到Queue (佇列--先進先出) 來紀錄過程中
展開的節點
The Breadth-First Search
The Breadth-First Search
a
Queue
a
b
c
b
c
d
e
d
e
f
g
f
g
h
h
Output
Depth-First Search
The Breadth-First Search
Depth-First Search
Step 1
• Form a one-element stack consisting of the root node.
Step 2
• Test to see if the top element in the stack is a goal node. If
it is, stop; otherwise, go to step 3.
Step 3
• Remove the top element from the stack and add the first
element’s descendants, if any, to the top of the stack.
Step 4
• If the stack is empty, then failure. Otherwise, go to Step 2.
The Breadth-First Search
Depth-First Search
深度優先搜尋(DFS)演算法
 Depth-first search (DFS) is a general techniquefor
traversing a graph
 DFS on a graph with n vertices and m edges takes
O(n + m ) time
 先走訪越深的子節點, 直到該點沒有子節點後,回溯到最
近尚有未走訪子節點的節點,再繼續下訪其他節點
 DFS 會使用到Stack (堆疊—後進先出) 來紀錄過程中展
開的節點
The Breadth-First Search
Depth-First Search
a
b
Output
c
d
f
ebh
d
e
h
f
g
cg
a
-----Stack
日常生活中的例子:深度搜尋法(Depth-first search)
Hill Climbing
Hill Climbing
Step 1
• Form a one-element stack consisting of the root node.
Step 2
• Test to see if the top element in the stack is a goal node. If it is, stop;
otherwise, go to step 3.
Step 3
• Remove the top element from the stack and expand the element. Add
the descendants of the element into the stack ordered by the
evaluation function.
Step 4
• If the list is empty, then failure. Otherwise, go to Step 2.
Hill Climbing
 基本的Hill Climbing 演算法
1. 從搜尋空間中亂數取一點a作為出發點
2. 考慮a點周圍可用的狀態點
3. 取a點周圍最好品質(錯位少)的一點b,並移往b點
4. 重複2~4,直到找不到更好的點
5. 則最後的狀態點就是用Hill Climbing找到的最佳解
6. 若有兩點以上是最好解,則亂數擇一
 Hill Climbing並不能保證得到最佳化 solution,但卻可
以有近似 solution
Hill Climbing
 8-puzzle problem
 Given a initial arrangement and the goal state,
the problem is to determine whether there exists a sequence of
movements from initial state to goal state, where each item can be
moved only horizontally or vertically to the empty spot.
Example:
The initial arrangement and the goal state of the 8-puzzle problem.
Hill Climbing
 Hill Climbing strategy for 8-puzzle problem
 Evaluation function f(n) = w(n), where w(n) is # of
misplaced tiles in node n.
 The hill climbing strategy is to select the least f(n) to
expand the present node
Ex:
(3)
1, 2, 8 are misplace, f(n)=3
Hill Climbing
 An 8-puzzle problem solved
by a hill climbing method.
1
2
8
7
3
4
6
goal state
5
Best-First Search Strategy
Best-First Search Strategy
Step 1
• Construct a heap by using the evaluation function. First, form a
one-element heap consisting of the node.
Step 2
• Test to see if the root element in the heap is a goal node. If it is,
stop; otherwise, go to step 3.
Step 3
• Remove the heap element from the heap and expand the element.
Add the descendants of the element into the heap.
Step 4
• If the heap is empty, then failure. Otherwise, go to Step 2.
Best-First Search Strategy
 Combine depth-first search and breadth-first
search.
 這個搜尋法只是根據最佳化的評估函數來選擇下
一個搜尋的節點
 當評估函數的準確度愈高,則愈可能找到最佳的節點
 反之,評估函數可能無作用,甚至可能導至錯誤的搜
尋。
Best-First Search Strategy
 An 8-puzzle problem solved
by a hill climbing method.
1
2
8
7
3
4
6
5
goal state
Goal Node

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