Question 1 A* is an informed search algorithm. What is an informed search? How is it different from uninformed search? Question 2 A* uses a heuristic function f(n) in its search for a solution. Explain the components of f(n). Why do you think f(n) is more effective than h(n), the heuristic function used by greedy best-first? Question 3 For A* to return the minimum-cost solution, the heuristic function used should be admissible and consistent. Explain what these two terms mean.
Answer the following questions
Question 1
A* is an informed search algorithm. What is an informed search? How is it different from uninformed search?
Question 2
A* uses a heuristic function f(n) in its search for a solution. Explain the components of f(n). Why do you think f(n) is more effective than h(n), the heuristic function used by greedy best-first?
Question 3
For A* to return the minimum-cost solution, the heuristic function used should be admissible and consistent. Explain what these two terms mean.
Question 4
For the 9-tile soring problem, assume that you start from this initial state
| 7 | 2 | 4 |
| 5 | 6 | |
| 8 | 3 | 1 |
The Goal State is:
| 1 | 2 | 3 |
| 4 | 5 | 6 |
| 7 | 8 |
The cost of moving any tile is 1.
Let the heuristic function h(n) = number of misplaced tiles.
For the shown configuration, there are four options for the next move:
- Move 5 to the right
- Move 6 to the left
- Move 2 down
- Move 3 up
Each of these moves has a value f(n) = h(n) + g(n).
- If we choose to Move 5 to the right, then
- g(n) = 1. That is, it took us one step to reach this state from the initial state.
- h(n) = number of misplaced tiles. The misplaced tiles are {7,4,8,3,1}. So the number of misplaced tiles = h(n) = 5.
If we choose to Move 6 to the left, g(n) is still = 1, but h(n) will change because the number of misplaced tiles is different.
A* works by computing f(n) = h(n) + g(n) for each of these possible moves. Then it chooses the move with the lowest f(n).
Apply A* to generate 3 states starting at the initial state above. That is, show the next three moves that will be chosen by A*. Show your calculations to compute g(n), h(n) and f(n) for all the possible moves (states).
Question 5
Repeat the exercise above with the 9-tile sorting problem using the heuristic function:
h(n) = sum of distances of tiles from their goal position
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Hi please answer the following follow up questions as well, posted them as another question.
Question 4
For the 9-tile soring problem, assume that you start from this initial state
| 7 | 2 | 4 |
| 5 | 6 | |
| 8 | 3 | 1 |
The Goal State is:
| 1 | 2 | 3 |
| 4 | 5 | 6 |
| 7 | 8 |
The cost of moving any tile is 1.
Let the heuristic function h(n) = number of misplaced tiles.
For the shown configuration, there are four options for the next move:
- Move 5 to the right
- Move 6 to the left
- Move 2 down
- Move 3 up
Each of these moves has a value f(n) = h(n) + g(n).
- If we choose to Move 5 to the right, then
- g(n) = 1. That is, it took us one step to reach this state from the initial state.
- h(n) = number of misplaced tiles. The misplaced tiles are {7,4,8,3,1}. So the number of misplaced tiles = h(n) = 5.
If we choose to Move 6 to the left, g(n) is still = 1, but h(n) will change because the number of misplaced tiles is different.
A* works by computing f(n) = h(n) + g(n) for each of these possible moves. Then it chooses the move with the lowest f(n).
Apply A* to generate 3 states starting at the initial state above. That is, show the next three moves that will be chosen by A*. Show your calculations to compute g(n), h(n) and f(n) for all the possible moves (states).
Question 5
Repeat the exercise above with the 9-tile sorting problem using the heuristic function:
h(n) = sum of distances of tiles from their goal position
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