1. A Las Vegas Algorithm for the 8 Queens problem
Lecture 35
CS 312

2. The Final In the testing center Use their calculators.
(or .doc)
In the testing center
Use their calculators.
Multiple choice.
Show work for partial credit
Review on Wednesday

3. Objectives Finish project 4
Explain the difference between Monte Carlo and Las Vegas algorithms
Decide how many queens to place at random in 8 queens.

4. QueensLV queensLV (n,stopLV) : bool =
place stopLV of the queens at random
so that no queens attack each other.
use backtracking to place the remaining n-stopLV queens
if successful, report a solution otherwise fail.

5. QueensLV 1 2
Random 3 4 5
Backtrack 6 7 8 1 2 3 4 5 6 7 8

6. How many nodes explored?
suppose s(n) nodes to succeed
and f(n) nodes to fail
with probability p(n) of succeeding

7. How many nodes explored?
suppose s(n) nodes to succeed
and f(n) nodes to fail
with probability p(n) of succeeding
t(x) = p(x)s(x) + (1-p(x))(f(x) + t(x)), or

8. Nodes Explored

9. How much time?
Authors report that for 8-queens, backtracking is still faster.
takes a long time to gen. a random number
For 39 queens, queensLV is faster.
41 hours using backtracking
8.5 ms using queensLV

10. Homework
None. Cancelled.