A Las Vegas Algorithm for the 8 Queens

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

The Final • http: //faculty. cs. byu. edu/~jones/312/sample_final. pdf (or. doc) • • • In the testing center Use their calculators. Multiple choice. Show work for partial credit Review on Wednesday

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.

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

Queens. LV 1 Random 2 3 4 5 Backtrack 6 7 8 1 2 3 4 5 6 7 8

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

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

Nodes Explored

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, queens. LV is faster. – 41 hours using backtracking – 8. 5 ms using queens. LV

Homework • None. Cancelled.