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16-recursive_backtracking-2

# 16-recursive_backtracking-2 - CSE143 Lecture16...

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CSE 143 Lecture 16 More Recursive Backtracking slides created by Marty Stepp and Ethan Apter http://www.cs.washington.edu/143/

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2 The "8 Queens" problem Consider the problem of trying to place 8 queens on a chess  board such that no queen can attack another queen. What are the "choices"? How do we "make" or "un-make" a choice? How do we know when to stop? Q Q Q Q Q Q Q Q
3 Naive algorithm for (each square on board): Place a queen there. Try to place the rest of the queens. Un-place the queen. How large is the solution space for this algorithm? 64 * 63 * 62 * ... 1 2 3 4 5 6 7 8 1 Q ... ... ... ... ... ... ... 2 ... ... ... ... ... ... ... ... 3 ... 4 5 6 7 8

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4 Better algorithm idea Observation: In a working solution, exactly 1 queen must appear in each row and in each column. Redefine a "choice" to be valid placement of a queen in a particular column. How large is the solution space now? 8 * 8 * 8 * ... 1 2 3 4 5 6 7 8 1 Q ... ... 2 ... ... 3 Q ... 4 ... 5 Q 6 7 8
5 Exercise Suppose we have a  Board  class with the following methods: Write a method  solveQueens  that accepts a  Board  as a  parameter and tries to place 8 queens on it safely. Your method should stop exploring if it finds a solution. Method/Constructor Description public Board (int size) construct empty board public boolean isSafe (int row, int column) true  if queen can be safely placed here public void place

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16-recursive_backtracking-2 - CSE143 Lecture16...

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