Figure 5.1 a) Five queens that cannot attack each other, but that can attack all of column 6; b) backtracking to column 5 to try another square for the.

Slides:



Advertisements
Similar presentations
Polynomial Time Algorithms for the N-Queen Problem Rok sosic and Jun Gu.
Advertisements

8 Queens. Problem: Placing 8 queens on a chessboard such that they don’t attack each other Three different Prolog programs are suggessted as solutions.
AB 11 22 33 44 55 66 77 88 99 10  20  19  18  17  16  15  14  13  12  11  21  22  23  24  25  26  27  28.
Eight queens puzzle. The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard such that none of them are able to capture.
© 2006 Pearson Addison-Wesley. All rights reserved6-1 Chapter 6 Recursion as a Problem- Solving Technique.
Chapter 5 Recursion as a Problem-Solving Technique.
P247. Figure 9-1 p248 Figure 9-2 p251 p251 Figure 9-3 p253.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. C H A P T E R S E V E N Object-Oriented Programming.
8.6 Examples Example 1 STUV has at least one pair of consecutive sides that are congruent. What type of quadrilateral meets this condition? (rhombus,
COSC2007 Data Structures II
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley. Ver Chapter 5: Recursion as a Problem-Solving Technique Data Abstraction.
Back Tracking Project Due August 11, 1999 N-queens: –A classic puzzle for chess buffs is the N- Queens problem. Simply stated: is it possible to place.
HISTORY The problem was originally proposed in 1848 by the chess player Max Bezzel, and over the years, many mathematicians, including Gauss have worked.
Recursion as a Problem- Solving Technique Chapter 5 Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013.
Algebra 1 Notes: Lesson 1-1: Variables and Expressions
Data Structures Using C++ 2E1 Recursion and Backtracking: DFS Depth first search (a way to traverse a tree or graph) Backtracking can be regarded as a.
EXAMPLES OF RECURSION Towers of Hanoi Writing Linked Lists Backwards Recursive Insert 8 Queens Recognizing Simple Languages Prefix Expressions Conversion.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley. Ver Chapter 5: Recursion as a Problem-Solving Technique Data Abstraction.
Recursion as a Problem- Solving Technique Chapter 5 Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013.
Tuesday, July 1 Special Factoring. Difference of Squares Example: m 2 – 64 (m) 2 – (8) 2 (m + 8)(m – 8)
Special Factoring. Difference of Squares General Formula: (x) 2 – (y) 2 = (x + y)(x – y)
© 2006 Pearson Addison-Wesley. All rights reserved 6-1 Chapter 6 Recursion as a Problem- Solving Technique.
Factor completely EXAMPLE 4 Factor the polynomial completely. a.a. n 2 – + 2n –1 SOLUTION a.a. The terms of the polynomial have no common monomial factor.
Problem of the Day Problem of the Day Geometry Squares next.
$200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200.
Eight Queens Problem The problem is to place 8 queens on a chess board so that none of them can attack the other. A chess board can be considered a plain.
GEOMETRY A Review of Shapes in Geometry Grades 9-12 Jon Dressler Forward.
Non-Standard Measurement
Chapter 5 Recursion as a Problem-Solving Technique
Edit from old slide since 2000 P. Chongstitvatana 26 Nov 2010
Intro to Computer Science II
1.4 Sketching Intersections
Additional Example 3 Additional Example 4
Fundamentals of Programming II Backtracking with Stacks
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"?
Do Now Factor. 18a5b2 – 30a3b7 64 – x2 x2 – 10x + 24.
Properties of Addition and Multiplication
BACK SOLUTION:
Surface Area of Pyramids, Cones and Spheres
Back Tracking.
Number Words   two one three.
Line, line segment and rays.
Surface Area of Pyramids, Cones and Spheres
THE BUSY BEE BAŞLA The bee is very busy learning the numbers. Help her with the matching.
Warm-Up: Write down what remains. c..
Example: If line AB is parallel to line CD and s is parallel to t, find the measure of all the angles when m< 1 = 100°. Justify your answers. t
Value to Make Ratios Equal
CS Software Studio Assignment 1
Prabhas Chongstitvatana
Proportion.
Surface Area of Pyramids, Cones and Spheres
Try again! Try again! Well done!
Parallel and intersecting lines
In order to draw parallel lines
Recursion as a Problem-Solving Technique
½ of 6 = 3.
Difference of Two Squares
CHOOSE THE CORRECT NUMBER
6 Figure Grid References
Algebraic Deduced Identities
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"?
Where do these graphs intersect
Area of combined figures
Angles at a point.
Proportion – Finding Missing Value
Factorization by identity (x + a)(x + b).
Announcements Assignment #4 is due tonight. Last lab program is going to be assigned this Wednesday. ◦ A backtracking problem.
Factoring Polynomials, Special Cases
Factorization by identity a3 + b3.
What’s the time? CLICK ON THE CLOCK.
Presentation transcript:

Figure 5.1 a) Five queens that cannot attack each other, but that can attack all of column 6; b) backtracking to column 5 to try another square for the queen; c) backtracking to column 4 to try another square for the queen and then considering column 5 again

Figure 5.2 A solution to the Eight Queens problem

Figure 5.3 A syntax diagram for Java identifiers

Figure 5.4a Trace of isId(“A2B”)

Figure 5.4b Trace of isId(“A2B”)

Figure 5.5a Trace of endPre(first, last), where strExp is +/ab-cd

Figure 5.5b Trace of endPre(first, last), where strExp is +/ab-cd

Figure 5.5c Trace of endPre(first, last), where strExp is +/ab-cd

Figure 5.5d Trace of endPre(first, last), where strExp is +/ab-cd