C++ How to Program (Early Objects Version)
10th Edition
ISBN: 9780134448824
Author: Paul Deitel; Harvey M. Deitel
Publisher: Pearson Education (US)
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Chapter 7, Problem 7.23E
(Knight's Tour: Brute Forty Approaches ) In Exercise 7.22, we developed a solution to the Knight's Tour problem. The approach used, called the "'accessibility heuristic," generates many solutions and executes efficiently.
As computers continue increasing in power, we'll be able to solve more problems with sheer computer power and relatively unsophisticated algorithms. This is the "brute force" approach to problem solving.
- Use random number generation to enable the knight to walk around the chessboard (in its legitimate L—shaped moves, of course) at random, Your
program should run one tour and print the final chessboard. How far did the knight get? - Most likely, the preceding program produced a relatively short tour. Now modify your program to attempt 1000 tours. Use a one-dimensional array to keep track of the number of tours of each length. When your program finishes attempting the 1000 tours, it should print this information in near tabular format. What was the best result?
- Most likely, the preceding program gave you some "respectable" tours, but no full tours. NOW "pull all the stops out" and simply let your program run until it produces a full Tour. [Caution. This version of the program could run for hours on a powerful computer. ] Once again, keep a table of the number of tours of each length, and print this when the first full tour is found. How many tours did your program attempt before producing a full tour? How much time did it take?
- Compare the brute force version Of the Knight's Tour with the accessibility heuristic version. Which required a more careful study of the problem? Which
algorithm was more difficult to develop? Which required more computer power? Could we be certain (in advance) of obtaining a full tour with the accessibility heuristic approach? Could we be certain (in advance) of obtaining a full tour with the brute force approach? Argue the pros and cons of brute-force problem-solving in general.
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The Towers of Hanoi is a famous problem for studying recursion in computer science and searching in artificial intelligence. We start with N discs of varying sizes on a peg (stacked in order according to size), and two empty pegs. We are allowed to move a disc from one peg to another, but we are never allowed to move a larger disc on top of a smaller disc. The goal is to move all the discs to the rightmost peg (see figure). To solve the problem by using search methods, we need first formulate the problem. Supposing there are K pegs and N disk.
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Develop a solver for the n-queens problem: n queens are to be placed on an n x n chessboard so that no pair of queens can attack each other. Recall that in chess, a queen can attack any piece that lies in the same row, column, or diagonal as itself.
A brief treatment of this problem for the case where n = 8 is given below (from the 3rd edition of AIMA).
N-queens is a useful test problem for search, with two main kinds of formulation. An incremental formulation involves operators that augment the state description, starting with an empty state; for the 8-queens problem, this means that each action adds a queen to the state. A complete-state formulation starts with all 8 queens on the board and moves them around. (In either case, the path cost is of no interest because only the final state counts.) The first incremental formulation one might try is…
Chapter 7 Solutions
C++ How to Program (Early Objects Version)
Ch. 7 - Exercises 7.6(Fill in the Blanks) Fill in the...Ch. 7 - (True or False) Determine whether each of the...Ch. 7 - (Write C++ Statements) Write C++ statements to...Ch. 7 - (Two-Dimensional array Questions) Consider a...Ch. 7 - (Salesperson Salary Ranges) Use a one-dimensional...Ch. 7 - (One-Dimensional array Questions) Write statements...Ch. 7 - (Find the Errors) Find the error(s) in each of the...Ch. 7 - (Duplicate Elimination with array) Use a...Ch. 7 - Prob. 7.14ECh. 7 - Prob. 7.15E
Ch. 7 - (Dice Rolling) Write a program that simulates...Ch. 7 - ( What Does This Code Do?) What does the following...Ch. 7 - (Craps Game Modification) Modify the program of...Ch. 7 - (Converting vector Example of Section 7.10 to...Ch. 7 - Prob. 7.20ECh. 7 - (Sales Summary) Use a two-dimensional array to...Ch. 7 - (Knight's Tour) One of the more interesting...Ch. 7 - (Knight's Tour: Brute Forty Approaches ) In...Ch. 7 - (Eight Queens) Another puzzler for chess buffs is...Ch. 7 - (Eight Queens: Brute Force Approaches) In this...Ch. 7 - Prob. 7.26ECh. 7 - (The Sieve of Eratosthenes) A prime integer is any...Ch. 7 - Prob. 7.28RECh. 7 - (Eight Queens) Modify the Eight Queens program you...Ch. 7 - (Print an array) Write a recursive function...Ch. 7 - Prob. 7.31RECh. 7 - Prob. 7.32RECh. 7 - (Maze Traversal) The grid of hashes (#) and dots...Ch. 7 - Prob. 7.34RECh. 7 - Making a Difference 7.35 (Polling) The Internet...
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