Compare the number of queen positions examined and the elapsed time for the programs that you wrote for Exercises 12, 13, and 14, respectively. Exercises 12, 13, and 14 *To make another improvement to...

Compare the number of queen positions examined and the elapsed time for the programs that you wrote for Exercises 12, 13, and 14, respectively.

Exercises 12, 13, and 14

*To make another improvement to the eight queens problem, notice that every row on the chessboard must hold a single queen. Modify the program you wrote for Exercise 13 so that each call to the Eight Queens method searches only the next row for the new queen’s position.

Exercise 13

*One improvement that you can make to the eight queens problem is to keep track of how many queens can attack a particular position on the board. Then, when you are considering adding a queen to the board, you can ignore any positions where this value isn’t 0. Modify the program you wrote for Exercise 12 to use this improvement.

Exercise 12

*Write a program that solves the eight queens problem. In addition to the solution, display the number of queen positions examined and the time the program takes to solve the problem.