CSC212 Homework 5 2014

--D. Thiebaut (talk) 23:24, 22 October 2014 (EDT)

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Problem #1

• Write a recursive Java program called Hw5_1.java that implements a modified recursive binary search that, instead of returning the index where the key was found, returns an ArrayList of all the indexes where the key is located.
• You must use this function to create a sorted array of dimension N:

        private static int[] initSortedArray( int N ) {
                if ( N<10 ) N = 10;
                int[] array = new int[N];
                array[0] = 3;
                for ( int i=1; i<N; i++ ) 
                        array[ i ] = array[i-1] + (i*11)%7;
               
                // duplicate some keys 
                for ( int i=1; i<4; i++ )
                        array[ N/3 + i] = array[N/3];
                
                return array;
        }

This way the indexes for a given key will be known to the testing program in Moodle. For verification, this is the array created by the function for N = 20:

3 7 8 13 15 21 24 24 24 24 34 36 42 45 45 49 50 55 57 63 

• If the array contains [3 7 8 13 15 21 24 24 24 24 34 36 42 45 45 49 50 55 57 63], and we are searching for key 24, then your program will output

6
7
8
9

• You cannot use an iterative method that is not recursive.
• Submit your program on Moodle, in the Homework 5, Problem 1 section.

Problem #2

• Modify the N-Queens problem seen in Lab #9 and make it compute the total number of different solutions existing for an NxN board. The program as we have seen in the lab stops when it finds a solution, but there might be many different possible ways of putting N queens on the NxN board. Make your program compute the total number of such solutions.
• Call your program Hw5_2.java.
• The output of your program should just be an integer number representing the number of solutions.
• Your program will get N from the command line, as in:

 java Hw5_2  20

which will compute the total number of different ways we can organize 20 queens on a 20x20 chessboard.