C allows statements of the form # include filenamewhich reads filename and inserts its

Write a program to solve the selection problem. Let K=N/2. Draw a table showing the running time of your program for various values of N.

Write a program to solve the word puzzle problem

Write a method to output an arbitrary double number (which might be negative) using only printDigit for I/O.

C allows statements of the form # include filename which reads filename and inserts its contents in place of the include statement. Include statements may be nested; in other words, the file filename may itself contain an include statement, but, obviously, a file cant include itself in any chain. Write a program that reads in a file and outputs the file as modified by the include statements.

Write a recursive method that returns the number of 1s in the binary representation of N. Use the fact that this is equal to the number of 1s in the representation of N/2, plus 1, if N is odd.

Write the routines with the following declarations: public void permute( String str ); private void permute( char [ ] str, int low, int high ); The first routine is a driver that calls the second and prints all the permutations of the characters in String str. If str is "abc", then the strings that are output are abc, acb, bac, bca, cab, and cba. Use recursion for the second routine.

Prove the following formulas: a. log X < X for all X > 0 b. log(AB) = B log A

Evaluate the following sums: a. i=0 1 4i b. i=0 i 4i c. i=0 i 2 4i d. i=0 i N 4i 1

Estimate N i= N/2

What is 2100 (mod 5)?

Let Fi be the Fibonacci numbers as defined in Section 1.2. Prove the following: a. N2 i=1 Fi = FN 2 b. FN < N, with = (1 + 5)/2 c. Give a precise closed-form expression for FN. 1

Prove the following formulas: a. N i=1(2i 1) = N2 b. N i=1i 3 = N i=1i 2 1.

Design a generic class, Collection, that stores a collection of Objects (in an array), along with the current size of the collection. Provide public methods isEmpty, makeEmpty, insert, remove, and isPresent. isPresent(x) returns true if and only if an Object that is equal to x (as defined by equals) is present in the collection.

Design a generic class, Collection, that stores a collection of Objects (in an array), along with the current size of the collection. Provide public methods isEmpty, makeEmpty, insert, remove, and isPresent. isPresent(x) returns true if and only if an Object that is equal to x (as defined by equals) is present in the collection.

Define a Rectangle class that provides getLength and getWidth methods. Using the findMax routines in Figure 1.18, write a main that creates an array of Rectangle and finds the largest Rectangle first on the basis of area, and then on the basis of perimeter.