Introduction to Programming (22C:16, 22C:106)

Homework 2: Due Thursday, 2/6/97

Problem 1: [7 points]

This problem is partly a puzzle and partly an exercise in writing a simple C++ program. Write a C++ program that reads in an integer x and produces as output the value of the expression:

So the main task that your program needs to perform is computing the value of the above expression. This is fairly straightforward given what you have already learned. But, I want your program to satisfy some additional requirements: your program should use no more than 4 addition operations (in all) and no more than 3 multiplication operations (in all). It may be possible to do it using fewer arithmetic operations. This additional requirement does not affect the correctness of the program you write, but it does affect the efficiency (that is the amount of time taken to run) of your program.

Hint: In my solution the only addition operations used are increment operations, that is, operations that increase a value by 1.

Problem 2: [7 points]

Write a C++ program to solve the following problem:

Given an integer called key and a sequence of 100 integers determine whether key is an element in the given sequence.

Problem 3: [6 points]

Consider the following program:

 
	#include <iostream.h>
	void dream()
	{
		cout << "I have a dream today." << endl;
		cout << "I have a dream that one day" << endl;
	}

	void manyDreams()
	{
		cout << "every valley will be exalted. " << endl;
		dream();
		cout << "this nation will rise up and live out"
		<< "the true meaning of its creed." << endl;
		dream();
	}

	int main()
	{
		dream();
		manyDreams();
		cout << "this land will be transformed into " <<
		<< "an oasis of freedom and justice." << endl;
		return 0;
	}

(a)

Label the statements in this program so as to show the flow of control of the program. In other words, label the statement that gets executed first 1, label the statement that gets executed next 2 and so on. Note that a statement might get labeled several times.

(b)

Write down the output produced by the above program.

Acknowledgement: The influence on this problem of the 1963 speech in Washington D.C. by Dr. Martin Luther King, Jr. is acknowledged.