Arrays

First of all, my solution to the last homework assignment (the 5 functions that you had to write) is given below. Notice that there are lots of ways you could write square root and cube root in, but this is the most primitive and straightforward way and it is what I expected of you guys to be able to write. Thanks to someone from the afternoon section for pointing out that the original cube root function I had written didn't take care of negative numbers (that you pass in). It is now corrected and does so correctly.

#include <stdio.h>
#include "../inc/simpio.h"

#define Epsilon 0.000001

double RaiseRealToPower(double x, int k) {
	int i;
	double answer = 1;
	if (k < 0) {
		k = -k;
		for (i = 0; i < k; i++) {
			answer *= x;
		}
		return (1/answer);
	} else {
		for (i = 0; i < k; i++) {
			answer *= x;
		}
		return answer;
	}
}

double AbsoluteValue(double x) {
	if (x < 0) {
		return -x;
	} else {
		return x;
	}
}

bool ApproximatelyEqual(double x, double y) {
	double result;
	if (AbsoluteValue(x) < AbsoluteValue(y)) {
		result = AbsoluteValue(x-y)/AbsoluteValue(x);
	} else {
		result = AbsoluteValue(x-y)/AbsoluteValue(y);
	}
	return (result < Epsilon);
}

double sqrt(double x) {
	double i;
	if (x < 0)
		return 0;
	for (i = 0; (!ApproximatelyEqual(RaiseRealToPower(i, 2), x)) && i < x; i += 0.000001);
	return i;
}

double cbrt(double x) {
	double i, cubed = x;
	if (x < 0)
		cubed = -cubed;
	for (i = 0; (!ApproximatelyEqual(RaiseRealToPower(i, 3), cubed)) && i < cubed; i += 0.000001);
	if (x < 0)
		return -i;
	else
		return i;
}

int main() {
	int i;
	double result, k;
	for (i = -10; i <= 10; i++) {
		result = RaiseRealToPower(2, i);
		printf("%d^%d = %f\n", 2, i, result);
	}
	printf("AbsoluteValue(%f) = %f\n", -5.4, AbsoluteValue(-5.4));
	printf("AbsoluteValue(%f) = %f\n", 3.2, AbsoluteValue(3.2));
	for (k = -5; k <= 5; k += 1.0) {
		result = sqrt(k);
		printf("sqrt(%f) = %f\n", k, result);
	}
	for (k = -5; k <= 5; k += 1.0) {
		result = cbrt(k);
		printf("cbrt(%f) = %f\n", k, result);
	}
}

Arrays are a series of consecutive memory locations that all have the same name.

To declare an array declare it just like any other variable:

int grades[100];

In C the memory allocations are labeled from 0-99. This means that grade[0] is the first element of the array and grade[1] is he second element of the array. The number inside the brackets is called a subscript.

Array elements can be initialized at the time of declaration:

int counter[5] = {0,1,2,3,4};
char letters[4] = {'a','b','c','d'};

You do not have to initialize the whole array. If you initialize the first part of the array the rest of the elements are set to 0. In a character array the rest of the characters are set to null ('\0').

If you wish to initialize an array after declaration, you cannot use this last method we discussed. You must use a loop to initialize the elements:

for (i = 0; i < 5; i++)
	counter[i] = 0;

In the statement:

char word[] = {'H','e','l','l','o','!'};

You don’t have to specify the size of the array, the computer Will automatically make the size equal to the number of initialized characters. In this case the size of the array is six and there is no room reserved for the null. Another shortcut to initialize this array is to do the following:

char word[] = {"Hello!"};    // 7 elements long

Reasons for using arrays:

1. For holding areas in memory
2. For accumulations and to store totals
3. For table making
4. To form strings

Macros are used when you want to define a set number to a name and make that available to all functions.

#define MAX 10
// MAX is not a variable but is accessible to all functions.

You are a meteorologist and your job is to find the average temperature of each month. Your boss, however, wants you to print out a chart for him that shows him, in addition to the average temperature of the month, the daily temperatures and their deviation from the average.

Hint: The deviation is calculated by taking the temperature and subtracting the average temperature of the month.

Use the macro MAX 30 in your program.

You are a judge for the Miss America contest. Your boss is tired of the corruption that has been happening in previous contests so he tells you to fix this. Your job is to design a program that tallies the votes of the judges, prints out the results, and prints out who the winner is. (hint: when girl number is 0 print out results and print out winner)

Enter vote by typing in girl number #
...
Girl #     # of Votes
            3
...     
The winner is girl number 3!

Your homework assignment is to:

1. finish the classwork programs that you did not finish in class.
2. think of one question that you think should be on the midterm, and bring it on Friday.
3. think of questions that you want to ask us in the review session in class on Friday, like anything you don't understand well and want us to explain again.