A6: Asmt#6: Integration using trapezoids

Write a C program to do the following.

The first integer value (not prompted nor echoed) determines how the output is displayed, in the manner of previous works. For more information, see Debugging via output .

You are given the following data as a list. All values are floating point approximations.

A width of each sample (first data value, a positive value).
A collection of height data points (rest of the data values, all non-negative).

You are to compute and output the following.

A number and area of each trapezoid.
At the end, display the area under the curve of using the trapezoid method.

If the requirements are unclear in any way, use any provided input and output to resolve the discrepancy.

See Guidelines for C programs .

The following coding examples and/or notes may be of use for this requirement.

To get started, you should be familiar with each program in the following pages.

Use the "+=" or "-=" (or similar) operators when they can be used. For example incrementing a counter or adding to a sum. It is best to not use the "++" or "--" operators except within for loops (where for loops are the best choice).

Use a while loop where a while loop is best. There is a major deduction for using a for loop when not appropriate. A for loop is best for going 0 to n-1 or from 1 to n or the other way.

All code should be written in single-entry single-exit style. This means no continue or break statements in loops and all return statements need to be at the end of a function (as in the main function).

For all works, there is a major deduction for submitting a program that does not terminate. For example, a program that contains an infinite loop.

Make all necessary assumptions. Make no unnecessary assumptions.

In addition to specific coding examples, you should be familiar with all concepts covered to this point in the course.

Domain knowledge is the background knowledge that is useful in solving a problem, designing a solution, implementing the solution, etc. The following domain knowledge may be useful for this requirement.

Note: In addition to specific domain knowledge, you should be familiar with all concepts covered to this point in the course.

You are provided with the following starter program in file integration.c.

Do not remove any comment that starts with three slashes.

Here is the C code.

/// File: integration.c
/// Purpose: Integration using trapezoids
/// Author: (your name)
/// Help received:
// (add here)
/// pseudo-code:
// (add here)

#include <stdio.h>

int main() {
	///:BEGIN ToDo

	///:END ToDo
	return 0;
	}

You are to fill in the missing parts of the program according to the work requirements (see above).

In the comments at the top, you are to fill in the author (your name), help received (person and type of help), and pseudo-code parts which are not in the solution (usually provided, but you need to add them). Remove the parentheses too.

Begin solution

Here is a possible solution to the above problem. Note: Once a solution is provided, or the day before the next class, further submissions for this work receive no credit.

/// File: integration.c
/// Purpose: Integration using trapezoids
/// Author: (your name)
/// Help received:
// (add here)
/// pseudo-code:
// (add here)

#include <stdio.h>

int main() {
	///:BEGIN ToDo
	int show1;
	char units1[255];
	double eachWidth1;
	double leftHeight1;
	double rightHeight1;
	double areaOne1;
	double areaAll1;
	int dataPos1;
	int pairPos1;
	scanf("%d",&show1);
	if (show1 > 1) {
		printf("Enter units.\n");
		}
	scanf("\n%[^\n]s",&units1);
	if (show1 > 1) {
		printf("You entered units as \"%s\"\n",units1);
		printf("\n");
		printf("Enter width of each trapezoid.\n");
		}
	scanf("%lf",&eachWidth1);
	if (show1 > 1) {
		printf("You entered width as %0.2lf %s.\n",eachWidth1,units1);
		}
	areaAll1 = 0.0;
	dataPos1 = 0;
	pairPos1 = 0;
	if (show1 > 1) {
		printf("\n");
		printf("Enter heights, negative height to stop.\n");
		printf("\n");
		}
	scanf("%lf",&rightHeight1);
	while (rightHeight1 >= 0) {
		dataPos1 += 1;
		if (dataPos1 != 1) {
			pairPos1 += 1;
			areaOne1 = eachWidth1 * 0.5*(leftHeight1+rightHeight1);
			areaAll1 += areaOne1;
			if (show1 > 0) {
				printf("trap %d: w=%0.3lf y1=%0.3lf y2=%0.3lf a=%0.3lf\n",pairPos1,eachWidth1,leftHeight1,rightHeight1,areaOne1);
				}
			}
		leftHeight1 = rightHeight1;
		scanf("%lf",&rightHeight1);
		}
	printf("\n");
	printf("Area of %d trapezoids is %0.3lf square %s.\n",pairPos1,areaAll1,units1);
	///:END ToDo
	return 0;
	}

End solution

Here are some examples of input and output for the above program code.

Here is an example input from file input1.txt.

2
inches
1.00
0.20
0.16
0.13
0.11
0.09
0.07
0.06
0.05
0.04
0.03
0.03
-1.0

For the above example input, here is the expected output.

Enter units.
You entered units as "inches"

Enter width of each trapezoid.
You entered width as 1.00 inches.

Enter heights, negative height to stop.

trap 1: w=1.000 y1=0.200 y2=0.160 a=0.180
trap 2: w=1.000 y1=0.160 y2=0.130 a=0.145
trap 3: w=1.000 y1=0.130 y2=0.110 a=0.120
trap 4: w=1.000 y1=0.110 y2=0.090 a=0.100
trap 5: w=1.000 y1=0.090 y2=0.070 a=0.080
trap 6: w=1.000 y1=0.070 y2=0.060 a=0.065
trap 7: w=1.000 y1=0.060 y2=0.050 a=0.055
trap 8: w=1.000 y1=0.050 y2=0.040 a=0.045
trap 9: w=1.000 y1=0.040 y2=0.030 a=0.035
trap 10: w=1.000 y1=0.030 y2=0.030 a=0.030

Area of 10 trapezoids is 0.855 square inches.

Here is an example input from file input2.txt.

1
centimeters
0.40
0.05
0.11
0.19
0.29
0.37
0.40
0.37
0.29
0.19
0.11
0.05
-1.0

For the above example input, here is the expected output.

trap 1: w=0.400 y1=0.050 y2=0.110 a=0.032
trap 2: w=0.400 y1=0.110 y2=0.190 a=0.060
trap 3: w=0.400 y1=0.190 y2=0.290 a=0.096
trap 4: w=0.400 y1=0.290 y2=0.370 a=0.132
trap 5: w=0.400 y1=0.370 y2=0.400 a=0.154
trap 6: w=0.400 y1=0.400 y2=0.370 a=0.154
trap 7: w=0.400 y1=0.370 y2=0.290 a=0.132
trap 8: w=0.400 y1=0.290 y2=0.190 a=0.096
trap 9: w=0.400 y1=0.190 y2=0.110 a=0.060
trap 10: w=0.400 y1=0.110 y2=0.050 a=0.032

Area of 10 trapezoids is 0.948 square centimeters.

Here is an example input from file input3.txt.

0
feet
0.50
2.00
2.75
3.50
4.25
5.00
5.75
6.50
7.25
8.00
8.75
9.50
-1.0

For the above example input, here is the expected output.

Area of 10 trapezoids is 28.750 square feet.

Pseudo-code is a "false" code. It is not really code, but a simplified English explanation that is somewhat similar to code. Pseudo-code is useful for understanding what a program does. For this work, the following can be used as the pseudo-code. Adjust if needed.

Get the units of each trapezoid
Get the width of each trapezoid
Set the cumulative area to zero.
For each pair of adjacent y value pairs Do
	Determine the area of that trapezoid.
	Add that area to the cumulative area.
	End For
Output the area under the curve.

Note: Only some essential details are included. Some details, such as input, prompts, input echo, and obviously needed output are omitted.

The best way to copy-paste pseudo-code that includes indented code (e.g., with tabs) is as follows (in the code file) using a multi-line comment.

/* (pasted pseudo-code here) */

The pseudo-code should be indented just like code.

Note: One should never put raw tabs in the middle of a line since they can appear different in different output media.

So, if one copy-pastes the pseudo-code, one can add singe line comments to each line (which gets cumbersome and inhibits readability) and then convert tabs to spaces, or one can use multi-line comments as in the following (no tab change necessary).

/// pseudo-code: /* (paste pseudo-code here) */

Remember to remove parentheses in the header comments and supply your own information.

Note: Echoing input and computations along the way are not part of the pseudo-code (unless important to the method).

Note: An order of the y value pairs is not specified. In the code, an order needs to be used - usually the easiest order to use. But the pseudo-code does not specify that order (unless important to the method).

CS 101 - A6 : Asmt#6: Integration using trapezoids Your grade: _ / 40 [LATE] Late or redo penalty: _ / -40 [SUBMIT] Not submitted properly: _ / -40 [RUN] Does not compile, run-time crash, etc.: _ / -40 [ETHICS] Ethical issues: _ / -40 [HEADER] Header comments not done as required: _ / -20 [STYLE] Inconsistant style or indentation: _ / -20 [CODE] Code guidelines ignored: _ / -40 [XCODE] Code used not yet covered: _ / -20 [REMOVED] Triple slash comments removed: _ / -20 [ADDED] Code added outside of marked areas: _ / -20 [OUTPUT] Functional requirements met: _ / 40 [CREDIT] Extra credit: _ / +8 Comments: