1. Case study 1: Calculate the approximation of Pi
Calculate the approximation of Pi by formula
with error 1e-4.
Algorithm
pi = 0, s = 1, n = 1, t = s/n
while fabs(t) > 1e-4 do
pi = pi + t
n = n +2
s = -s
t = s / n;
end while
Pi = 4 * pi

2. Implementation #include <stdio.h> #include <math.h>
main(){
int s = 1;
double n = 1, t = 1, pi = 0;
while (fabs(t)>= 1e-4) {
pi = pi + t;
n += 2;
s = - s;
t = s/n; }
pi = pi * 4;
printf("%10.6f\n", pi);

3. Case Study 2: Fibonacci Sequence
Calculate the first 40 number of Fibonacci sequence: F(1) = 1, F(2) = 1, …, F(n) = F(n-1) + F(n-2)
Algorithm
f1 = 1, f2 = 1, i = 1
For i from 1 to 20 do
Print f1 and f2
f1 = f1 + f2
f2 = f2 + f1
End of for loop

4. Implementation #include <stdio.h> main(){ long int f1, f2;
int i;
f1 = 1;
f2 = 1;
for (i = 1; i<=20; i++) {
printf("%12ld %12ld ", f1, f2);
if(i%2==0) printf("\n");
f1 = f1 + f2;
f2 = f2 + f1; }

5. Case Study 3: Simple Encryption and Decryption
Problem:
Convert a plain text to a cipher text by alphabet of module k. Where 0<k<26 is an integer, used a key to encode and decode. For example if k = 3, A will be encrypted to D, and y will be encrypted to b.
Encryption Algorithm:
Get a key k
While the input character c is not \n
Convert c into its cipher text by using the kth letter forward
End while
For key k
Convert c into its plain text by using the kth letter backward

6. Implementation #include <stdio.h> main(){ char c; int key;
printf("Input a key between 1 and 25: \n");
scanf("%d", &key);
while ((c = getchar())!='*') {
if ((c >= 'a' && c <= 'z') || (c >= 'A' && c <= 'Z'))
c = c + key;
if (c > 'Z' && c <='Z'+key || c >'z')
c = c - 26; }
printf("%c",c);

7. Reading Data from a File
#include <stdio.h> /* defines fopen, fclose, fscanf fprintf, and EOF */
int
main(void) {
FILE *inp; /* input file pointer */
int sum = 0, /* sum of scores input so far */
score, /* current score */
input_status; /* status value returned by fscanf */
inp = fopen("scores.dat", "r"); /* open a file for reading */
printf("Scores\n");
input_status = fscanf(inp, "%d", &score); /* read the first line from the file */
while (input_status != EOF) { /* if not the end of file sign */
printf("%5d\n", score);
sum += score;
input_status = fscanf(inp, "%d", &score); /* continue to read the next line */ }
printf("\nSum of exam scores is %d\n", sum);
fclose(inp); /* close the file */
Run by command line

8. Structure Chart for Computing Solar Collecting Area Size

9. Program to Approximate Solar Collecting Area Size

10. Program to Approximate Solar Collecting Area Size (cont’d)

11. Program to Approximate Solar Collecting Area Size (cont’d)