Task:

Output in ascending order all regular irreducible fractions ranging from 0 to 1, denominators of which do not exceed 15. The numerator and denominator should be represented as pointers to type int.

Block-schemes of the solution:

C++ implementation:

#include<iostream> using namespace std; int n;//amount of fractions int lcd(int a, int b)//find NSD of two numbers; Evclid algorithm { int t; while (b != 0) { t = b; b = a%b; a = t; } return a; } void init(int*up, int*down, float*fraction, int num)//initialize the array { for (int i = 1; i <= num; i++)//cycle for fractions for (int k = 1; k<i; k++)//numerator < denumerator if (lcd(i, k) == 1)//irreducable { up[n] = k;//denumerator down[n] = i;//numerator fraction[n] = (float)up[n] / (float)down[n];//calculate value of fraction n++;//number of fractions } } void output(int*up, int*down, float*fraction, int num)//output in ascending order { for (;;)//find min and output { float min = 1;//due to the condition that all fractions are less than 1 int number;//number of element of array for (int i = 0; i<n; i++)//cycle for fractions { if (min>fraction[i]) { min = fraction[i];//find min number = i;//remember number of min } } if (min == 1) break;//fractions are over cout << up[number] << '/' << down[number] << '\t';//output min fraction[number] = 1;//avoid repetition } } void main() { int num = 15;//max denumerator int *up = new int[num*num];//dynamic array of numerators int *down = new int[num*num];//dynamic array of denumerators float *fraction = new float[num*num];//dynamic array of fraction values init(up, down, fraction, num); output(up, down, fraction, num); system("pause"); }

Screenshots

Analysis of the reliability of the results:

1/15=0.0666667

1/14=0.0714286

1/13=0.0769231

1/12=0.0833333

1/11=0.0909091

1/10=0.1

1/9=0.111111

1/8=0.125

2/15=0.133333

1/7=0.142857

2/13=0.153846

1/6=0.166667

2/11=0.181818

1/5=0.2

3/14=0.214286

2/9=0.222222

3/13=0.230769

1/4=0.25

4/15=0.266667

3/11=0.272727

2/7=0.285714

3/10=0.3

4/13=0.307692

1/3=0.333333

5/14=0.357143

4/11=0.363636

3/8=0.375

5/13=0.384615

2/5=0.4

5/12=0.416667

3/7=0.428571

4/9=0.444444

5/11=0.454545

6/13=0.461538

7/15=0.466667

1/2=0.5

8/15=0.533333

7/13=0.538462

6/11=0.545455

5/9=0.555556

4/7=0.571429

7/12=0.583333

3/5=0.6

8/13=0.615385

5/8=0.625

7/11=0.636364

9/14=0.642857

2/3=0.666667

9/13=0.692308

7/10=0.7

5/7=0.714286

8/11=0.727273

11/15=0.733333

3/4=0.75

10/13=0.769231

7/9=0.777778

11/14=0.785714

4/5=0.8

9/11=0.818182

5/6=0.833333

11/13=0.846154

6/7=0.857143

13/15=0.866667

7/8=0.875

8/9=0.888889

9/10=0.9

10/11=0.909091

11/12=0.916667

12/13=0.923077

13/14=0.928571

14/15=0.933333

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