Comparing two triangles in C (3, 3, 4 and 4, 3, 3 for example)

Question

I need to find all possible triangles in a set of integers. I successfully got the result, but I have many duplicates, for example:
A(3, 3, 4) == B(4, 3, 3)
I don't need to find similar triangles, I need to know when they are equal.
I tried to save my triangles as structs and wanted to compare them:
struct triangle
{
    int a;
    int b;     // I stored all found triangles this way
    int c;
};

int getNumberOfDuplicates(struct triangle savedTriangles[], int size) {
    int count = 0;
    for (int i = 0; i < size; i++) {
        for (int j = 0; j < size; j++) {
            int a,b,c,x,y,z;
            if (i != j) {
                a = savedTriangles[i].a; b = savedTriangles[i].b; c = savedTriangles[i].c;
                x = savedTriangles[j].a; y = savedTriangles[j].b; z = savedTriangles[j].c;

if (areTheSame) {  // Here I don't know how to compare them
                count++;
            }
        }
    }
}
return count;

Is there any mathematical way to compare them? Or any programming way?

Bill Lynch · Accepted Answer

The simplest solution would be to sort the three numbers.
void swap(int *a, int *b) {
  int tmp = *a;
  *a = *b;
  *b = tmp;
}

void bubble_sort(int *a, int *b, int *c) {
  if (a > b) swap(&a, &b);
  if (b > c) swap(&b, &c);
  if (a > b) swap(&a, &b);
}

At which point it should be trivial to compare if they are equal.

dxiv · Answer

Assuming the list is complete, every triangle will be repeated for every permutation of its sides a, b, c. Therefore each triangle is a duplicate of one with a <= b <= c, so it is enough to only check those, and automatically count any triangle with b < a or c < b as a duplicate.
int getNumberOfDuplicates(struct triangle savedTriangles[], int size){
    int count = 0;
    for (int i = 0; i < size; i++){
        int a = savedTriangles[i].a,
            b = savedTriangles[i].b,
            c = savedTriangles[i].c;
        if(b < a || c < b){
            count++;
            continue;
        }
        for (int j = i + 1; j < size; j++){
            int x = savedTriangles[j].a,
                y = savedTriangles[j].b,
                z = savedTriangles[j].c;
            if(a == x && b == y && c == z){
                count++;
                break;
            }
        }
    }
    return count;
}

AbdelAziz AbdelLatef · Answer

You have to do two modifications to your code:

Just compare a triangle to the followers only, you are now counting it twice, which will give you double the desired result.
Sort the lengths in ascending order by using min and max, then compare them.

So your code should look like this:
for (int i = 0; i < size - 1; i++) {
    for (int j = i + 1; j < size; j++) { //Start from i + 1 not 0
        int a, b, c, x, y, z, a1, b1, c1, x1, y1, z1;
        a = savedTriangles[i].a; b = savedTriangles[i].b; c = savedTriangles[i].c;
        x = savedTriangles[j].a; y = savedTriangles[j].b; z = savedTriangles[j].c;
        a1 = min(a, min(b, c));
        c1 = max(a, max(b, c));
        b1 = a + b + c - a1 - c1;
        x1 = min(x, min(y, z));
        z1 = max(x, max(y, z));
        y1 = x + y + z - x1 - z1;

if (a1 == x1 && b1 == y1 && c1 == z1)
            count++;
    }
}

int min (int a, int b)
{
    return a < b ? a : b;
}

int max (int a, int b)
{
    return a > b ? a : b;
}

There is a mathematical way by getting their sum, product and sum of their squares without the need to sort them, any triplet will give a unique set of results regardless of their order according to this, so the alternative code should look like this:
for (int i = 0; i < size - 1; i++) {
    for (int j = i + 1; j < size; j++) {
        int a, b, c, x, y, z, s1, s2, ss1, ss2, p1, p2;
        a = savedTriangles[i].a; b = savedTriangles[i].b; c = savedTriangles[i].c;
        x = savedTriangles[j].a; y = savedTriangles[j].b; z = savedTriangles[j].c;
        s1 = a + b + c;
        ss1 = a * a + b * b + c * c;
        p1 = a * b * c;
        s2 = x + y + c;
        ss2 = x * x + y * y + z * z;
        p2 = x * y * z;
        if (s1 == s2 && ss1 == ss2 && p1 == p2)
            count++;
    }
}

Comparing two triangles in C (3, 3, 4 and 4, 3, 3 for example)

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