finding a pythagorean triplet (project euler)

I'm well aware this brute force method is bad and that I should be using something like Euclid's formula, and that the final loop isn't needed as c = 1000 - (a + b) etc... but right now I just want this to work.

bool isPythagorean(int a, int b, int c) {
    if((a*a + b*b) == c*c && a < b && b < c) {
        cout << a << " " << b << " " << c << endl;
        return true;
    } else {
        return false;
    }
}

int 开发者_StackOverflow社区main()
{
    int a = 1;
    int b = 2;
    int c = 3;

    for(a = 1; a < b; ++a) {
        for(b = 2; b < c; ++b) {
            for(c = 3; a + b + c != 1000 && !isPythagorean(a, b, c); ++c) {
            }
        }
    }

    return 0;
}

For the most part, the code works as I expect it to. I cannot figure out why it is stopping shy of a + b + c = 1000.

My final triplet is 280 < 294 < 406, totalling 980.

If I remove the a < b < c check, the triplet becomes 332, 249, 415 totalling 996.

All results fit the pythagorean theorem -- I just cannot land a + b + c = 1000.

What is preventing me?

---

This part of the code iterates very strangely:

for(a = 1; a < b; ++a) {
    for(b = 2; b < c; ++b) {
        for(c = 3; a + b + c != 1000 && !isPythagorean(a, b, c); ++c) {
        }
    }
}

Initially, a = 1, b = 2, c = 3. But upon the first for(c), c=997, so the second iteration of for(b) will run up to b=996. Keep doing this, and at some point you find a triple (a,b,c), at that point, c is probably not close to 1000, b will iterate up to whatever state c was is in... and so on. I don't think you can accurately predict the way it's going to come up with triples.

I suggest you go with something like

for(a = 1; 3*a < 1000; ++a) {
    for(b = a+1; a+2*b < 1000; ++b) {
        for(c = b+1; a + b + c != 1000 && !isPythagorean(a, b, c); ++c) {
        }
    }
}

That way, loops won't depend on the previously found triple.

... and you really should use Euclid's method.

---

The condition in your innermost for loop explicitly says to never test anything where a + b + c is equal to 1000. Did you mean a + b + c <= 1000?

---

Alternate possible Solution:

#include <iostream>
#define S(x) x*x

int main() {
int c = 0;
for(int a=1;a<(1000/3);++a) {
    // a < b; so b is at-least a+1 
    // If a < b < c and a + b + c = 1000 then 'a' can't be greater than 1000/3  
    // 'b' can't be greater than 1000/2. 
    for(int b=a+1;b<(1000/2);++b) {         
        c = (1000 - a - b); // problem condition
        if(S(c) == (S(a) + S(b) ))
            std::cout<<a*b*c;
        }
    }       
return 0;
}

For additional reference please refer the following posts Finding Pythagorean Triples: Euclid's Formula Generating unique, ordered Pythagorean triplets