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  1. #include <iostream>
  2. #include <vector>
  3. #include <set>
  4. #include <algorithm>
  5. #include <sstream>
  6. #include <cmath>
  7. #include <cassert>
  8. using namespace std;
  9.  
  10. struct Triple {
  11.         unsigned int values[3];
  12.         Triple(unsigned int newA, unsigned int newB, unsigned int newC) 
  13.          : values{newA, newB, newC} {}
  14.         unsigned int a() const  { return values[0]; }
  15.         unsigned int b() const { return values[1]; }
  16.         unsigned int c() const { return values[2]; }
  17.         unsigned int sum() const { return accumulate(values, values + 3, 0); }
  18.         bool operator<(const Triple& second) const {
  19.                 return lexicographical_compare(values, values + 3,
  20.                                                second.values, second.values + 3);
  21.         }
  22. };
  23.  
  24. Triple getTriple(unsigned int k, unsigned int m, unsigned int n) {
  25.         assert(m > n);
  26.         return {k*(m*m-n*n), k*2*m*n, k*(m*m + n*n)};
  27. }
  28.  
  29. set<unsigned int> factors(unsigned int n) {
  30.         set<unsigned int> res;
  31.         unsigned int root = sqrt(n);
  32.         for(unsigned int i = 1; i <= root; i++) {
  33.                 if(n % i == 0) {
  34.                         res.insert(i);
  35.                         res.insert(n/i);
  36.                 }
  37.         }
  38.         return res;
  39. }
  40.  
  41. set<Triple> triangles(unsigned int sum) {
  42.         auto factorSet = factors(sum);
  43.         set<Triple> results;
  44.         for(unsigned int k : factorSet)
  45.         for(unsigned int m : factorSet) {
  46.                 unsigned int n = sum/(2*m*k) - m;
  47.                 if( !n || !((m - n) % 2) || (n >= m) || k*2*m*m >= sum)
  48.                         continue;
  49.  
  50.                 Triple triple = getTriple(k, m, n);
  51.                 if(triple.sum() == sum)
  52.                         results.insert(triple);
  53.         }
  54.         return results;
  55. }
  56.  
  57. int main(int argc, char** argv) {
  58.         unsigned int amount;
  59.         if(argc != 2) {
  60.                 cin >> amount;
  61.         }
  62.         else {
  63.                 stringstream ss(argv[1]);
  64.                 ss >> amount;
  65.         }
  66.         auto results = triangles(amount);
  67.         for(auto& triple : results) {
  68.                 cout << triple.a() << " " << triple.b() << " " << triple.c() << "\n";
  69.         }
  70. }
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https://ideone.com/8oDRU
language:
C++14 (gcc 8.3)
created:
12 years ago
visibility:
secret

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