UVa 11565 - Simple Equations

Accepted date: 2014-07-20
Ranking (as of 2014-07-20): 199 out of 757
Language: C++

/*
  UVa 11565 - Simple Equations

  To build using Visual Studio 2012:
    cl -EHsc -O2 UVa_11565_Simple_Equations.cpp
*/

#include <algorithm>
#include <cstdio>
#include <cmath>
using namespace std;

const int ABC_max = 10000;
int nr_factors, factors[ABC_max];

bool satisfy_equation(int A, int B, int C, int x, int y, int& z)
{
  int k = x * y;
  if (!(B % k)) {
    z = B / k;
    if (x != z && y != z && x + y + z == A && x * x + y * y + z * z == C)
      return true;
  }
  return false;
}

bool solve_equation(int A, int B, int C, int& x, int& y, int& z)
{
  int i, j;
  for (i = nr_factors - 1; i > 0; i--) {
    x = -factors[i];
    for (j = i - 1; j >= 0; j--) {
      y = -factors[j];
      if (satisfy_equation(A, B, C, x, y, z))
        return true;
    }
    for (j = 0; j < i; j++) {
      y = factors[j];
      if (satisfy_equation(A, B, C, x, y, z))
        return true;
    }
  }
  for (int i = 0; i < nr_factors - 1; i++) {
    x = factors[i];
    for (int j = nr_factors - 1; j > i; j--) {
      y = -factors[j];
      if (satisfy_equation(A, B, C, x, y, z))
        return true;
    }
    for (int j = i + 1; j < nr_factors; j++) {
      y = factors[j];
      if (satisfy_equation(A, B, C, x, y, z))
        return true;
    }
  }

  return false;
}

int main()
{
  int N;
  scanf("%d", &N);
  while (N--) {
    int A, B, C;
    scanf("%d %d %d", &A, &B, &C);
    nr_factors = 0;
    for (int i = 1, j = static_cast<int>(sqrt(static_cast<double>(B)));
      i <= j; i++)
      if (!(B % i)) {
        factors[nr_factors++] = i;
        if (i < B / i)
          factors[nr_factors++] = B / i;
      }
    sort(factors, factors + nr_factors);
    int x, y, z;
    if (solve_equation(A, B, C, x, y, z))
      printf("%d %d %d\n", x, y, z);
    else
      puts("No solution.");
  }
  return 0;
}