魔方陣の解の数を一瞬で求めるプログラム 4x4の魔方陣の場合 http://blog.unfindable.net/archives/7466

magicsquare4.cc

#include <iostream>
const int s = 34;
constexpr int eq(int a, int b) { return a != b ? 0 : a; }
constexpr int check(int used, int x1, int x4, int x13, int x16, int x2, int x3, int x5, int x6, int x7, int x8, int x9, int x10, int x11, int x12, int x14, int x15) {
  return (x15 < 1 || x15 > 16) ? 0 : 
  (((used & (1 << x15)) ? 0 : 1));
}
constexpr int check(int used, int x1, int x4, int x13, int x16, int x2, int x3, int x5, int x6, int x7, int x8, int x9, int x10, int x11, int x12, int x14) {
  return (x14 < 1 || x14 > 16) ? 0 : 
  (((used & (1 << x14)) ? 0 : check(used + (1 << x14), x1, x4, x13, x16, x2, x3, x5, x6, x7, x8, x9, x10, x11, x12, x14, eq(s - x13 - x14 - x16, s - x3 - x7 - x11))));
}
constexpr int check(int used, int x1, int x4, int x13, int x16, int x2, int x3, int x5, int x6, int x7, int x8, int x9, int x10, int x11, int x12) {
  return (x12 < 1 || x12 > 16) ? 0 : 
  (((used & (1 << x12)) ? 0 : check(used + (1 << x12), x1, x4, x13, x16, x2, x3, x5, x6, x7, x8, x9, x10, x11, x12, s - x2 - x6 - x10)));
}
constexpr int check(int used, int x1, int x4, int x13, int x16, int x2, int x3, int x5, int x6, int x7, int x8, int x9, int x10, int x11) {
  return (x11 < 1 || x11 > 16) ? 0 : 
  (((used & (1 << x11)) ? 0 : check(used + (1 << x11), x1, x4, x13, x16, x2, x3, x5, x6, x7, x8, x9, x10, x11, eq(s - x9 - x10 - x11, s - x4 - x8 - x16))));
}
constexpr int check(int used, int x1, int x4, int x13, int x16, int x2, int x3, int x5, int x6, int x7, int x8, int x9, int x10) {
  return (x10 < 1 || x10 > 16) ? 0 : 
  (((used & (1 << x10)) ? 0 : check(used + (1 << x10), x1, x4, x13, x16, x2, x3, x5, x6, x7, x8, x9, x10, s - x1 - x6 - x16)));
}
constexpr int check(int used, int x1, int x4, int x13, int x16, int x2, int x3, int x5, int x6, int x7, int x8, int x9) {
  return (x9 < 1 || x9 > 16) ? 0 : 
  (((used & (1 << x9)) ? 0 : check(used + (1 << x9), x1, x4, x13, x16, x2, x3, x5, x6, x7, x8, x9, s - x4 - x7 - x13)));
}
constexpr int check(int used, int x1, int x4, int x13, int x16, int x2, int x3, int x5, int x6, int x7, int x8) {
  return (x8 < 1 || x8 > 16) ? 0 : 
  (((used & (1 << x8)) ? 0 : check(used + (1 << x8), x1, x4, x13, x16, x2, x3, x5, x6, x7, x8, s - x1 - x5 - x13)));
}
constexpr int check(int used, int x1, int x4, int x13, int x16, int x2, int x3, int x5, int x6, int x7) {
  return (x7 > 16) ? 0 : 
  (((used & (1 << x7)) ? 0 : check(used + (1 << x7), x1, x4, x13, x16, x2, x3, x5, x6, x7, s - x5 - x6 - x7))
   + check(used, x1, x4, x13, x16, x2, x3, x5, x6, x7 + 1));
}
constexpr int check(int used, int x1, int x4, int x13, int x16, int x2, int x3, int x5, int x6) {
  return (x6 > 16) ? 0 : 
  (((used & (1 << x6)) ? 0 : check(used + (1 << x6), x1, x4, x13, x16, x2, x3, x5, x6, 1))
   + check(used, x1, x4, x13, x16, x2, x3, x5, x6 + 1));
}
constexpr int check(int used, int x1, int x4, int x13, int x16, int x2, int x3, int x5) {
  return (x5 > 16) ? 0 : 
  (((used & (1 << x5)) ? 0 : check(used + (1 << x5), x1, x4, x13, x16, x2, x3, x5, 1))
   + check(used, x1, x4, x13, x16, x2, x3, x5 + 1));
}
constexpr int check(int used, int x1, int x4, int x13, int x16, int x2, int x3) {
  return (x3 < 1 || x3 > 16) ? 0 : 
  (((used & (1 << x3)) ? 0 : check(used + (1 << x3), x1, x4, x13, x16, x2, x3, 1)));
}
constexpr int check(int used, int x1, int x4, int x13, int x16, int x2) {
  return (x2 > 16) ? 0 : 
  (((used & (1 << x2)) ? 0 : check(used + (1 << x2), x1, x4, x13, x16, x2, s - x1 - x2 - x4))
   + check(used, x1, x4, x13, x16, x2 + 1));
}
constexpr int check(int used, int x1, int x4, int x13, int x16) {
  return (x16 > 16) ? 0 : 
  (((used & (1 << x16)) ? 0 : check(used + (1 << x16), x1, x4, x13, x16, 1))
   + check(used, x1, x4, x13, x16 + 1));
}
constexpr int check(int used, int x1, int x4, int x13) {
  return (x13 > 16) ? 0 : 
  (((used & (1 << x13)) ? 0 : check(used + (1 << x13), x1, x4, x13, x1 + 1))
   + check(used, x1, x4, x13 + 1));
}
constexpr int check(int used, int x1, int x4) {
  return (x4 > 16) ? 0 : 
  (((used & (1 << x4)) ? 0 : check(used + (1 << x4), x1, x4, x4 + 1))
   + check(used, x1, x4 + 1));
}
constexpr int check(int used, int x1) {
  return (x1 > 13) ? 0 : 
  (((used & (1 << x1)) ? 0 : check(used + (1 << x1), x1, x1 + 1))
   + check(used, x1 + 1));
}
int main() {
  constexpr int result = check(0,1);
  std::cout << result << std::endl;
}