CareerCup

Concat x and y and add an extra number to know where to split the coordinates. Example: f((45,3))=4530 and f((4,53))=4531

If integers are unsigned, just concatenate bits; if they are signed, reserve two bits for signes:

template<typename T>
T f(T x, T y) {
	if constexpr (std::is_signed_v<T>) {
		const bool is_neg_x = (x < 0);
		const bool is_neg_y = (y < 0);

		const T xy = (std::abs(x) << (4 * sizeof(T) - 1)) | std::abs(y);
		return (xy << 2) | (is_neg_x ? 1 : 0) | (is_neg_y ? 2 : 0);
	}
	else
		return (x << (4 * sizeof(T))) | y;
}

template<typename T>
std::pair<T, T> f_inv(T i) {
	if constexpr (std::is_signed_v<T>) {
		const bool is_neg_x = (i & 1);
		const bool is_neg_y = (i & 2);

		constexpr T mask = (T{1} << (4 * sizeof(T) - 1)) - 1;
		const T x = (i >> (4 * sizeof(T) + 1)) & mask;
		const T y = (i >> 2                  ) & mask;

		return {is_neg_x ? -x : x, is_neg_y ? -y : y};
	}
	else {
		constexpr T mask = (T{1} << (4 * sizeof(T))) - 1;
		return {i >> (4 * sizeof(T)), i & mask};
	}
}

if x>=y:
F(x,y) = x^2 + x+ y
else:
F(x,y) = x + y^2

if(x>=y):
		F(z) = x^2 + x + y;
	else:
		F(z) = y^2 + x;

We may use the cantor function to solve this:
en.wikipedia.org/wiki/Pairing_function