snail.cpp

#include <iostream>
#include <array>

using namespace std;

/* ----------------------------------------------------------------
	DEFINITIONS
---------------------------------------------------------------- */
template <size_t N> using Row = array<int, N>;
template <size_t N> using Matrix = array<Row<N>, N>;

enum Direction : int 
{
	RIGHT = 0, 
	DOWN = 1, 
	LEFT = 2, 
	UP = 3
};

template <size_t N, size_t R = 0, size_t C = 0, 
	int Direct = Direction::RIGHT, 
	size_t Step = 0,
	size_t Size = N,
	size_t Turn = 0,
	int K = 1>
void snail(Matrix<N> &matrix);

template <size_t N, size_t R, size_t C, 
	int Direct, size_t Step, size_t Size, size_t Turn, 
	int K>
void advance(Matrix<N> &matrix);

template <size_t N, size_t R, size_t C, 
	int Direct, size_t Step, size_t Size, size_t Turn, 
	int K>
void turn(Matrix<N> &matrix);

/* ----------------------------------------------------------------
	IMPLEMENTATIONS
---------------------------------------------------------------- */
template <size_t N, size_t R, size_t C, 
	int Direct, size_t Step, size_t Size, size_t Turn,
	int K>
void snail(Matrix<N> &matrix)
{
	if constexpr (Size != 0)
	{
		matrix[R][C] = K;
		if constexpr (Step + 1 == Size)
		{
			if constexpr (Direct == Direction::UP)
				turn<N, R, C, Direction::RIGHT, Step+1, Size, Turn, K>(matrix);
			else
				turn<N, R, C, Direct+1, Step+1, Size, Turn, K>(matrix);
		}
		else
			advance<N, R, C, Direct, Step+1, Size, Turn, K>(matrix);
	}
}

template <size_t N, size_t R, size_t C, 
	int Direct, size_t Step, size_t Size, size_t Turn, 
	int K>
void advance(Matrix<N> &matrix)
{
	if constexpr (Direct == Direction::RIGHT)
		snail<N, R, C+1, Direct, Step, Size, Turn, K+1>(matrix);
	else if constexpr (Direct == Direction::DOWN)
		snail<N, R+1, C, Direct, Step, Size, Turn, K+1>(matrix);
	else if constexpr (Direct == Direction::LEFT)
		snail<N, R, C-1, Direct, Step, Size, Turn, K+1>(matrix);
	else
		snail<N, R-1, C, Direct, Step, Size, Turn, K+1>(matrix);
}

template <size_t N, size_t R, size_t C, 
	int Direct, size_t Step, size_t Size, size_t Turn, 
	int K>
void turn(Matrix<N> &matrix)
{
	if constexpr (Turn % 2 == 0)
		advance<N, R, C, Direct, 0, Size-1, Turn + 1, K>(matrix);
	else
		advance<N, R, C, Direct, 0, Size, Turn + 1, K>(matrix);
}

/* ----------------------------------------------------------------
	THE MAIN FUNCTION
---------------------------------------------------------------- */
template <size_t N, size_t R = 0, size_t C = 0>
void print(const Matrix<N> &matrix)
{
	cout << matrix[R][C] << '\t';
	if constexpr (C + 1 < N)
		print<N, R, C + 1>(matrix);
	else if constexpr (R + 1 < N)
	{
		cout << endl;
		print<N, R + 1, 0>(matrix);
	}
};

int main()
{
	Matrix<5> matrix;

	snail(matrix);
	print(matrix);

	return 0;
}

https://wandbox.org/permlink/7rEMICaoBiXsqYjB