/*
 * @brief [Magic sequence](https://www.csplib.org/Problems/prob019/)
 *
 * @details
 *
 * @author [Jxtopher](https://github.com/jxtopher)
 */

#include <algorithm>
#include <cassert>
#include <iostream>
#include <list>
#include <numeric>
#include <vector>

namespace backtracking {
namespace magic_sequence {
    using sequence_t = std::vector<unsigned int>;

    void print(const sequence_t& s) {
        for(auto item : s) std::cout << item << " ";
        std::cout << std::endl;
    }

    // Check if it's a magic sequence
    bool is_magic(const sequence_t& s) {
        for(unsigned int i = 0; i < s.size(); i++)
            if(std::count(s.cbegin(), s.cend(), i) != s[i]) return false;
        return true;
    }

    // Filtering of sub-solutions
    // true if the sub-solution is valid otherwise false
    bool filtering(const sequence_t& s, unsigned int depth) {
        return std::accumulate(s.cbegin(), s.cbegin() + depth, static_cast<unsigned int>(0)) <=
               s.size();
    }

    void solve(sequence_t& s, std::list<sequence_t>& ret, unsigned int depth = 0) {
        if(depth == s.size()) {
            if(is_magic(s)) ret.push_back(s);
        } else {
            for(unsigned int i = 0; i < s.size(); i++) {
                s[depth] = i;
                if(filtering(s, depth + 1)) solve(s, ret, depth + 1);
            }
        }
    }

} // namespace magic_sequence

} // namespace backtracking

using namespace backtracking::magic_sequence;

static void test() {
    sequence_t s_magic = {6, 2, 1, 0, 0, 0, 1, 0, 0, 0};
    assert(is_magic(s_magic));

    sequence_t s_not_magic = {5, 2, 1, 0, 0, 0, 1, 0, 0, 0};
    assert(!is_magic(s_not_magic));
}

int main() {
    test();

    for(unsigned int i = 2; i < 12; i++) {
        std::cout << "Solution for n = " << i << std::endl;
        std::list<sequence_t> r1;
        sequence_t s1(i, i);
        solve(s1, r1);
        for(auto item : r1) print(item);
    }
}