C++: std::map, find cycles, algorithm - c++

Question

Suppose the following data structure:
std::map <int, std::vector<int> > M,
where val is represented by the sequence of vertices of the graph, and the key is the first vertex of the sequence. For example
{1} {1, 8, 12, 7}
{4} {4, 3, 5}
{7} {7, 9, 13, 18, 0, 2}
{2} {2, 11, 1}
{5} {5, 17, 10, 4}
{9} {9, 6, 19, 14}
{14} {14, 15, 9}
How to find all cycles (analogous start and end vertex) from the segments {}
C1: {1 8 12 7} {7 9 13 18 0 2} {2 11 1}
C2: {4 3 5} {5 17 10 4}
C3: {9 6 19 14} {14, 15, 9}
and how to avoid the duplicate sequence of segments, with the low time complexity (map may contain hundreds of thousands of sequences). Any cycle may contain n segments {}, where n>=1.
The initialization phase:
std::map <int, std::vector <int> > M;
M[1] = std::vector<int>{ 1, 8, 12, 7 };
M[4] = std::vector<int>{ 4, 3, 5 };
M[7] = std::vector<int>{ 7, 9, 13, 18, 0, 2 };
M[2] = std::vector<int>{ 2, 11, 1 };
M[5] = std::vector<int>{ 5, 17, 10, 4 };
M[9] = std::vector<int>{ 9, 6, 19, 14 };
M[14] = std::vector<int>{ 14, 15, 9 };
The draft of the algorithm:
std::vector<std::vector <int> > R;
for (auto im = M.begin(); im != M.end();)
{
std::vector<int> r, ri = im->second;
for(;;)
{
r.insert(r.end(), ri.begin(), ri.end());
ri = M[r.back()];
im = M.erase(M.find(im->first));
if (r.back() == r.front()) break;
}
R.push_back(r);
}
Unfortunately, the repeated deletion represents an expensive operation... I hope, there is a more beautiful and efficient solution :-)
Thanks for your help...

Answer 1

First, your inner loop needs to be a function (what if the paths don't cycle?)
Then, declare failure if either
The end node is numerically less than the start node (could be a cycle, but is not a canonical, so we won't print this shifted version)
The end node isn't found in the master table of paths
And that leads to a solution:
bool try_follow(int from, std::vector<int>& result)
{
int current = from;
while (true) {
auto path = M.find(current);
if (path == M.end()) return false;
current = path->second.back();
if (current < from) return false;
result.insert(result.end(), path->second.begin()+1, path->second.end());
if (current == from) return true;
}
}
int main(void)
{
for( auto& kvp : M )
{
std::vector<int> x;
if (try_follow(kvp.first, x)) {
std::cout << kvp.first;
for( int y : x )
std::cout << " - " << y;
std::cout << std::endl;
}
}
}
Demo: https://rextester.com/DWWZ9457

Answer 2

My first crack:
for (auto it : M)
{
if (it.first < it.second.back() && it.second.front() == M[it.second.back()].back())
std::cout << "Cycle between " << it.first << " and " << it.second.back() << '\n';
}
Won't find cycles that involve 3+ paths, of course.