# competitive-programming-library

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View the Project on GitHub kmyk/competitive-programming-library

# get a central path of a catapillar graph (graph/catapillar_graph.hpp)

## Code

/**
* @brief get a central path of a catapillar graph
* @arg g is a tree
* @return a central path; i.e. a longest path
* @note $O(n)$
* @note an empty vector if g is not a catapillar
* @see https://en.wikipedia.org/wiki/Caterpillar_tree
*/
vector<int> get_catapillar_central_path(const vector<vector<int> > & g) {
int n = g.size();

// construct the tree with non-leaf vertices
int m = 0;
vector<vector<int> > h(n);
REP (i, n) if (g[i].size() != 1) {
++ m;
for (int j : g[i]) if (g[j].size() != 1) {
h[i].push_back(j);
}
}

// the tree must be a path graph
REP (i, n) {
if (h[i].size() >= 3) {
return vector<int>();
}
}

// reconstruct the path
if (m == 0) {
if (n == 1) {
return vector<int>({ 0 });
} else if (n == 2) {
return vector<int>({ 0, 1 });
} else {
assert (false);
}

} else {
assert (n >= 3);
vector<int> path;
int i = 0;
while (g[i].size() == 1 or h[i].size() == 2) {
++ i;
}
for (int j : g[i]) if (g[i].size() == 1) {
path.push_back(j);
break;
}
int parent = path.back();
while (true) {
path.push_back(i);
bool found = false;
for (int j : h[i]) if (j != parent) {
parent = i;
i = j;
found = true;
break;
}
break;
}
}
for (int j : g[i]) if (g[i].size() == 1 and j != parent) {
path.push_back(j);
break;
}
return path;
}
}



#line 1 "graph/catapillar_graph.hpp"
/**
* @brief get a central path of a catapillar graph
* @arg g is a tree
* @return a central path; i.e. a longest path
* @note $O(n)$
* @note an empty vector if g is not a catapillar
* @see https://en.wikipedia.org/wiki/Caterpillar_tree
*/
vector<int> get_catapillar_central_path(const vector<vector<int> > & g) {
int n = g.size();

// construct the tree with non-leaf vertices
int m = 0;
vector<vector<int> > h(n);
REP (i, n) if (g[i].size() != 1) {
++ m;
for (int j : g[i]) if (g[j].size() != 1) {
h[i].push_back(j);
}
}

// the tree must be a path graph
REP (i, n) {
if (h[i].size() >= 3) {
return vector<int>();
}
}

// reconstruct the path
if (m == 0) {
if (n == 1) {
return vector<int>({ 0 });
} else if (n == 2) {
return vector<int>({ 0, 1 });
} else {
assert (false);
}

} else {
assert (n >= 3);
vector<int> path;
int i = 0;
while (g[i].size() == 1 or h[i].size() == 2) {
++ i;
}
for (int j : g[i]) if (g[i].size() == 1) {
path.push_back(j);
break;
}
int parent = path.back();
while (true) {
path.push_back(i);
bool found = false;
for (int j : h[i]) if (j != parent) {
parent = i;
i = j;
found = true;
break;
}
break;
}
}
for (int j : g[i]) if (g[i].size() == 1 and j != parent) {
path.push_back(j);
break;
}
return path;
}
}