# competitive-programming-library

This documentation is automatically generated by online-judge-tools/verification-helper

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

# old/dominator-tree.inc.cpp

## Code

// http://sigma425.hatenablog.com/entry/2015/12/25/224053
vector<int> dominator_tree(vector<vector<int> > const & g, int root_g) { // G is a digraph which any vertex can be reached from the root
int n = g.size();
vector<vector<int> > invert_g(n);
repeat (i,n) for (int j : g[i]) invert_g[j].push_back(i);
// 1. make dfs tree
vector<int> to_rank(n, -1); // index on original digraph G -> index on dfs-tree T
vector<int> from_rank(n);
vector<int> parent(n, -1); // on dfs-tree T, indexed on G
{ // init
int next_rank = 0;
function<void (int)> dfs = [&](int i) {
to_rank[i] = next_rank;
from_rank[next_rank] = i;
++ next_rank;
for (int j : g[i]) if (to_rank[j] == -1) {
parent[j] = i;
dfs(j);
}
};
dfs(root_g);
}
// x. check connectivity
repeat (i,n) assert (to_rank[i] != -1); // or disconnected graph
// 2. compute sdom
vector<int> sdom(n);
repeat (i,n) sdom[i] = to_rank[i];
vector<int> foo(n, -1); // vertex, used in 3.
// 2.1. union-find tree
vector<int> root(n); whole(iota, root, 0);
vector<int> min_sdom_index(n); whole(iota, min_sdom_index, 0); // data on union-find tree
function<int (int)> find = [&](int i) {
if (root[i] == i) return i;
int j = find(root[i]);
if (sdom[min_sdom_index[root[i]]] < sdom[min_sdom_index[i]]) {
min_sdom_index[i] = min_sdom_index[root[i]];
}
return root[i] = j;
};
auto link = [&](int i, int j) {
assert (root[j] == j);
root[j] = i;
};
vector<vector<int> > bucket(n);
for (int rank_i = n-1; rank_i >= 1; -- rank_i) {
// 2.2. compute sdom
int i = from_rank[rank_i];
for (int j : invert_g[i]) {
// int rank_j = to_rank[j];
// if (rank_j < rank_i) { // up
//     setmin(sdom[i], rank_j);
// }
find(j);
setmin(sdom[i], sdom[min_sdom_index[j]]);
}
// 2.3. compute foo
bucket[from_rank[sdom[i]]].push_back(i);
for (int j : bucket[parent[i]]) {
find(j);
foo[j] = min_sdom_index[j];
}
bucket[parent[i]] = vector<int>(); // clear
}
// 3. compute idom
vector<int> idom(n);
repeat_from (rank_i,1,n) {
int i = from_rank[rank_i];
int j = foo[i];
idom[i] = (sdom[i] == sdom[j] ? sdom : idom)[j];
}
vector<int> result(n);
repeat (i,n) if (i != root_g) {
result[i] = from_rank[idom[i]];
}
result[root_g] = -1;
return result;
}



#line 1 "old/dominator-tree.inc.cpp"
// http://sigma425.hatenablog.com/entry/2015/12/25/224053
vector<int> dominator_tree(vector<vector<int> > const & g, int root_g) { // G is a digraph which any vertex can be reached from the root
int n = g.size();
vector<vector<int> > invert_g(n);
repeat (i,n) for (int j : g[i]) invert_g[j].push_back(i);
// 1. make dfs tree
vector<int> to_rank(n, -1); // index on original digraph G -> index on dfs-tree T
vector<int> from_rank(n);
vector<int> parent(n, -1); // on dfs-tree T, indexed on G
{ // init
int next_rank = 0;
function<void (int)> dfs = [&](int i) {
to_rank[i] = next_rank;
from_rank[next_rank] = i;
++ next_rank;
for (int j : g[i]) if (to_rank[j] == -1) {
parent[j] = i;
dfs(j);
}
};
dfs(root_g);
}
// x. check connectivity
repeat (i,n) assert (to_rank[i] != -1); // or disconnected graph
// 2. compute sdom
vector<int> sdom(n);
repeat (i,n) sdom[i] = to_rank[i];
vector<int> foo(n, -1); // vertex, used in 3.
// 2.1. union-find tree
vector<int> root(n); whole(iota, root, 0);
vector<int> min_sdom_index(n); whole(iota, min_sdom_index, 0); // data on union-find tree
function<int (int)> find = [&](int i) {
if (root[i] == i) return i;
int j = find(root[i]);
if (sdom[min_sdom_index[root[i]]] < sdom[min_sdom_index[i]]) {
min_sdom_index[i] = min_sdom_index[root[i]];
}
return root[i] = j;
};
auto link = [&](int i, int j) {
assert (root[j] == j);
root[j] = i;
};
vector<vector<int> > bucket(n);
for (int rank_i = n-1; rank_i >= 1; -- rank_i) {
// 2.2. compute sdom
int i = from_rank[rank_i];
for (int j : invert_g[i]) {
// int rank_j = to_rank[j];
// if (rank_j < rank_i) { // up
//     setmin(sdom[i], rank_j);
// }
find(j);
setmin(sdom[i], sdom[min_sdom_index[j]]);
}
// 2.3. compute foo
bucket[from_rank[sdom[i]]].push_back(i);
for (int j : bucket[parent[i]]) {
find(j);
foo[j] = min_sdom_index[j];
}
bucket[parent[i]] = vector<int>(); // clear
}
// 3. compute idom
vector<int> idom(n);
repeat_from (rank_i,1,n) {
int i = from_rank[rank_i];
int j = foo[i];
idom[i] = (sdom[i] == sdom[j] ? sdom : idom)[j];
}
vector<int> result(n);
repeat (i,n) if (i != root_g) {
result[i] = from_rank[idom[i]];
}
result[root_g] = -1;
return result;
}