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#include "graph/connected-components/incremental-bridge-connectivity.hpp"
辺の追加クエリのみ存在するとき, 二重辺連結成分を効率的に管理するデータ構造.
IncrementalBridgeConnectivity(sz)
: sz
頂点で初期化する.find(k)
: 頂点 k
が属する二重辺連結成分(の代表元)を求める.bridge_size()
: 現在の橋の個数を返す.add_edge(x, y)
: 頂点 x
と y
との間に無向辺を追加する.ならし $O(n \log n)$
Incremental Bridge-Connectivity - data-structures
#pragma once
#include "../../structure/union-find/union-find.hpp"
struct IncrementalBridgeConnectivity {
private:
UnionFind cc, bcc;
vector<int> bbf;
size_t bridge;
int size() { return bbf.size(); }
int par(int x) { return bbf[x] == size() ? size() : bcc.find(bbf[x]); }
int lca(int x, int y) {
unordered_set<int> used;
for (;;) {
if (x != size()) {
if (!used.insert(x).second) return x;
x = par(x);
}
swap(x, y);
}
}
void compress(int x, int y) {
while (bcc.find(x) != bcc.find(y)) {
int nxt = par(x);
bbf[x] = bbf[y];
bcc.unite(x, y);
x = nxt;
--bridge;
}
}
void link(int x, int y) {
int v = x, pre = y;
while (v != size()) {
int nxt = par(v);
bbf[v] = pre;
pre = v;
v = nxt;
}
}
public:
IncrementalBridgeConnectivity() = default;
explicit IncrementalBridgeConnectivity(int sz)
: cc(sz), bcc(sz), bbf(sz, sz), bridge(0) {}
int find(int k) { return bcc.find(k); }
size_t bridge_size() const { return bridge; }
void add_edge(int x, int y) {
x = bcc.find(x);
y = bcc.find(y);
if (cc.find(x) == cc.find(y)) {
int w = lca(x, y);
compress(x, w);
compress(y, w);
} else {
if (cc.size(x) > cc.size(y)) swap(x, y);
link(x, y);
cc.unite(x, y);
++bridge;
}
}
};
#line 2 "graph/connected-components/incremental-bridge-connectivity.hpp"
#line 2 "structure/union-find/union-find.hpp"
struct UnionFind {
vector<int> data;
UnionFind() = default;
explicit UnionFind(size_t sz) : data(sz, -1) {}
bool unite(int x, int y) {
x = find(x), y = find(y);
if (x == y) return false;
if (data[x] > data[y]) swap(x, y);
data[x] += data[y];
data[y] = x;
return true;
}
int find(int k) {
if (data[k] < 0) return (k);
return data[k] = find(data[k]);
}
int size(int k) { return -data[find(k)]; }
bool same(int x, int y) { return find(x) == find(y); }
vector<vector<int> > groups() {
int n = (int)data.size();
vector<vector<int> > ret(n);
for (int i = 0; i < n; i++) {
ret[find(i)].emplace_back(i);
}
ret.erase(remove_if(begin(ret), end(ret),
[&](const vector<int> &v) { return v.empty(); }),
end(ret));
return ret;
}
};
#line 4 "graph/connected-components/incremental-bridge-connectivity.hpp"
struct IncrementalBridgeConnectivity {
private:
UnionFind cc, bcc;
vector<int> bbf;
size_t bridge;
int size() { return bbf.size(); }
int par(int x) { return bbf[x] == size() ? size() : bcc.find(bbf[x]); }
int lca(int x, int y) {
unordered_set<int> used;
for (;;) {
if (x != size()) {
if (!used.insert(x).second) return x;
x = par(x);
}
swap(x, y);
}
}
void compress(int x, int y) {
while (bcc.find(x) != bcc.find(y)) {
int nxt = par(x);
bbf[x] = bbf[y];
bcc.unite(x, y);
x = nxt;
--bridge;
}
}
void link(int x, int y) {
int v = x, pre = y;
while (v != size()) {
int nxt = par(v);
bbf[v] = pre;
pre = v;
v = nxt;
}
}
public:
IncrementalBridgeConnectivity() = default;
explicit IncrementalBridgeConnectivity(int sz)
: cc(sz), bcc(sz), bbf(sz, sz), bridge(0) {}
int find(int k) { return bcc.find(k); }
size_t bridge_size() const { return bridge; }
void add_edge(int x, int y) {
x = bcc.find(x);
y = bcc.find(y);
if (cc.find(x) == cc.find(y)) {
int w = lca(x, y);
compress(x, w);
compress(y, w);
} else {
if (cc.size(x) > cc.size(y)) swap(x, y);
link(x, y);
cc.unite(x, y);
++bridge;
}
}
};