1 files changed, 65 insertions, 0 deletions
diff --git a/graph/cycleCounting.cpp b/graph/cycleCounting.cpp
new file mode 100644
index 0000000..800f27e
--- /dev/null
+++ b/graph/cycleCounting.cpp
@@ -0,0 +1,65 @@
+constexpr ll maxEdges = 128;
+using cycle = bitset<maxEdges>;
+struct cylces {
+	ll n;
+	vector<vector<pair<ll, ll>>> adj;
+	vector<bool> seen;
+	vector<cycle> paths, base;
+	vector<pair<ll, ll>> edges;
+
+	cylces(ll n) : n(n), adj(n), seen(n), paths(n) {}
+
+	void addEdge(ll a, ll b) {
+		adj[a].push_back({b, sz(edges)});
+		adj[b].push_back({a, sz(edges)});
+		edges.push_back({a, b});
+	}
+
+	void addBase(cycle cur) {
+		for (cycle o : base) {
+			o ^= cur;
+			if (o._Find_first() > cur._Find_first()) cur = o;
+		}
+		if (cur.any()) base.push_back(cur);
+	}
+
+	void findBase(ll c = 0, ll p = -1, cycle cur = {}) {
+		if (n == 0) return;
+		if (seen[c]) {
+			addBase(cur ^ paths[c]);
+		} else {
+			seen[c] = true;
+			paths[c] = cur;
+			for (auto e : adj[c]) {
+				if (e.first == p) continue;
+				cur[e.second].flip();
+				findBase(e.first, c, cur);
+				cur[e.second].flip();
+	}}}
+
+	//cycle must be constrcuted from base
+	bool isCycle(cycle cur) {
+		if (cur.none()) return false;
+		init(n);
+		for (ll i = 0; i < sz(edges); i++) {
+			if (cur[i]) {
+				cur[i] = false;
+				if (findSet(edges[i].first) == 
+					findSet(edges[i].second)) break;
+				unionSets(edges[i].first, edges[i].second);
+		}}
+		return cur.none();
+	};
+
+	ll count() {
+		findBase();
+		ll res = 0;
+		for (ll i = 1; i < (1ll << sz(base)); i++) {
+			cycle cur;
+			for (ll j = 0; j < sz(base); j++) {
+				if (((i >> j) & 1) != 0) cur ^= base[j];
+			if (isCycle(cur)) res++;
+		}
+		return res;
+	}
+};