add LCA test and remove unused parent in DFS

2 files changed, 92 insertions, 2 deletions

diff --git a/graph/LCA_sparse.cpp b/graph/LCA_sparse.cpp
index 2a864c0..0f2fe22 100644
--- a/graph/LCA_sparse.cpp
+++ b/graph/LCA_sparse.cpp
@@ -13,13 +13,13 @@ struct LCA {
 		st.init(&depth);
 	}
 
-	void dfs(vector<vector<int>>& adj, int v, ll d=0, int p=-1) {
+	void dfs(vector<vector<int>>& adj, int v, ll d=0) {
 		visited[idx] = v, depth[idx] = d;
 		first[v] = min(idx, first[v]), idx++;
 
 		for (int u : adj[v]) {
 			if (first[u] == 2 * sz(adj)) {
-				dfs(adj, u, d + 1, v);
+				dfs(adj, u, d + 1);
 				visited[idx] = v, depth[idx] = d, idx++;
 	}}}
 
diff --git a/graph/test/LCA_sparse.cpp b/graph/test/LCA_sparse.cpp
new file mode 100644
index 0000000..53af57b
--- /dev/null
+++ b/graph/test/LCA_sparse.cpp
@@ -0,0 +1,90 @@
+#include <bits/stdc++.h>
+using namespace std;
+using ll = long long;
+
+#define sz(x) ((int)(x).size())
+#define all(x) (x).begin(), (x).end()
+#include "../../datastructures/sparseTable.cpp"
+#include "../LCA_sparse.cpp"
+
+mt19937 rd(0);
+
+void test(const vector<vector<int>> &old_adj, int root) {
+	int n = old_adj.size();
+	vector<int> perm(n);
+	iota(perm.begin(), perm.end(), 0);
+	ranges::shuffle(perm, rd);
+	vector<vector<int>> adj(n);
+	for (int i = 0; i < n; i++) {
+		auto &a = adj[perm[i]] = old_adj[i];
+		for (int &v: a) v = perm[v];
+		ranges::shuffle(a, rd);
+	}
+	root = perm[root];
+
+	vector<int> parent(n);
+	function<void(int,int)> dfs = [&](int u, int p) {
+		parent[u] = p;
+		for (int v: adj[u]) if (v != p) dfs(v, u);
+	};
+	dfs(root, -1);
+
+	function<bool(int, int)> is_ancestor = [&](int u, int v) {
+		while (v != -1 && u != v) v = parent[v];
+		return u == v;
+	};
+	function<int(int)> depth = [&](int v) {
+		int r = 0;
+		while ((v = parent[v]) != -1) r++;
+		return r;
+	};
+
+	LCA lca;
+	lca.init(adj, root);
+	for (int i = 0; i < n; i++) assert(lca.getDepth(i) == depth(i));
+	uniform_int_distribution<int> distrib(0, n-1);
+	for (int i = 0; i < 1000; i++) {
+		int u = distrib(rd);
+		int v = distrib(rd);
+		int l = lca.getLCA(u, v);
+		assert(is_ancestor(l, u));
+		assert(is_ancestor(l, v));
+		for (int p = parent[l]; int c: adj[l]) {
+			if (c == p) continue;
+			assert(!is_ancestor(c, u) || !is_ancestor(c, v));
+		}
+	}
+}
+
+int main() {
+	{
+		// Single vertex
+		vector<vector<int>> adj(1);
+		test(adj, 0);
+	}
+	{
+		// Path
+		vector<vector<int>> adj(100);
+		for (int i = 1; i < 100; i++) {
+			adj[i-1].push_back(i);
+			adj[i].push_back(i-1);
+		}
+		test(adj, 0);
+		test(adj, 99);
+		test(adj, 40);
+	}
+	{
+		// Random
+		vector<vector<int>> adj(1000);
+		for (int i = 1; i < 1000; i++) {
+			uniform_int_distribution<int> distrib(0, i-1);
+			int p = distrib(rd);
+			adj[p].push_back(i);
+			adj[i].push_back(p);
+		}
+		test(adj, 0);
+		test(adj, 300);
+		test(adj, 600);
+		test(adj, 900);
+	}
+}