3 files changed, 190 insertions, 0 deletions
diff --git a/graph/test/LCA_sparse.cpp b/graph/test/LCA_sparse.cpp
new file mode 100644
index 0000000..c8b0017
--- /dev/null
+++ b/graph/test/LCA_sparse.cpp
@@ -0,0 +1,63 @@
+#include "util.cpp"
+#define all(X) begin(X), end(X)
+#define sz ssize
+#include "../../datastructures/sparseTable.cpp"
+#include "../LCA_sparse.cpp"
+
+void test(vector<vector<int>> &adj, int root) {
+	int n = adj.size();
+
+	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));
+	for (int i = 0; i < 1000; i++) {
+		int u = util::randint(n);
+		int v = util::randint(n);
+		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 = util::path(100);
+		int left = 0, mid = 40, right = 99;
+		util::shuffle_graph(adj, left, mid, right);
+		test(adj, left);
+		test(adj, mid);
+		test(adj, right);
+	}
+	{
+		// Random
+		vector<vector<int>> adj = util::random_tree(1000);
+		test(adj, 0);
+	}
+}
diff --git a/graph/test/binary_lifting.cpp b/graph/test/binary_lifting.cpp
new file mode 100644
index 0000000..05b903a
--- /dev/null
+++ b/graph/test/binary_lifting.cpp
@@ -0,0 +1,67 @@
+#include "util.cpp"
+#include "../binary_lifting.cpp"
+
+void test(vector<vector<int>> &adj, int root) {
+	int n = adj.size();
+
+	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;
+	};
+
+	Lift lift(adj, root);
+	for (int i = 0; i < n; i++) assert(lift.depth(i) == depth(i));
+	for (int i = 0; i < 1000; i++) {
+		int v = util::randint(n);
+		int d = util::randint(n);
+		int u = lift.lift(v, d);
+		assert(is_ancestor(u, v));
+		if (d <= depth(v)) assert(depth(u) == d);
+		else assert(u == v);
+	}
+	for (int i = 0; i < 1000; i++) {
+		int u = util::randint(n);
+		int v = util::randint(n);
+		int lca = lift.lca(u, v);
+		assert(is_ancestor(lca, u));
+		assert(is_ancestor(lca, v));
+		for (int p = parent[lca]; int c: adj[lca]) {
+			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 = util::path(100);
+		int left = 0, mid = 40, right = 99;
+		util::shuffle_graph(adj, left, mid, right);
+		test(adj, left);
+		test(adj, mid);
+		test(adj, right);
+	}
+	{
+		// Random
+		vector<vector<int>> adj = util::random_tree(1000);
+		test(adj, 0);
+	}
+}
diff --git a/graph/test/util.cpp b/graph/test/util.cpp
new file mode 100644
index 0000000..8c14b5c
--- /dev/null
+++ b/graph/test/util.cpp
@@ -0,0 +1,60 @@
+
+namespace util {
+
+void shuffle_adj_lists(vector<vector<int>> &adj) {
+	for (auto &a: adj) ranges::shuffle(a, rd);
+}
+
+vector<vector<int>> random_tree(int n) {
+	vector<vector<int>> adj(n);
+
+	vector<vector<int>> components(n);
+	for (int i = 0; i < n; i++) components[i].push_back(i);
+	while (components.size() > 1) {
+		int c1 = randint(components.size());
+		int c2 = randint(components.size()-1);
+		c2 += (c2 >= c1);
+
+		int v1 = components[c1][randint(components[c1].size())];
+		int v2 = components[c2][randint(components[c2].size())];
+
+		adj[v1].push_back(v2);
+		adj[v2].push_back(v1);
+
+		if (components[c1].size() < components[c2].size()) swap(c1, c2);
+		for (int v: components[c2]) components[c1].push_back(v);
+		swap(components[c2], components.back());
+		components.pop_back();
+	}
+
+	shuffle_adj_lists(adj);
+	return adj;
+}
+
+vector<vector<int>> path(int n) {
+	vector<vector<int>> adj(n);
+	for (int i = 1; i < n; i++) {
+		adj[i-1].push_back(i);
+		adj[i].push_back(i-1);
+	}
+	return adj;
+}
+
+template<typename... Ts>
+void shuffle_graph(vector<vector<int>> &adj, Ts &...vertex) {
+	int n = adj.size();
+	vector<int> perm(n);
+	iota(perm.begin(), perm.end(), 0);
+	ranges::shuffle(perm, rd);
+
+	vector<vector<int>> new_adj(n);
+	for (int i = 0; i < n; i++) {
+		auto &a = new_adj[perm[i]] = move(adj[i]);
+		for (int &v: a) v = perm[v];
+	}
+	adj = move(new_adj);
+	shuffle_adj_lists(adj);
+	((vertex = perm[vertex]), ...);
+}
+
+}