Templatized graph algs (#119)

* saving progress

* [auto-verifier] verify commit 31974ee

* changes

* a fix

* fix compile error

* fix

* more fixes

* final fix

* remove old readme

* add templatized versions of graphs

* some more fixes

* final fix

* more fixes

* actually let's not use this

* final fixes

* some fixes

* supress

---------

Co-authored-by: GitHub <noreply@github.com>

Author: lrvideckis

.verify-helper/timestamps.remote.json

@@ -49,14 +49,6 @@
 "tests/library_checker_aizu_tests/flow/dinic_lib_checker.test.cpp": "2024-11-17 14:04:03 -0600",
 "tests/library_checker_aizu_tests/flow/hungarian.test.cpp": "2024-11-17 14:04:03 -0600",
 "tests/library_checker_aizu_tests/flow/min_cost_max_flow.test.cpp": "2024-12-05 10:41:42 -0600",
-"tests/library_checker_aizu_tests/graphs/biconnected_components.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/graphs/connected_components_of_complement_graph.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/graphs/dijkstra_aizu.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/graphs/dijkstra_lib_checker.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/graphs/directed_cycle.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/graphs/enumerate_triangles.test.cpp": "2024-11-17 14:04:03 -0600",
-"tests/library_checker_aizu_tests/graphs/hopcroft_karp_aizu.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/graphs/hopcroft_karp_lib_checker.test.cpp": "2024-12-14 15:47:13 -0600",
 "tests/library_checker_aizu_tests/graphs/mst.test.cpp": "2024-11-17 14:04:03 -0600",
 "tests/library_checker_aizu_tests/graphs/offline_incremental_scc.test.cpp": "2024-12-14 15:47:13 -0600",
 "tests/library_checker_aizu_tests/graphs/strongly_connected_components_aizu.test.cpp": "2024-12-14 15:47:13 -0600",
@@ -68,18 +60,10 @@
 "tests/library_checker_aizu_tests/handmade_tests/edge_cd_small_trees.test.cpp": "2024-12-14 15:47:13 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/fib_matrix_expo.test.cpp": "2024-11-17 14:04:03 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/functional_graph.test.cpp": "2024-12-05 10:41:42 -0600",
-"tests/library_checker_aizu_tests/handmade_tests/lca_ladder_forest.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/handmade_tests/manacher.test.cpp": "2024-12-05 10:41:42 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/merge_st_and_wavelet.test.cpp": "2024-11-19 08:31:51 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/mobius.test.cpp": "2024-11-17 14:04:03 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/mod_int.test.cpp": "2024-11-17 14:04:03 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/n_choose_k.test.cpp": "2024-11-17 14:04:03 -0600",
-"tests/library_checker_aizu_tests/handmade_tests/permutation_tree_small.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/handmade_tests/rmq_small_n.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/handmade_tests/sa_find_subarray.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/handmade_tests/seg_tree_find.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/handmade_tests/seg_tree_find_small.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/handmade_tests/string_with_vector.test.cpp": "2024-12-14 15:47:13 -0600",
 "tests/library_checker_aizu_tests/loops/chooses.test.cpp": "2024-11-17 14:04:03 -0600",
 "tests/library_checker_aizu_tests/loops/quotients.test.cpp": "2024-11-17 14:04:03 -0600",
 "tests/library_checker_aizu_tests/loops/submasks.test.cpp": "2024-11-17 14:04:03 -0600",
@@ -101,28 +85,6 @@
 "tests/library_checker_aizu_tests/math/solve_linear_mod.test.cpp": "2024-12-14 15:47:13 -0600",
 "tests/library_checker_aizu_tests/math/tetration.test.cpp": "2024-11-17 14:04:03 -0600",
 "tests/library_checker_aizu_tests/math/totient.test.cpp": "2024-11-17 14:04:03 -0600",
-"tests/library_checker_aizu_tests/math/xor_basis.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/math/xor_basis_intersection.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/monotonic_stack_related/cartesian_binary_tree.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/monotonic_stack_related/cartesian_k_ary_tree.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/monotonic_stack_related/count_rectangles.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/monotonic_stack_related/max_rect_histogram.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/strings/kmp.test.cpp": "2024-12-05 10:41:42 -0600",
-"tests/library_checker_aizu_tests/strings/lcp_array.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/strings/lcp_query_palindrome.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/strings/lcp_query_zfunc.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/strings/lcs_dp.test.cpp": "2024-12-05 10:41:42 -0600",
-"tests/library_checker_aizu_tests/strings/lcs_queries.test.cpp": "2024-12-05 10:41:42 -0600",
-"tests/library_checker_aizu_tests/strings/lcs_queries_merge_sort_tree.test.cpp": "2024-12-05 10:41:42 -0600",
-"tests/library_checker_aizu_tests/strings/longest_common_substring.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/strings/manacher.test.cpp": "2024-11-17 14:04:03 -0600",
-"tests/library_checker_aizu_tests/strings/multi_matching_bs.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/strings/prefix_function.test.cpp": "2024-11-17 14:04:03 -0600",
-"tests/library_checker_aizu_tests/strings/sa_cmp.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/strings/sa_sort_pairs.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/strings/single_matching_bs.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/strings/suffix_array.test.cpp": "2024-12-14 15:47:13 -0600",
-"tests/library_checker_aizu_tests/strings/suffix_array_short.test.cpp": "2024-12-14 15:47:13 -0600",
 "tests/library_checker_aizu_tests/strings/trie.test.cpp": "2024-12-05 10:41:42 -0600",
 "tests/library_checker_aizu_tests/strings/wildcard_pattern_matching.test.cpp": "2024-11-17 14:04:03 -0600",
 "tests/library_checker_aizu_tests/trees/cd_jump_on_tree.test.cpp": "2024-12-14 15:47:13 -0600",

library/graphs/bridges_cuts/block_vertex_tree.hpp

@@ -4,6 +4,9 @@
 //!   vector<vector<pii>> adj(n);
 //!   cuts cc(adj, m);
 //!   vector<vi> bvt = block_vertex_tree(adj, cc);
+//!   vector<basic_string<array<int, 2>>> adj1(n);
+//!   cuts cc1(adj1, m);
+//!   vector<vi> bvt1 = block_vertex_tree(adj1, cc1);
 //!   //to loop over each unique bcc containing a node u:
 //!   for (int bccid : bvt[v]) {
 //!     bccid -= n;
@@ -15,8 +18,9 @@
 //! [n, n + num_bccs) are BCC nodes
 //! @time O(n + m)
 //! @time O(n)
-vector<vi> block_vertex_tree(
-  const vector<vector<pii>>& adj, const cuts& cc) {
+template<class G>
+vector<vi> block_vertex_tree(const G& adj,
+  const cuts<G>& cc) {
   int n = sz(adj);
   vector<vi> bvt(n + cc.num_bccs);
   vector<bool> vis(cc.num_bccs);

library/graphs/bridges_cuts/bridge_tree.hpp

@@ -4,11 +4,15 @@
 //!   vector<vector<pii>> adj(n);
 //!   bridges br(adj, m);
 //!   vector<vi> bt = bridge_tree(adj, br);
+//!   vector<basic_string<array<int, 2>>> adj1(n);
+//!   bridges br1(adj1, m);
+//!   vector<vi> bt1 = bridge_tree(adj1, br1);
 //! @endcode
 //! @time O(n + m)
 //! @space O(n)
-vector<vi> bridge_tree(const vector<vector<pii>>& adj,
-  const bridges& br) {
+template<class G>
+vector<vi> bridge_tree(const G& adj,
+  const bridges<G>& br) {
   vector<vi> tree(br.num_ccs);
   rep(i, 0, sz(adj)) for (auto [u, e_id] : adj[i]) if (
     br.is_bridge[e_id]) tree[br.br_id[i]]

library/graphs/bridges_cuts/bridges.hpp

@@ -10,16 +10,19 @@
 //!     adj[v].emplace_back(u, i);
 //!   }
 //!   auto [num_ccs, is_bridge, br_id] = bridges(adj, m);
+//!   vector<basic_string<array<int,2>>> adj1(n);
+//!   auto [num_ccs1, is_bridge1, br_id1] = bridges(adj1,
+//!   m);
 //! @endcode
 //! is_bridge[edge id] = 1 iff bridge edge
 //! br_id[v] = id, 0<=id<num_ccs
 //! @time O(n + m)
 //! @space O(n + m)
-struct bridges {
+template<class G> struct bridges {
   int num_ccs = 0;
   vector<bool> is_bridge;
   vi br_id;
-  bridges(const vector<vector<pii>>& adj, int m):
+  bridges(const G& adj, int m):
     is_bridge(m), br_id(sz(adj), -1) {
     int n = sz(adj), timer = 1;
     vi tin(n), st;

library/graphs/bridges_cuts/cuts.hpp

@@ -11,16 +11,18 @@
 //!     adj[v].emplace_back(u, i);
 //!   }
 //!   auto [num_bccs, is_cut, bcc_id] = cuts(adj, m);
+//!   vector<basic_string<array<int,2>>> adj1(n);
+//!   auto [num_bccs1, is_cut1, bcc_id1] = cuts(adj1, m);
 //! @endcode
 //! is_cut[v] = 1 iff cut node
 //! bcc_id[edge id] = id, 0<=id<num_bccs
 //! @time O(n + m)
 //! @space O(n + m)
-struct cuts {
+template<class G> struct cuts {
   int num_bccs = 0;
   vector<bool> is_cut;
   vi bcc_id;
-  cuts(const vector<vector<pii>>& adj, int m):
+  cuts(const G& adj, int m):
     is_cut(sz(adj)), bcc_id(m, -1) {
     int n = sz(adj), timer = 1;
     vi tin(n), st;

library/graphs/complement_graph_ccs.hpp

@@ -1,15 +1,18 @@
 #pragma once
 //! @code
 //!   vector<vi> adj(n);
-//!   auto cc_id = get_complement_graph_ccs(adj);
+//!   vi cc_id = get_complement_graph_ccs(adj);
+//!   vector<basic_string<int>> adj1;
+//!   vi cc_id2 = get_complement_graph_ccs(adj1);
 //! @endcode
 //! 0<=cc_id[v]<number of connected components
 //!   in the complement graph
 //! cc_id[u] == cc_id[v] if u,v are in the same
 //!   cc in the compliment graph
 //! @time O(n + m)
 //! @space O(n)
-vi get_complement_graph_ccs(const vector<vi> &adj) {
+template<class G>
+vi get_complement_graph_ccs(const G& adj) {
   int n = sz(adj);
   vi cc_id(n), unseen(n);
   iota(all(unseen), 0);

library/graphs/dijkstra.hpp

@@ -2,12 +2,14 @@
 //! @code
 //!   vector<vector<pair<int, ll>>> adj(n);
 //!   auto d = dijkstra(adj, source);
+//!   vector<basic_string<array<int, 2>>> adj1(n);
+//!   auto d1 = dijkstra(adj1, source);
 //! @endcode
 //! d[v] = min dist from source->..->v
 //! @time O(n + (m log m))
 //! @space O(n + m)
-vector<ll> dijkstra(
-  const vector<vector<pair<int, ll>>>& adj, int s) {
+template<class G>
+vector<ll> dijkstra(const G& adj, int s) {
   using p = pair<ll, int>;
   priority_queue<p, vector<p>, greater<>> pq;
   pq.emplace(0, s);

library/graphs/hopcroft_karp.hpp

@@ -5,6 +5,8 @@
 //!   adj[l].push_back(r); // add edge l <-> r
 //!   auto [matching_size, to_r, to_l,
 //!     mvc_l, mvc_r] = hopcroft_karp(adj, rsz);
+//!   vector<basic_string<int>> adj1(lsz);
+//!   hopcroft_karp match(adj1, rsz);
 //! @endcode
 //! 0<=l<lsz; 0<=r<rsz
 //! l <-> to_r[l] in matching if to_r[l]!=-1
@@ -13,11 +15,11 @@
 //! mvc_r[r] is 1 if r in Min Vertex Cover
 //! @time O(n + m * sqrt(n)) n = lsz + rsz
 //! @space O(n)
-struct hopcroft_karp {
+template<class G> struct hopcroft_karp {
   int m_sz = 0;
   vi to_r, to_l;
   vector<bool> mvc_l, mvc_r;
-  hopcroft_karp(const vector<vi>& adj, int rsz):
+  hopcroft_karp(const G& adj, int rsz):
     to_r(sz(adj), -1), to_l(rsz, -1) {
     int lsz = sz(adj);
     while (1) {

library/graphs/strongly_connected_components/scc.hpp

@@ -3,15 +3,17 @@
 //! @code
 //!   vector<vi> adj(n);
 //!   auto [num_sccs, scc_id] = sccs(adj);
+//!   vector<basic_string<int>> adj1(n);
+//!   auto [num_sccs1, scc_id1] = sccs(adj1);
 //! @endcode
 //! scc_id[v] = id, 0<=id<num_sccs
 //! for each edge u -> v: scc_id[u] >= scc_id[v]
 //! @time O(n + m)
 //! @space O(n)
-struct sccs {
+template<class G> struct sccs {
   int num_sccs = 0;
   vi scc_id;
-  sccs(const vector<vi>& adj): scc_id(sz(adj), -1) {
+  sccs(const G& adj): scc_id(sz(adj), -1) {
     int n = sz(adj), timer = 1;
     vi tin(n), st;
     auto dfs = [&](auto&& self, int v) -> int {

library/strings/knuth_morris_pratt.hpp library/strings/kmp.hpplibrary/strings/knuth_morris_pratt.hpp renamed to library/strings/kmp.hpp

@@ -1,8 +1,12 @@
 #pragma once
 #include "prefix_function.hpp"
 //! @code
+//!   string s,t;
 //!   KMP kmp(t);
 //!   auto match = kmp.find_str(s);
+//!   vi s_vec,t_vec;
+//!   KMP kmp1(t_vec);
+//!   auto match2 = kmp1.find_str(s_vec);
 //! @endcode
 //! if match[i] == 1 then s[i,sz(t)) == t
 //! @time O(|s| + |t|)