Remove mod int (#163)

* add single function for mod division

* [auto-verifier] verify commit 32fc223

* fixed some tests

* more fixes

* another fix

* final fix

* add KACTL macro

* add more KACTL macros

---------

Co-authored-by: GitHub <[email protected]>

Author: lrvideckis

.verify-helper/timestamps.remote.json

@@ -40,7 +40,6 @@
 "tests/library_checker_aizu_tests/data_structures/persistent_seg_tree.test.cpp": "2024-12-05 10:41:42 -0600",
 "tests/library_checker_aizu_tests/data_structures/pq_ds_undo_sliding_window.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/data_structures/pq_ds_undo_with_dsu.test.cpp": "2025-02-10 14:50:36 -0700",
-"tests/library_checker_aizu_tests/data_structures/range_parallel_dsu.test.cpp": "2025-08-28 13:19:16 -0600",
 "tests/library_checker_aizu_tests/data_structures/rmq_disjoint_sparse_table.test.cpp": "2024-12-15 14:34:10 -0600",
 "tests/library_checker_aizu_tests/data_structures/rmq_linear.test.cpp": "2025-08-14 12:01:15 -0600",
 "tests/library_checker_aizu_tests/data_structures/rmq_sparse_table.test.cpp": "2025-08-14 12:01:15 -0600",
@@ -65,20 +64,18 @@
 "tests/library_checker_aizu_tests/graphs/hopcroft_karp_aizu.test.cpp": "2025-08-14 10:27:46 -0600",
 "tests/library_checker_aizu_tests/graphs/hopcroft_karp_lib_checker.test.cpp": "2025-08-14 10:27:46 -0600",
 "tests/library_checker_aizu_tests/graphs/mst.test.cpp": "2025-08-22 13:27:42 -0600",
-"tests/library_checker_aizu_tests/graphs/offline_incremental_scc.test.cpp": "2025-08-28 13:19:16 -0600",
 "tests/library_checker_aizu_tests/graphs/strongly_connected_components_aizu.test.cpp": "2025-08-14 10:27:46 -0600",
 "tests/library_checker_aizu_tests/graphs/strongly_connected_components_lib_checker.test.cpp": "2025-08-14 10:27:46 -0600",
 "tests/library_checker_aizu_tests/graphs/two_edge_components.test.cpp": "2025-08-14 10:27:46 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/count_paths.test.cpp": "2025-08-28 13:57:36 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/dsu.test.cpp": "2025-08-22 13:14:15 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/dsu_size.test.cpp": "2024-12-14 19:50:29 -0600",
-"tests/library_checker_aizu_tests/handmade_tests/edge_cd_small_trees.test.cpp": "2025-08-28 13:19:16 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/fib_matrix_expo.test.cpp": "2025-08-28 13:19:16 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/functional_graph.test.cpp": "2025-08-06 16:18:37 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/manacher.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/merge_st_and_wavelet.test.cpp": "2025-08-04 17:01:28 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/mobius.test.cpp": "2025-02-10 14:50:36 -0700",
-"tests/library_checker_aizu_tests/handmade_tests/mod_int.test.cpp": "2025-08-28 13:19:16 -0600",
+"tests/library_checker_aizu_tests/handmade_tests/mod_division.test.cpp": "2025-09-07 15:15:17 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/n_choose_k.test.cpp": "2025-08-28 13:19:16 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/permutation_tree_small.test.cpp": "2025-08-14 12:01:15 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/rmq_small_n.test.cpp": "2025-08-14 12:01:15 -0600",
@@ -89,21 +86,14 @@
 "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": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/loops/supermasks.test.cpp": "2025-02-10 14:50:36 -0700",
-"tests/library_checker_aizu_tests/math/binary_exponentiation_mod.test.cpp": "2025-08-28 13:19:16 -0600",
 "tests/library_checker_aizu_tests/math/binary_matrix_mult.test.cpp": "2024-11-17 14:04:03 -0600",
 "tests/library_checker_aizu_tests/math/count_paths.test.cpp": "2025-08-28 13:19:16 -0600",
 "tests/library_checker_aizu_tests/math/derangement.test.cpp": "2024-11-17 14:04:03 -0600",
-"tests/library_checker_aizu_tests/math/matrix_determinant.test.cpp": "2025-08-28 13:19:16 -0600",
 "tests/library_checker_aizu_tests/math/matrix_mult.test.cpp": "2024-11-17 14:04:03 -0600",
-"tests/library_checker_aizu_tests/math/mod_int_derangement.test.cpp": "2025-08-28 13:19:16 -0600",
-"tests/library_checker_aizu_tests/math/mod_int_gcd_convolution.test.cpp": "2025-08-28 13:19:16 -0600",
-"tests/library_checker_aizu_tests/math/mod_int_n_choose_k.test.cpp": "2025-08-28 13:19:16 -0600",
-"tests/library_checker_aizu_tests/math/mod_int_tetration.test.cpp": "2025-08-28 13:19:16 -0600",
 "tests/library_checker_aizu_tests/math/n_choose_k.test.cpp": "2025-08-28 13:19:16 -0600",
 "tests/library_checker_aizu_tests/math/num_subsequences.test.cpp": "2024-11-17 14:04:03 -0600",
 "tests/library_checker_aizu_tests/math/partitions.test.cpp": "2025-08-28 13:19:16 -0600",
 "tests/library_checker_aizu_tests/math/prime_sieve.test.cpp": "2024-11-22 11:54:52 -0600",
-"tests/library_checker_aizu_tests/math/solve_linear_mod.test.cpp": "2025-08-28 13:19:16 -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": "2025-08-04 20:35:27 -0600",
@@ -133,7 +123,6 @@
 "tests/library_checker_aizu_tests/trees/edge_cd_contour_range_query.test.cpp": "2025-08-14 10:27:46 -0600",
 "tests/library_checker_aizu_tests/trees/edge_cd_contour_range_update.test.cpp": "2025-08-14 10:27:46 -0600",
 "tests/library_checker_aizu_tests/trees/edge_cd_count_paths_per_length.test.cpp": "2025-08-14 10:27:46 -0600",
-"tests/library_checker_aizu_tests/trees/edge_cd_reroot_dp.test.cpp": "2025-08-28 13:19:16 -0600",
 "tests/library_checker_aizu_tests/trees/hld_aizu1.test.cpp": "2025-08-24 19:27:23 -0600",
 "tests/library_checker_aizu_tests/trees/hld_aizu2.test.cpp": "2025-08-24 19:27:23 -0600",
 "tests/library_checker_aizu_tests/trees/hld_lib_checker_path.test.cpp": "2025-08-24 19:27:23 -0600",
@@ -145,6 +134,5 @@
 "tests/library_checker_aizu_tests/trees/lca_all_methods_aizu.test.cpp": "2025-08-21 12:17:27 -0600",
 "tests/library_checker_aizu_tests/trees/lca_all_methods_lib_checker.test.cpp": "2025-08-21 12:17:27 -0600",
 "tests/library_checker_aizu_tests/trees/shallowest_aizu_tree_height.test.cpp": "2025-09-03 10:32:09 -0600",
-"tests/library_checker_aizu_tests/trees/shallowest_lib_checker_tree_path_composite.test.cpp": "2025-09-03 10:32:09 -0600",
 "tests/library_checker_aizu_tests/trees/subtree_isomorphism.test.cpp": "2025-08-14 10:27:46 -0600"
 }

library/math/matrix_related/row_reduce.hpp

@@ -1,5 +1,5 @@
 #pragma once
-#include "../mod_int.hpp"
+#include "../mod_division.hpp"
 //! @code
 //!   auto [rank, det] = row_reduce(mat, cols);
 //! @endcode
@@ -8,28 +8,30 @@
 //!   affected by row operations
 //! @time O(n * m * min(cols, n))
 //! @space O(1)
-pair<int, mint> row_reduce(vector<vector<mint>>& mat,
-  int cols) {
+pii row_reduce(vector<vi>& mat, int cols) {
   int n = sz(mat), m = sz(mat[0]), rank = 0;
-  mint det = 1;
+  int det = 1;
   for (int col = 0; col < cols && rank < n; col++) {
     auto it = find_if(rank + all(mat),
-      [&](auto& v) { return v[col].x; });
+      [&](auto& v) { return v[col]; });
     if (it == end(mat)) {
       det = 0;
       continue;
     }
     if (it != begin(mat) + rank) {
-      det = mint(0) - det;
+      det = (mod - det) % mod;
       iter_swap(begin(mat) + rank, it);
     }
-    det = det * mat[rank][col];
-    mint a_inv = mint(1) / mat[rank][col];
-    for (mint& num : mat[rank]) num = num * a_inv;
-    rep(i, 0, n) if (i != rank && mat[i][col].x != 0) {
-      mint num = mat[i][col];
+    det = 1LL * det * mat[rank][col] % mod;
+    int a_inv = mod_div(1, mat[rank][col]);
+    for (int& num : mat[rank])
+      num = 1LL * num * a_inv % mod;
+    rep(i, 0, n) if (i != rank && mat[i][col] != 0) {
+      int num = mat[i][col];
       rep(j, 0, m) mat[i][j] =
-        mat[i][j] - mat[rank][j] * num;
+        ((mat[i][j] - 1LL * mat[rank][j] * num) % mod +
+          mod) %
+        mod;
     }
     rank++;
   }

library/math/matrix_related/solve_linear_mod.hpp

@@ -11,22 +11,20 @@
 //! @time O(n * m * min(n, m))
 //! @space O(m)
 struct solve_linear_mod {
-  int rank;
-  mint det;
-  vector<mint> sol;
-  solve_linear_mod(vector<vector<mint>>& mat,
-    const vector<mint>& rhs) {
+  int rank, det;
+  vi sol;
+  solve_linear_mod(vector<vi>& mat, const vi& rhs) {
     int n = sz(mat), m = sz(mat[0]);
     rep(i, 0, n) mat[i].push_back(rhs[i]);
     tie(rank, det) = row_reduce(mat, m);
     if (any_of(rank + all(mat),
-          [](auto& v) { return v.back().x; })) {
+          [](vi& v) { return v.back(); })) {
       return;
     }
     sol.resize(m);
     int j = 0;
-    for_each(begin(mat), begin(mat) + rank, [&](auto& v) {
-      while (v[j].x == 0) j++;
+    for_each(begin(mat), begin(mat) + rank, [&](vi& v) {
+      while (!v[j]) j++;
       sol[j] = v.back();
     });
   }

library/math/mod_division.hpp

@@ -0,0 +1,8 @@
+#pragma once
+const int mod = 998244353;
+int mod_div(int x, int y) {
+  int m = mod, u = 1, v = 0;
+  while (m) swap(u -= y / m * v, v), swap(y %= m, m);
+  assert(y == 1);
+  return 1LL * x * (u + mod) % mod;
+}

library/math/mod_int.hpp

@@ -4,23 +4,19 @@
 #include "../template.hpp"
 #include "../../../library/data_structures/dsu/range_parallel_dsu.hpp"
 #include "../../../library/data_structures/dsu/range_parallel_equivalence_classes.hpp"
-#include "../../../library/math/mod_int.hpp"
+const int mod = 998244353;
 int main() {
   cin.tie(0)->sync_with_stdio(0);
   int n, q;
   cin >> n >> q;
   rp_dsu dsu(n);
-  vector<mint> y(n);
-  for (int i = 0; i < n; i++) {
-    int num;
-    cin >> num;
-    y[i] = num;
-  }
-  vector<mint> x = y;
-  mint ans = 0;
+  vi y(n);
+  for (int i = 0; i < n; i++) cin >> y[i];
+  vi x = y;
+  int ans = 0;
   auto f = [&](int u, int v) {
-    ans = ans + x[u] * x[v];
-    x[u] = x[u] + x[v];
+    ans = (ans + 1LL * x[u] * x[v]) % mod;
+    x[u] = (x[u] + x[v]) % mod;
   };
   vector<array<int, 3>> queries;
   queries.reserve(q);
@@ -29,18 +25,19 @@ int main() {
     cin >> k >> a >> b;
     dsu.join(a, b, k, f);
     queries.push_back({a, b, k});
-    cout << ans.x << '\n';
+    cout << ans << '\n';
     if (qq == 0 || qq == 1 || qq == 10 || qq == 1000 ||
       qq == 100'000 || qq == q - 1) {
       auto uf = get_rp_dsu(queries, n);
-      vector<mint> sums(n);
-      mint offline_ans = 0;
+      vi sums(n);
+      int offline_ans = 0;
       for (int i = 0; i < n; i++) {
         int id = uf.find(i);
-        offline_ans = offline_ans + sums[id] * y[i];
-        sums[id] = sums[id] + y[i];
+        offline_ans =
+          (offline_ans + 1LL * sums[id] * y[i]) % mod;
+        sums[id] = (sums[id] + y[i]) % mod;
       }
-      assert(ans.x == offline_ans.x);
+      assert(ans == offline_ans);
     }
   }
   return 0;

library/math/mod_int_division.hpp

@@ -3,13 +3,13 @@
 #include "../template.hpp"
 #include "../../../library/graphs/strongly_connected_components/offline_incremental_scc.hpp"
 #include "../../../library/data_structures/dsu/dsu.hpp"
-#include "../../../library/math/mod_int.hpp"
+const int mod = 998244353;
 int main() {
   cin.tie(0)->sync_with_stdio(0);
   int n, m;
   cin >> n >> m;
-  vector<mint> xs(n);
-  for (int i = 0; i < n; i++) cin >> xs[i].x;
+  vector<int> xs(n);
+  for (int i = 0; i < n; i++) cin >> xs[i];
   vector<array<int, 2>> eds(m);
   for (auto& [u, v] : eds) cin >> u >> v;
   auto joins = offline_incremental_scc(eds, n);
@@ -21,22 +21,22 @@ int main() {
   ranges::sort(all(order), {},
     [&](int i) { return joins[i]; });
   DSU dsu(n);
-  mint sum = 0;
+  int sum = 0;
   for (int t = 0, it = 0; t < m; t++) {
     while (it < m && joins[order[it]] <= t) {
       auto [u, v] = eds[order[it]];
       u = dsu.go(u);
       v = dsu.go(v);
       if (dsu.e[u] > dsu.e[v]) swap(u, v);
       if (u != v) {
-        sum = sum + xs[u] * xs[v];
-        xs[u] = xs[u] + xs[v];
+        sum = (sum + 1LL * xs[u] * xs[v]) % mod;
+        xs[u] = (xs[u] + xs[v]) % mod;
         xs[v] = xs[u];
       }
       dsu.join(u, v);
       it++;
     }
-    cout << sum.x << '\n';
+    cout << sum << '\n';
   }
   return 0;
 }

library/math/mod_int_pow.hpp

@@ -3,7 +3,6 @@
 #include "../template.hpp"
 #include "../edge_cd_asserts.hpp"
 #include "../../../kactl/stress-tests/utilities/genTree.h"
-#include "../../../library/math/mod_int_pow.hpp"
 #include "../../../library/trees/edge_cd.hpp"
 int main() {
   {
@@ -21,7 +20,9 @@ int main() {
       });
   }
   for (int n = 2; n <= 7; n++) {
-    int num_codes = mpow(n, n - 2).x;
+    int num_codes = 1;
+    for (int k = 0; k < n - 2; k++) num_codes *= n;
+    // int num_codes = mpow(n, n - 2).x;
     vector<vector<int>> pruf_codes(num_codes,
       vector<int>(n - 2));
     for (int i = 0; i < num_codes; i++) {