first draft of hilbert (#165)

* first draft of hilbert

* [auto-verifier] verify commit 00332a7

* format

* [auto-verifier] verify commit be8cbef

---------

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

Author: lrvideckis

.verify-helper/timestamps.remote.json

@@ -75,6 +75,7 @@
 "tests/library_checker_aizu_tests/handmade_tests/edge_cd_small_trees.test.cpp": "2025-09-07 15:50:55 -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/hilbert_mos.test.cpp": "2026-01-07 15:45:02 -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",

library/data_structures/uncommon/hilbert_mos.hpp

@@ -0,0 +1,23 @@
+#pragma once
+//! https://codeforces.com/blog/entry/61203?#comment-1064868
+//! @code
+//!   vector<pii> queries;
+//!   ranges::sort(queries, {}, [&](pii& x) {
+//!     return hilbert(x.first, x.second);
+//!   });
+//! @endcode
+//! @time O(log(n))
+//! @space O(1)
+ll hilbert(int x, int y) {
+  ll d = 0, mx = 1;
+  while (mx <= max(x, y)) mx *= 4;
+  for (int s = mx / 2; s; s /= 2) {
+    bool rx = x & s, ry = y & s;
+    d = d * 4 | (ry * 3 ^ rx);
+    if (!rx) {
+      if (ry) x ^= mx - 1, y ^= mx - 1;
+      swap(x, y);
+    }
+  }
+  return d;
+}

tests/library_checker_aizu_tests/handmade_tests/hilbert_mos.test.cpp

@@ -0,0 +1,34 @@
+#define PROBLEM \
+  "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A"
+#include "../template.hpp"
+#include "../../../library/contest/random.hpp"
+#include "../../../library/data_structures/uncommon/hilbert_mos.hpp"
+const vector<int> di = {1, -1, 0, 0};
+const vector<int> dj = {0, 0, 1, -1};
+void test(int i, int j) {
+  ll res = hilbert(i, j);
+  int cnt_prev = 0;
+  int cnt_next = 0;
+  for (int k = 0; k < 4; k++) {
+    int to_i = i + di[k];
+    int to_j = j + dj[k];
+    if (to_i >= 0 && to_j >= 0) {
+      cnt_prev += (res - 1 == hilbert(to_i, to_j));
+      cnt_next += (res + 1 == hilbert(to_i, to_j));
+    }
+  }
+  if (i == 0 && j == 0) assert(res == 0);
+  else assert(cnt_prev == 1);
+  assert(cnt_next == 1);
+}
+int main() {
+  cin.tie(0)->sync_with_stdio(0);
+  for (int i = 0; i < 3000; i++)
+    for (int j = 0; j < 3000; j++) test(i, j);
+  for (int iter = 50000; iter--;) {
+    int i = rnd(0, 1'000'000'000);
+    int j = rnd(0, 1'000'000'000);
+    test(i, j);
+  }
+  cout << "Hello World\n";
+}