Kd bit (#184)

* first draft

* add another test

* add docs now

* fix script

* another fix

* fix compile error

* add more docs

* [auto-verifier] verify commit 0470395

---------

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

Author: lrvideckis

.verify-helper/timestamps.remote.json

@@ -23,6 +23,7 @@
 "tests/library_checker_aizu_tests/data_structures/dsu_restorable.test.cpp": "2026-01-18 02:20:40 +0000",
 "tests/library_checker_aizu_tests/data_structures/dsu_segtree_undo_trick.test.cpp": "2026-01-23 04:31:29 +0000",
 "tests/library_checker_aizu_tests/data_structures/implicit_seg_tree.test.cpp": "2026-01-18 11:15:41 +0000",
+"tests/library_checker_aizu_tests/data_structures/kd_bit_1d.test.cpp": "2026-02-19 11:51:03 -0700",
 "tests/library_checker_aizu_tests/data_structures/kruskal_tree_aizu.test.cpp": "2026-01-18 02:20:40 +0000",
 "tests/library_checker_aizu_tests/data_structures/kth_smallest_pst.test.cpp": "2026-01-18 11:15:41 +0000",
 "tests/library_checker_aizu_tests/data_structures/kth_smallest_wavelet_matrix.test.cpp": "2026-02-04 02:50:53 +0000",
@@ -76,6 +77,7 @@
 "tests/library_checker_aizu_tests/handmade_tests/fib_matrix_expo.test.cpp": "2026-01-28 21:48:16 -0700",
 "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": "2026-01-18 02:20:40 +0000",
+"tests/library_checker_aizu_tests/handmade_tests/kd_bit.test.cpp": "2026-02-19 11:51:03 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/manacher.test.cpp": "2026-01-18 11:15:41 +0000",
 "tests/library_checker_aizu_tests/handmade_tests/merge_st_and_wavelet.test.cpp": "2026-02-04 02:50:53 +0000",
 "tests/library_checker_aizu_tests/handmade_tests/mobius.test.cpp": "2025-02-10 14:50:36 -0700",

library/data_structures_[l,r)/bit_uncommon/kd_bit.hpp

@@ -0,0 +1,32 @@
+#pragma once
+//! https://github.com/ucf-programming-team/hackpack-cpp/blob/master/content/data-structures/KDBIT.h
+//! @code
+//!   KD_BIT<2> bit(n, m);
+//!   bit.update(i, j, 5);
+//!   bit.query(i1, i2, j1, j2);
+//!   // 0 <= i1 <= i2 <= n
+//!   // 0 <= j1 <= j2 <= m
+//! @endcode
+//! @time O(n^k + q * log^k n)
+//! @space O(n^k)
+// NOLINTNEXTLINE(readability-identifier-naming)
+template<int K> struct KD_BIT;
+template<> struct KD_BIT<0> {
+  ll s = 0;
+  void update(ll v) { s += v; }
+  ll query() { return s; }
+};
+template<int K> struct KD_BIT {
+  vector<KD_BIT<K - 1>> s;
+  template<class... A>
+  KD_BIT(int n, A... a): s(n, KD_BIT<K - 1>(a...)) {}
+  template<class... A> void update(int i, A... a) {
+    for (; i < sz(s); i |= i + 1) s[i].update(a...);
+  }
+  template<class... A> ll query(int l, int r, A... a) {
+    ll ans = 0;
+    for (; l < r; r &= r - 1) ans += s[r - 1].query(a...);
+    for (; r < l; l &= l - 1) ans -= s[l - 1].query(a...);
+    return ans;
+  }
+};

tests/library_checker_aizu_tests/data_structures/kd_bit_1d.test.cpp

@@ -0,0 +1,34 @@
+#define PROBLEM \
+  "https://judge.yosupo.jp/problem/point_add_range_sum"
+#include "../template.hpp"
+#include "../../../library/data_structures_[l,r)/bit_uncommon/kd_bit.hpp"
+int main() {
+  cin.tie(0)->sync_with_stdio(0);
+  int n, q;
+  cin >> n >> q;
+  KD_BIT<1> bit1(n);
+  KD_BIT<2> bit2(1, n);
+  for (int i = 0; i < n; i++) {
+    int val;
+    cin >> val;
+    bit1.update(i, val);
+    bit2.update(0, i, val);
+  }
+  while (q--) {
+    int type;
+    cin >> type;
+    if (type == 0) {
+      int p, x;
+      cin >> p >> x;
+      bit1.update(p, x);
+      bit2.update(0, p, x);
+    } else {
+      int l, r;
+      cin >> l >> r;
+      ll res = bit1.query(l, r);
+      assert(res == bit2.query(0, 1, l, r));
+      cout << res << '\n';
+    }
+  }
+  return 0;
+}

tests/library_checker_aizu_tests/handmade_tests/kd_bit.test.cpp

@@ -0,0 +1,36 @@
+#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_[l,r)/bit_uncommon/kd_bit.hpp"
+int main() {
+  cin.tie(0)->sync_with_stdio(0);
+  for (int num_tests = 0; num_tests < 100; num_tests++) {
+    int n = rnd(1, 100);
+    int m = rnd(1, 100);
+    KD_BIT<2> bit(n, m);
+    vector<vector<ll>> a(n, vector<ll>(m, 0));
+    for (int events = 0; events < 100; events++) {
+      if (events % 2 == 0) {
+        int i = rnd(0, n - 1);
+        int j = rnd(0, m - 1);
+        ll upd = rnd(INT_MIN, INT_MAX);
+        a[i][j] += upd;
+        bit.update(i, j, upd);
+      } else {
+        int i1 = rnd(0, n);
+        int j1 = rnd(0, m);
+        int i2 = rnd(0, n);
+        int j2 = rnd(0, m);
+        if (i1 > i2) swap(i1, i2);
+        if (j1 > j2) swap(j1, j2);
+        ll naive = 0;
+        for (int i = i1; i < i2; i++)
+          for (int j = j1; j < j2; j++) naive += a[i][j];
+        assert(naive == bit.query(i1, i2, j1, j2));
+      }
+    }
+  }
+  cout << "Hello World\n";
+  return 0;
+}

tests/scripts/compile_commented_snippets.sh

@@ -25,7 +25,7 @@ git submodule update
 	echo "vi rhs;"
 	echo "vector<vi> mat;"
 	echo "vector<vector<bool>> grid;"
-	echo "int n,m,k,tl,tr,l,r,l1,r1,l2,r2,s_l,s_r,root_l,root_r,source,sink,total_flow,bccid,u,v,lsz,rsz,cols,cap,num,x,y;"
+	echo "int n,m,k,tl,tr,l,r,l1,r1,l2,r2,s_l,s_r,root_l,root_r,source,sink,total_flow,bccid,u,v,lsz,rsz,cols,cap,num,x,y,i,j,i1,i2,j1,j2;"
 } >entire_library_without_main
 
 {