Add kth access to binary trie

Author: KKT89

docsrc/library/data_structure/binary_trie.md

@@ -6,7 +6,9 @@
 
 ```cpp
 binary_trie<T, LOG> bt;               // 空の集合で初期化 (T は整数型, LOG はビット幅)
+int n = bt.size();                    // 要素数
 bt.insert(x);                         // x を追加
 bt.erase(x);                          // x を 1 つ削除 (存在前提)
+T x = bt[k];                          // k 番目 (0-indexed) に小さい値を取得
 int cnt = bt.count_xor_leq(val, k);   // x XOR val <= k を満たす x の個数
 ```

include/data_structure/binary_trie.hpp

@@ -1,5 +1,6 @@
 #pragma once
 #include <array>
+#include <cassert>
 #include <vector>
 
 template <class T, int LOG> struct binary_trie {
@@ -11,6 +12,8 @@ template <class T, int LOG> struct binary_trie {
 
     binary_trie() { nodes.emplace_back(); }
 
+    int size() const { return nodes[0].cnt; }
+
     void insert(T x) {
         int cur = 0;
         nodes[cur].cnt++;
@@ -35,6 +38,24 @@ template <class T, int LOG> struct binary_trie {
         }
     }
 
+    T operator[](int k) const {
+        assert(0 <= k && k < size());
+        int cur = 0;
+        T x = 0;
+        for (int i = LOG - 1; i >= 0; --i) {
+            int left = nodes[cur].ch[0];
+            int left_cnt = left == -1 ? 0 : nodes[left].cnt;
+            if (k < left_cnt) {
+                cur = left;
+            } else {
+                k -= left_cnt;
+                cur = nodes[cur].ch[1];
+                x |= (T(1) << i);
+            }
+        }
+        return x;
+    }
+
     // x XOR val <= k となる整数 x の個数
     int count_xor_leq(T val, T k) {
         int cur = 0;

verify/atcoder/abc458_d_chalkboard_median.cpp

@@ -0,0 +1,23 @@
+#include <bits/stdc++.h>
+using namespace std;
+typedef long long ll;
+
+#include "data_structure/binary_trie.hpp"
+
+int main() {
+    ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+    int x;
+    cin >> x;
+    binary_trie<int, 30> bt;
+    bt.insert(x);
+    int q;
+    cin >> q;
+    while (q--) {
+        int a, b;
+        cin >> a >> b;
+        bt.insert(a);
+        bt.insert(b);
+        cout << bt[(bt.size() - 1) / 2] << "\n";
+    }
+}

verify/status.json

@@ -24,8 +24,8 @@
     "title": "Z Algorithm"
   },
   "verify/atcoder/abc451_g_minimum_xor_walk.cpp": {
-    "bundled_hash": "sha256:d266f898b580d1197a7cf29a26e4ceb975c7bd33b2c8c50a455e51648d6770d8",
-    "verified_at": "2026-04-03T16:55:13+09:00",
+    "bundled_hash": "sha256:2a3f71e3976951bc89e7368b62777c2ee1d6ffbe2f6b4a075b1abb63f9d67628",
+    "verified_at": "2026-05-26T10:58:36+09:00",
     "judge_url": "https://atcoder.jp/contests/abc451/tasks/abc451_g",
     "title": "ABC451 G - Minimum XOR Walk"
   },
@@ -34,5 +34,11 @@
     "verified_at": "2026-05-19T14:54:32+09:00",
     "judge_url": "https://atcoder.jp/contests/abc453/tasks/abc453_g",
     "title": "ABC453 G - Copy Query"
+  },
+  "verify/atcoder/abc458_d_chalkboard_median.cpp": {
+    "bundled_hash": "sha256:a90e5d31eaf6074a782c025dc6e88e222e73fb9bd9112fac47907117bbc3663c",
+    "verified_at": "2026-05-26T10:58:14+09:00",
+    "judge_url": "https://atcoder.jp/contests/abc458/tasks/abc458_d",
+    "title": "ABC458 D - Chalkboard Median"
   }
 }