add seg tree walk (#179)

* add seg tree walk

* [auto-verifier] verify commit b20b54c

* update docs

---------

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

Author: lrvideckis

.verify-helper/timestamps.remote.json

@@ -44,8 +44,9 @@
 "tests/library_checker_aizu_tests/data_structures/rmq_sparse_table.test.cpp": "2026-01-18 11:15:41 +0000",
 "tests/library_checker_aizu_tests/data_structures/rmq_sparse_table_inc.test.cpp": "2026-01-18 11:15:41 +0000",
 "tests/library_checker_aizu_tests/data_structures/simple_tree.test.cpp": "2026-01-28 21:53:13 -0700",
-"tests/library_checker_aizu_tests/data_structures/simple_tree_inc.test.cpp": "2026-01-28 21:53:13 -0700",
-"tests/library_checker_aizu_tests/data_structures/simple_tree_inc_line.test.cpp": "2026-01-28 21:53:13 -0700",
+"tests/library_checker_aizu_tests/data_structures/simple_tree_inc.test.cpp": "2026-02-05 11:36:54 -0700",
+"tests/library_checker_aizu_tests/data_structures/simple_tree_inc_line.test.cpp": "2026-02-05 11:36:54 -0700",
+"tests/library_checker_aizu_tests/data_structures/simple_tree_inc_walk.test.cpp": "2026-02-05 11:36:54 -0700",
 "tests/library_checker_aizu_tests/data_structures/simple_tree_line.test.cpp": "2026-01-28 21:53:13 -0700",
 "tests/library_checker_aizu_tests/flow/dinic_aizu.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",

library/data_structures_[l,r]/seg_tree.hpp

@@ -2,11 +2,19 @@
 //! https://codeforces.com/blog/entry/118682
 //! @code
 //!   {
-//!     tree st(n, 0LL, [&](ll l, ll r) {
-//!       return l + r;
+//!     tree st(a, [&](int vl, int vr) {
+//!       return vl & vr;
 //!     });
 //!   }
-//!   tree st(n, INT_MAX, ranges::min);
+//!   {
+//!     tree st(n, 0LL, plus<ll>{});
+//!   }
+//!   {
+//!     tree st(n, INT_MAX, ranges::min);
+//!     int idx = st.walk(l, r, [&](int value) {
+//!       return value <= x;
+//!     }); // smallest index in [l, r] s.t. f is true
+//!   }
 //! @endcode
 //! @time O(n + q log n)
 //! @space O(n)
@@ -30,4 +38,5 @@ template<class T, class F> struct tree {
     while (l <= r) x = op(x, s[nxt(l, r)]);
     return x;
   }
+#include "seg_tree_uncommon/walk.hpp"
 };

library/data_structures_[l,r]/seg_tree_uncommon/walk.hpp

@@ -0,0 +1,10 @@
+T walk(int l, int r, function<bool(T)> f) {
+  for (l += n, r += n; l <= r;)
+    if (int u = nxt(l, r); f(s[u])) {
+      while (u < n)
+        if (f(s[2 * u])) u = 2 * u;
+        else u = 2 * u + 1;
+      return u - n;
+    }
+  return -1;
+}

tests/library_checker_aizu_tests/data_structures/simple_tree_inc_walk.test.cpp

@@ -0,0 +1,44 @@
+#define PROBLEM \
+  "https://judge.yosupo.jp/problem/predecessor_problem"
+#include "../template.hpp"
+#include "../../../library/data_structures_[l,r]/seg_tree.hpp"
+int main() {
+  cin.tie(0)->sync_with_stdio(0);
+  int n, q;
+  cin >> n >> q;
+  string s;
+  cin >> s;
+  vector<int> init(n);
+  for (int i = 0; i < n; i++) init[i] = s[i] - '0';
+  tree st(init, plus<int>{});
+  while (q--) {
+    int type, k;
+    cin >> type >> k;
+    if (type == 0) {
+      if (st.query(k, k) == 0) st.update(k, 1);
+    } else if (type == 1) {
+      if (st.query(k, k) == 1) st.update(k, 0);
+    } else if (type == 2) {
+      cout << st.query(k, k) << '\n';
+    } else if (type == 3) {
+      // returns first element in [k,n-1] such that sum > 0
+      cout << st.walk(k, n - 1, [&](int sum) {
+        return sum > 0;
+      }) << '\n';
+    } else {
+      assert(type == 4);
+      int total = st.query(0, k);
+      if (total == 0) {
+        cout << -1 << '\n';
+      } else {
+        int pref_sum = 0;
+        cout << st.walk(0, k, [&](int sum) {
+          if (pref_sum + sum == total) return 1;
+          pref_sum += sum;
+          return 0;
+        }) << '\n';
+      }
+    }
+  }
+  return 0;
+}