From 6062bbb4807a424fc4ca238edd32b81d18804af3 Mon Sep 17 00:00:00 2001
From: hitonanode <32937551+hitonanode@users.noreply.github.com>
Date: Tue, 7 Oct 2025 09:40:50 +0900
Subject: [PATCH 1/2] fix doubling

---
 other_algorithms/doubling.hpp                 | 46 +++++++++++--------
 other_algorithms/doubling.md                  | 28 +++++++++++
 .../test/doubling.yuki3305.test.cpp           | 35 ++++++++++++++
 3 files changed, 89 insertions(+), 20 deletions(-)
 create mode 100644 other_algorithms/doubling.md
 create mode 100644 other_algorithms/test/doubling.yuki3305.test.cpp

diff --git a/other_algorithms/doubling.hpp b/other_algorithms/doubling.hpp
index 039752bc..bf0c9c2d 100644
--- a/other_algorithms/doubling.hpp
+++ b/other_algorithms/doubling.hpp
@@ -1,45 +1,51 @@
 #pragma once
-#include <cstdlib>
+#include <cassert>
 #include <vector>
 
-// CUT begin
 // Binary lifting / `Doubling`
 // Complexity: O(NlogN) precalculation / O(logN) per query
-// <https://atcoder.jp/contests/arc060/submissions/7039451>
+// https://atcoder.jp/contests/arc060/submissions/7039451
 struct BinaryLifting {
-    int N, INVALID, lgD;
+    int N, lgD;
+
+    bool is_valid(int idx) const { return 0 <= idx and idx < N; }
+
     std::vector<std::vector<int>> mat;
     BinaryLifting() : N(0), lgD(0) {}
-    BinaryLifting(const std::vector<int> &vec_nxt, int INVALID = -1, int lgd = 0)
-        : N(vec_nxt.size()), INVALID(INVALID), lgD(lgd) {
+    BinaryLifting(const std::vector<int> &to, int lgd = 0) : N(to.size()), lgD(lgd) {
         while ((1LL << lgD) < N) lgD++;
-        mat.assign(lgD, std::vector<int>(N, INVALID));
-        mat[0] = vec_nxt;
-        for (int i = 0; i < N; i++)
-            if (mat[0][i] < 0 or mat[0][i] >= N) mat[0][i] = INVALID;
+        mat.assign(lgD, std::vector<int>(N));
+        mat[0] = to;
+
         for (int d = 0; d < lgD - 1; d++) {
-            for (int i = 0; i < N; i++)
-                if (mat[d][i] != INVALID) mat[d + 1][i] = mat[d][mat[d][i]];
+            for (int i = 0; i < N; i++) {
+                mat[d + 1][i] = mat[d][is_valid(mat[d][i]) ? mat[d][i] : i];
+            }
         }
     }
-    int kth_next(int now, long long k) {
-        if (k >= (1LL << lgD)) exit(8);
-        for (int d = 0; k and now != INVALID; d++, k >>= 1)
+
+    int kth_next(int now, long long k) const {
+        assert(k >= 0);
+        assert(k < (1LL << lgD));
+        for (int d = 0; k and is_valid(now); d++, k >>= 1) {
             if (k & 1) now = mat[d][now];
+        }
         return now;
     }
 
     // Distance from l to [r, \infty)
-    // Requirement: mat[0][i] > i for all i (monotone increasing)
-    int distance(int l, int r) {
+    // Requirement: mat[0][i] >= r (i = r, r + 1, ...) (monotone)
+    int distance(int l, int r) const {
         if (l >= r) return 0;
         int ret = 0;
         for (int d = lgD - 1; d >= 0; d--) {
-            if (mat[d][l] < r and mat[d][l] != INVALID) ret += 1 << d, l = mat[d][l];
+            if (mat[d][l] < r and is_valid(mat[d][l])) ret += 1 << d, l = mat[d][l];
         }
-        if (mat[0][l] == INVALID or mat[0][l] >= r)
+
+        if (!is_valid(mat[0][l]) or mat[0][l] >= r) {
             return ret + 1;
-        else
+        } else {
             return -1; // Unable to reach
+        }
     }
 };
diff --git a/other_algorithms/doubling.md b/other_algorithms/doubling.md
new file mode 100644
index 00000000..b0550da3
--- /dev/null
+++ b/other_algorithms/doubling.md
@@ -0,0 +1,28 @@
+---
+title: Binary lifting / doubling （ダブリング）
+documentation_of: ./doubling.hpp
+---
+
+Functional graph 上のダブリングライブラリ． binary_lifting.hpp とは異なり辺に重みなどは載せられない．
+
+## 使用方法
+
+### `BinaryLifting binary_lifting(std::vector<int> to)`
+
+コンストラクタ．引数として $g(0), \ldots, g(n - 1)$ を与える．
+
+直感的には，各頂点 $i = 0, \ldots, n - 1$ について $i$ から頂点 $g(i)$ へ有向辺が張られている functional graph に相当する． $g(i)$ の値は $0$ 未満や $n$ 以上でも構わない（下記の各関数は， $[0, n)$ の範囲外の頂点 $i$ からは $i$ 自身への重み $e$ の自己ループが生えている，と解釈するとつじつまが合うように設計されている）．
+
+### `int kth_next(int s, long long k)`
+
+$g^k (s)$ の値（途中で $[0, n)$ の範囲外に出る場合はその値）を $O(\log k)$ で返す．
+
+### `int distance(int l, int r)`
+
+$g^k (s)$ の値が初めて `r` 以上になる $k$ を計算する．この条件が満たされることはない場合は `-1` を返す．
+
+この条件に関する単調性が必要．
+
+## 問題例
+
+- [No.3305 Shift Sort - yukicoder](https://yukicoder.me/problems/no/3305)
diff --git a/other_algorithms/test/doubling.yuki3305.test.cpp b/other_algorithms/test/doubling.yuki3305.test.cpp
new file mode 100644
index 00000000..d72385d9
--- /dev/null
+++ b/other_algorithms/test/doubling.yuki3305.test.cpp
@@ -0,0 +1,35 @@
+#define PROBLEM "https://yukicoder.me/problems/no/3305"
+#include "../doubling.hpp"
+
+#include <iostream>
+#include <utility>
+#include <vector>
+using namespace std;
+
+int main() {
+    cin.tie(nullptr), ios::sync_with_stdio(false);
+
+    int N, Q;
+    cin >> N >> Q;
+    vector<int> A(N);
+    for (auto &a : A) cin >> a;
+
+    vector<int> nexts(N, N);
+
+    vector<pair<int, int>> st;
+    st.emplace_back(N, N);
+    for (int i = N - 1; i >= 0; --i) {
+        while (st.back().first < A.at(i)) st.pop_back();
+        nexts.at(i) = st.back().second;
+        st.emplace_back(A.at(i), i);
+    }
+
+    const BinaryLifting binary_lifting(nexts);
+
+    while (Q--) {
+        int l, r;
+        cin >> l >> r;
+        --l;
+        cout << r - l - binary_lifting.distance(l, r) << '\n';
+    }
+}

From 1a32aa19470b7cee5335b008300aeb24bedfe663 Mon Sep 17 00:00:00 2001
From: hitonanode <32937551+hitonanode@users.noreply.github.com>
Date: Tue, 7 Oct 2025 09:41:07 +0900
Subject: [PATCH 2/2] fix lazy segtree

---
 segmenttree/acl_lazysegtree.hpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/segmenttree/acl_lazysegtree.hpp b/segmenttree/acl_lazysegtree.hpp
index e5e76430..7b8b2e03 100644
--- a/segmenttree/acl_lazysegtree.hpp
+++ b/segmenttree/acl_lazysegtree.hpp
@@ -60,7 +60,7 @@ constexpr int countr_zero_constexpr(unsigned int n) {
 #include <functional>
 #include <vector>
 
-#include "atcoder/internal_bit"
+// #include "atcoder/internal_bit"
 
 namespace atcoder {