ds/rmq/range_add_range_min.hpp

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• Last update: 2025-10-13 19:00:48+09:00
• Include: #include "ds/rmq/range_add_range_min.hpp"

Depends on

• ds/segtree/segtree.hpp

Verified with

• test/1_mytest/range_add_range_min.test.cpp

Code

#include "ds/segtree/segtree.hpp"

// INF+x==INF みたいな処理は入れていない
// N=Q=10^6 で lazysegtree より 20,30% 程度高速な場合がある
template <typename T>
struct Range_Add_Range_Min {
  struct Mono {
    using value_type = pair<T, T>;
    using X = value_type;
    static X op(X L, X R) { return {L.fi + R.fi, min(L.se, L.fi + R.se)}; }
    static constexpr X unit() { return {0, 2 * infty<T>}; }
    static constexpr bool commute = false;
  };
  int n;
  T lazy;
  SegTree<Mono> seg;

  Range_Add_Range_Min() {}
  Range_Add_Range_Min(int n) { build(n); }
  template <typename F>
  Range_Add_Range_Min(int n, F f) {
    build(n, f);
  }
  Range_Add_Range_Min(const vc<T>& v) { build(v); }

  void build(int m) {
    build(m, [](int i) -> T { return infty<T>; });
  }
  void build(const vc<T>& v) {
    build(len(v), [&](int i) -> T { return v[i]; });
  }
  template <typename F>
  void build(int m, F f) {
    lazy = 0;
    n = m;
    T pre = 0;
    seg.build(n, [&](int i) -> pair<T, T> {
      T t = f(i) - pre;
      pre += t;
      return {t, t};
    });
  }

  T prod(int L, int R) {
    if (L == R) return infty<T>;
    ll ans = seg.prod(L, R).se;
    L += seg.size;
    for (; L > 0; L /= 2) {
      if (L & 1) ans += seg.dat[--L].fi;
    }
    return ans + lazy;
  }

  T prod_all() { return prod(0, n); }

  // 基本デバッグ用というつもりでさぼり O(NlogN) になっている
  vc<T> get_all() {
    vc<T> ANS(n);
    FOR(i, n) ANS[i] = prod(i, i + 1);
    return ANS;
  }

  void apply(int L, int R, T x) { apply_suffix(L, x), apply_suffix(R, -x); }

  // [0,i)
  void apply_prefix(int i, T x) {
    lazy += x;
    apply_suffix(i, -x);
  }

  // [i,n)
  void apply_suffix(int i, T x) {
    if (i == n) return;
    T t = seg.get(i).fi + x;
    seg.set(i, {t, t});
  }
  void apply_all(T x) { lazy += x; }

  void set(int i, T x) {
    T now = prod(i, i + 1);
    apply(i, i + 1, x - now);
  }

  void multiply(int i, T x) {
    T now = prod(i, i + 1);
    if (now > x) apply(i, i + 1, x - now);
  }
};

#line 2 "ds/segtree/segtree.hpp"

template <class Monoid>
struct SegTree {
  using MX = Monoid;
  using X = typename MX::value_type;
  using value_type = X;
  vc<X> dat;
  int n, log, size;

  SegTree() {}
  SegTree(int n) { build(n); }
  template <typename F>
  SegTree(int n, F f) {
    build(n, f);
  }
  SegTree(const vc<X>& v) { build(v); }

  void build(int m) {
    build(m, [](int i) -> X { return MX::unit(); });
  }
  void build(const vc<X>& v) {
    build(len(v), [&](int i) -> X { return v[i]; });
  }
  template <typename F>
  void build(int m, F f) {
    n = m, log = 1;
    while ((1 << log) < n) ++log;
    size = 1 << log;
    dat.assign(size << 1, MX::unit());
    FOR(i, n) dat[size + i] = f(i);
    FOR_R(i, 1, size) update(i);
  }

  X get(int i) { return dat[size + i]; }
  vc<X> get_all() { return {dat.begin() + size, dat.begin() + size + n}; }

  void update(int i) { dat[i] = Monoid::op(dat[2 * i], dat[2 * i + 1]); }
  void set(int i, const X& x) {
    assert(i < n);
    dat[i += size] = x;
    while (i >>= 1) update(i);
  }

  void multiply(int i, const X& x) {
    assert(i < n);
    i += size;
    dat[i] = Monoid::op(dat[i], x);
    while (i >>= 1) update(i);
  }

  X prod(int L, int R) {
    assert(0 <= L && L <= R && R <= n);
    X vl = Monoid::unit(), vr = Monoid::unit();
    L += size, R += size;
    while (L < R) {
      if (L & 1) vl = Monoid::op(vl, dat[L++]);
      if (R & 1) vr = Monoid::op(dat[--R], vr);
      L >>= 1, R >>= 1;
    }
    return Monoid::op(vl, vr);
  }

  vc<int> prod_ids(int L, int R) {
    assert(0 <= L && L <= R && R <= n);
    vc<int> I, J;
    L += size, R += size;
    while (L < R) {
      if (L & 1) I.eb(L++);
      if (R & 1) J.eb(--R);
      L >>= 1, R >>= 1;
    }
    reverse(all(J));
    concat(I, J);
    return I;
  }

  X prod_all() { return dat[1]; }

  template <class F>
  int max_right(F check, int L) {
    assert(0 <= L && L <= n && check(Monoid::unit()));
    if (L == n) return n;
    L += size;
    X sm = Monoid::unit();
    do {
      while (L % 2 == 0) L >>= 1;
      if (!check(Monoid::op(sm, dat[L]))) {
        while (L < size) {
          L = 2 * L;
          if (check(Monoid::op(sm, dat[L]))) {
            sm = Monoid::op(sm, dat[L++]);
          }
        }
        return L - size;
      }
      sm = Monoid::op(sm, dat[L++]);
    } while ((L & -L) != L);
    return n;
  }

  template <class F>
  int min_left(F check, int R) {
    assert(0 <= R && R <= n && check(Monoid::unit()));
    if (R == 0) return 0;
    R += size;
    X sm = Monoid::unit();
    do {
      --R;
      while (R > 1 && (R % 2)) R >>= 1;
      if (!check(Monoid::op(dat[R], sm))) {
        while (R < size) {
          R = 2 * R + 1;
          if (check(Monoid::op(dat[R], sm))) {
            sm = Monoid::op(dat[R--], sm);
          }
        }
        return R + 1 - size;
      }
      sm = Monoid::op(dat[R], sm);
    } while ((R & -R) != R);
    return 0;
  }

  // prod_{l<=i<r} A[i xor x]
  X xor_prod(int l, int r, int xor_val) {
    static_assert(Monoid::commute);
    X x = Monoid::unit();
    for (int k = 0; k < log + 1; ++k) {
      if (l >= r) break;
      if (l & 1) {
        x = Monoid::op(x, dat[(size >> k) + ((l++) ^ xor_val)]);
      }
      if (r & 1) {
        x = Monoid::op(x, dat[(size >> k) + ((--r) ^ xor_val)]);
      }
      l /= 2, r /= 2, xor_val /= 2;
    }
    return x;
  }
};
#line 2 "ds/rmq/range_add_range_min.hpp"

// INF+x==INF みたいな処理は入れていない
// N=Q=10^6 で lazysegtree より 20,30% 程度高速な場合がある
template <typename T>
struct Range_Add_Range_Min {
  struct Mono {
    using value_type = pair<T, T>;
    using X = value_type;
    static X op(X L, X R) { return {L.fi + R.fi, min(L.se, L.fi + R.se)}; }
    static constexpr X unit() { return {0, 2 * infty<T>}; }
    static constexpr bool commute = false;
  };
  int n;
  T lazy;
  SegTree<Mono> seg;

  Range_Add_Range_Min() {}
  Range_Add_Range_Min(int n) { build(n); }
  template <typename F>
  Range_Add_Range_Min(int n, F f) {
    build(n, f);
  }
  Range_Add_Range_Min(const vc<T>& v) { build(v); }

  void build(int m) {
    build(m, [](int i) -> T { return infty<T>; });
  }
  void build(const vc<T>& v) {
    build(len(v), [&](int i) -> T { return v[i]; });
  }
  template <typename F>
  void build(int m, F f) {
    lazy = 0;
    n = m;
    T pre = 0;
    seg.build(n, [&](int i) -> pair<T, T> {
      T t = f(i) - pre;
      pre += t;
      return {t, t};
    });
  }

  T prod(int L, int R) {
    if (L == R) return infty<T>;
    ll ans = seg.prod(L, R).se;
    L += seg.size;
    for (; L > 0; L /= 2) {
      if (L & 1) ans += seg.dat[--L].fi;
    }
    return ans + lazy;
  }

  T prod_all() { return prod(0, n); }

  // 基本デバッグ用というつもりでさぼり O(NlogN) になっている
  vc<T> get_all() {
    vc<T> ANS(n);
    FOR(i, n) ANS[i] = prod(i, i + 1);
    return ANS;
  }

  void apply(int L, int R, T x) { apply_suffix(L, x), apply_suffix(R, -x); }

  // [0,i)
  void apply_prefix(int i, T x) {
    lazy += x;
    apply_suffix(i, -x);
  }

  // [i,n)
  void apply_suffix(int i, T x) {
    if (i == n) return;
    T t = seg.get(i).fi + x;
    seg.set(i, {t, t});
  }
  void apply_all(T x) { lazy += x; }

  void set(int i, T x) {
    T now = prod(i, i + 1);
    apply(i, i + 1, x - now);
  }

  void multiply(int i, T x) {
    T now = prod(i, i + 1);
    if (now > x) apply(i, i + 1, x - now);
  }
};

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