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:warning: Range Bitwise OR Bitwise AND
(data-structure/segment-tree/query/RangeBitwiseORBitwiseAND.hpp)

概要

todo

計算量

todo

Depends on

Code

#include "../ACLSegmentTreeBeatsChminChmax.hpp"

struct S {
    int mxpopcnt;
    int mxnum;
    uint64_t range_or, range_and;
    bool fail;
    S(uint64_t x = 0) : mxpopcnt(__builtin_popcountll(x)), mxnum(1), range_or(x), range_and(x), fail(false) {}
};

S e() {
    S ret(0ull);
    ret.range_and = ~0ull;
    ret.mxnum = 0;
    return ret;
}
S op(S a, S b) {
    a.range_or |= b.range_or;
    a.range_and &= b.range_and;
    if (a.mxpopcnt < b.mxpopcnt) {
        a.mxpopcnt = b.mxpopcnt;
        a.mxnum = b.mxnum;
    } else if (a.mxpopcnt == b.mxpopcnt) {
        a.mxnum += b.mxnum;
    }
    a.fail = false;
    return a;
}

struct F {
    uint64_t bit_or, bit_and;
    F() : bit_or(0ull), bit_and(~0ull) {}
    F(uint64_t o, uint64_t a) : bit_or(o), bit_and(a) {}
};

S mapping(F f, S x) {
    if ((x.range_and ^ x.range_or) & (~f.bit_and | f.bit_or)) {
        x.fail = true;
        return x;
    }
    x.mxpopcnt -= __builtin_popcountll(x.range_and & ~f.bit_and);
    x.range_and &= f.bit_and;
    x.range_or &= f.bit_and;
    x.mxpopcnt += __builtin_popcountll(~x.range_or & f.bit_or);
    x.range_and |= f.bit_or;
    x.range_or |= f.bit_or;
    return x;
}

F composition(F g, F f) {
    return {g.bit_or | (g.bit_and & f.bit_or), g.bit_and & f.bit_and};
}

F id() { return F(); }

class Rangebitwise {
   private:
    segtree_beats<S, op, e, F, mapping, composition, id> seg;

   public:
    Rangebitwise() {}
    Rangebitwise(const vector<uint64_t>& a) {
        int n = int(a.size());
        vector<S> v(n);
        for (int i = 0; i < n; i++) {
            v[i].range_and = v[i].range_or = a[i];
            v[i].mxpopcnt = __builtin_popcountll(a[i]);
            v[i].mxnum = 1;
            v[i].fail = false;
        }
        seg = segtree_beats<S, op, e, F, mapping, composition, id>(v);
    }

    void apply_bitwise_or(int l, int r, uint64_t x) {
        seg.apply(l, r, {x, ULLONG_MAX});
    }

    void apply_bitwise_and(int l, int r, uint64_t x) {
        seg.apply(l, r, {0ull, x});
    }

    pair<int, int> max_popcount(int l, int r) {
        S res = seg.prod(l, r);
        return {res.mxpopcnt, res.mxnum};
    }
};
#line 1 "data-structure/segment-tree/ACLSegmentTreeBeatsChminChmax.hpp"

template <class S,
          auto op,
          auto e,
          class F,
          auto mapping,
          auto composition,
          auto id>
struct segtree_beats {
   private:
    unsigned int seg_bit_ceil(unsigned int n) {
        unsigned int x = 1;
        while (x < (unsigned int)(n)) x *= 2;
        return x;
    }

   public:
    static_assert(std::is_convertible_v<decltype(op), std::function<S(S, S)>>,
                  "op must work as S(S, S)");
    static_assert(std::is_convertible_v<decltype(e), std::function<S()>>,
                  "e must work as S()");
    static_assert(
        std::is_convertible_v<decltype(mapping), std::function<S(F, S)>>,
        "mapping must work as F(F, S)");
    static_assert(
        std::is_convertible_v<decltype(composition), std::function<F(F, F)>>,
        "compostiion must work as F(F, F)");
    static_assert(std::is_convertible_v<decltype(id), std::function<F()>>,
                  "id must work as F()");
    segtree_beats() : segtree_beats(0) {}
    explicit segtree_beats(int n) : segtree_beats(std::vector<S>(n, e())) {}
    explicit segtree_beats(const std::vector<S>& v) : _n(int(v.size())) {
        size = (int)seg_bit_ceil((unsigned int)(_n));
        log = __builtin_ctz((unsigned int)size);
        d = std::vector<S>(2 * size, e());
        lz = std::vector<F>(size, id());
        for (int i = 0; i < _n; i++) d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }

    void set(int p, S x) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    S get(int p) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        return d[p];
    }

    S prod(int l, int r) {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r) return e();

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        S sml = e(), smr = e();
        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }

        return op(sml, smr);
    }

    S all_prod() { return d[1]; }

    void apply(int p, F f) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = mapping(f, d[p]);
        for (int i = 1; i <= log; i++) update(p >> i);
    }
    void apply(int l, int r, F f) {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r) return;

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        {
            int l2 = l, r2 = r;
            while (l < r) {
                if (l & 1) all_apply(l++, f);
                if (r & 1) all_apply(--r, f);
                l >>= 1;
                r >>= 1;
            }
            l = l2;
            r = r2;
        }

        for (int i = 1; i <= log; i++) {
            if (((l >> i) << i) != l) update(l >> i);
            if (((r >> i) << i) != r) update((r - 1) >> i);
        }
    }

    template <bool (*g)(S)>
    int max_right(int l) {
        return max_right(l, [](S x) { return g(x); });
    }
    template <class G>
    int max_right(int l, G g) {
        assert(0 <= l && l <= _n);
        assert(g(e()));
        if (l == _n) return _n;
        l += size;
        for (int i = log; i >= 1; i--) push(l >> i);
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!g(op(sm, d[l]))) {
                while (l < size) {
                    push(l);
                    l = (2 * l);
                    if (g(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    template <bool (*g)(S)>
    int min_left(int r) {
        return min_left(r, [](S x) { return g(x); });
    }
    template <class G>
    int min_left(int r, G g) {
        assert(0 <= r && r <= _n);
        assert(g(e()));
        if (r == 0) return 0;
        r += size;
        for (int i = log; i >= 1; i--) push((r - 1) >> i);
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!g(op(d[r], sm))) {
                while (r < size) {
                    push(r);
                    r = (2 * r + 1);
                    if (g(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

   private:
    int _n, size, log;
    std::vector<S> d;
    std::vector<F> lz;

    void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
    void all_apply(int k, F f) {
        d[k] = mapping(f, d[k]);
        if (k < size) {
            lz[k] = composition(f, lz[k]);
            if (d[k].fail) push(k), update(k);
        }
    }
    void push(int k) {
        all_apply(2 * k, lz[k]);
        all_apply(2 * k + 1, lz[k]);
        lz[k] = id();
    }
};
#line 2 "data-structure/segment-tree/query/RangeBitwiseORBitwiseAND.hpp"

struct S {
    int mxpopcnt;
    int mxnum;
    uint64_t range_or, range_and;
    bool fail;
    S(uint64_t x = 0) : mxpopcnt(__builtin_popcountll(x)), mxnum(1), range_or(x), range_and(x), fail(false) {}
};

S e() {
    S ret(0ull);
    ret.range_and = ~0ull;
    ret.mxnum = 0;
    return ret;
}
S op(S a, S b) {
    a.range_or |= b.range_or;
    a.range_and &= b.range_and;
    if (a.mxpopcnt < b.mxpopcnt) {
        a.mxpopcnt = b.mxpopcnt;
        a.mxnum = b.mxnum;
    } else if (a.mxpopcnt == b.mxpopcnt) {
        a.mxnum += b.mxnum;
    }
    a.fail = false;
    return a;
}

struct F {
    uint64_t bit_or, bit_and;
    F() : bit_or(0ull), bit_and(~0ull) {}
    F(uint64_t o, uint64_t a) : bit_or(o), bit_and(a) {}
};

S mapping(F f, S x) {
    if ((x.range_and ^ x.range_or) & (~f.bit_and | f.bit_or)) {
        x.fail = true;
        return x;
    }
    x.mxpopcnt -= __builtin_popcountll(x.range_and & ~f.bit_and);
    x.range_and &= f.bit_and;
    x.range_or &= f.bit_and;
    x.mxpopcnt += __builtin_popcountll(~x.range_or & f.bit_or);
    x.range_and |= f.bit_or;
    x.range_or |= f.bit_or;
    return x;
}

F composition(F g, F f) {
    return {g.bit_or | (g.bit_and & f.bit_or), g.bit_and & f.bit_and};
}

F id() { return F(); }

class Rangebitwise {
   private:
    segtree_beats<S, op, e, F, mapping, composition, id> seg;

   public:
    Rangebitwise() {}
    Rangebitwise(const vector<uint64_t>& a) {
        int n = int(a.size());
        vector<S> v(n);
        for (int i = 0; i < n; i++) {
            v[i].range_and = v[i].range_or = a[i];
            v[i].mxpopcnt = __builtin_popcountll(a[i]);
            v[i].mxnum = 1;
            v[i].fail = false;
        }
        seg = segtree_beats<S, op, e, F, mapping, composition, id>(v);
    }

    void apply_bitwise_or(int l, int r, uint64_t x) {
        seg.apply(l, r, {x, ULLONG_MAX});
    }

    void apply_bitwise_and(int l, int r, uint64_t x) {
        seg.apply(l, r, {0ull, x});
    }

    pair<int, int> max_popcount(int l, int r) {
        S res = seg.prod(l, r);
        return {res.mxpopcnt, res.mxnum};
    }
};
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