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:heavy_check_mark: segment_tree/test/lazy_segment_tree_min_index_plus.test.cpp

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Code

#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"

#include <iostream>
#include <limits>

#include "../../algebra/acted_monoid/acted_monoid_max_index_plus.hpp"
#include "../../algebra/acted_monoid/acted_monoid_min_index_plus.hpp"
#include "../../segment_tree/lazy_segment_tree.hpp"

constexpr int INF = std::numeric_limits<int>::max();

void test1_basic() {
    using AMMin = ActedMonoidMinIndexPlus<int, INF, true>;
    assert((AMMin::MS::identity().v == INF));
    assert((AMMin::MS::identity().i == -1));
    assert((AMMin::MS::commutative == true));
    assert((AMMin::MF::identity() == 0));
    assert((AMMin::MF::commutative == true));

    using AMMax = ActedMonoidMaxIndexPlus<int, INF, true>;
    assert((AMMax::MS::identity().v == -INF));
    assert((AMMax::MS::identity().i == -1));
    assert((AMMax::MS::commutative == true));
    assert((AMMax::MF::identity() == 0));
    assert((AMMax::MF::commutative == true));
}

void test2_query() {
    // a = {3, 1, 4, 1, 5}
    std::vector<ValueIndex<int>> a_min = {
        {3, 0}, {1, 1}, {4, 2}, {1, 3}, {5, 4}};
    std::vector<ValueIndex<int>> a_max = {
        {-3, 0}, {-1, 1}, {-4, 2}, {-1, 3}, {-5, 4}};
    LazySegmentTree<ActedMonoidMinIndexPlus<int, INF, true>> segmin(a_min);
    LazySegmentTree<ActedMonoidMaxIndexPlus<int, INF, true>> segmax(a_max);

    // []
    assert(segmin.prod(0, 0).v == INF);
    assert(segmin.prod(0, 0).i == -1);
    assert(segmax.prod(0, 0).v == -INF);
    assert(segmax.prod(0, 0).i == -1);
    // [3, 1]
    assert(segmin.prod(0, 2).v == 1);
    assert(segmin.prod(0, 2).i == 1);
    assert(segmax.prod(0, 2).v == -1);
    assert(segmax.prod(0, 2).i == 1);

    // [3, 1, 4, 1, 5]
    assert(segmin.prod(0, 5).v == 1);
    assert(segmin.prod(0, 5).i == 1);  // left = true
    assert(segmax.prod(0, 5).v == -1);
    assert(segmax.prod(0, 5).i == 1);  // left = true

    // apply +10 to [0, 3)
    // a = {13, 11, 14, 1, 5}
    segmin.apply(0, 3, 10);
    segmax.apply(0, 3, -10);
    assert(segmin.prod(0, 5).v == 1);
    assert(segmin.prod(0, 5).i == 3);
    assert(segmax.prod(0, 5).v == -1);
    assert(segmax.prod(0, 5).i == 3);

    // apply -20 to [2, 5)
    segmin.apply(2, 5, -20);
    segmax.apply(2, 5, 20);
    // a = {13, 11, -6, -19, -15}
    assert(segmin.prod(0, 5).v == -19);
    assert(segmin.prod(0, 5).i == 3);
    assert(segmax.prod(0, 5).v == 19);
    assert(segmax.prod(0, 5).i == 3);
}

void test3_smaller_index() {
    std::vector<ValueIndex<int>> a_min = {{1, 0}, {1, 1}};
    std::vector<ValueIndex<int>> a_max = {{1, 0}, {1, 1}};
    LazySegmentTree<ActedMonoidMinIndexPlus<int, INF, true>> segmin(a_min);
    LazySegmentTree<ActedMonoidMaxIndexPlus<int, INF, true>> segmax(a_max);
    assert(segmin.all_prod().i == 0);
    assert(segmax.all_prod().i == 0);
}

void test4_not_smaller_index() {
    std::vector<ValueIndex<int>> a_min = {{1, 0}, {1, 1}};
    std::vector<ValueIndex<int>> a_max = {{1, 0}, {1, 1}};
    LazySegmentTree<ActedMonoidMinIndexPlus<int, INF, false>> segmin(a_min);
    LazySegmentTree<ActedMonoidMaxIndexPlus<int, INF, false>> segmax(a_max);
    assert(segmin.all_prod().i == 1);
    assert(segmax.all_prod().i == 1);
}

int main() {
    test1_basic();
    test2_query();
    test3_smaller_index();
    test4_not_smaller_index();
    int a, b;
    std::cin >> a >> b;
    std::cout << a + b << '\n';
    return 0;
}
#line 1 "segment_tree/test/lazy_segment_tree_min_index_plus.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"

#include <iostream>
#include <limits>

#line 2 "algebra/acted_monoid/acted_monoid_max_index_plus.hpp"

#line 2 "algebra/monoid/monoid_max_index.hpp"

#line 2 "algebra/value_index.hpp"

template <class T> struct ValueIndex {
    T v;
    int i;
    friend std::ostream& operator<<(std::ostream& os, const ValueIndex& x) {
        return os << x.v;
    }
};
#line 4 "algebra/monoid/monoid_max_index.hpp"

template <class T, T inf, bool smaller_index> struct MonoidMaxIndex {
    using value_type = ValueIndex<T>;
    static constexpr value_type operation(const value_type& a,
                                          const value_type& b) {
        if (a.v > b.v) return a;
        if (a.v < b.v) return b;
        bool is_small = smaller_index ? (a.i < b.i) : (a.i >= b.i);
        return is_small ? a : b;
    }
    static constexpr value_type identity() noexcept { return {-inf, -1}; }
    static constexpr bool commutative = true;
};
#line 2 "algebra/monoid/monoid_plus.hpp"

template <class T> struct MonoidPlus {
    using value_type = T;
    static constexpr T operation(const T& a, const T& b) noexcept {
        return a + b;
    }
    static constexpr T identity() noexcept { return T(0); }
    static constexpr T inverse(const T& a) noexcept { return -a; }
    static constexpr bool commutative = true;
};
#line 5 "algebra/acted_monoid/acted_monoid_max_index_plus.hpp"

template <class T, T inf, bool smaller_index> struct ActedMonoidMaxIndexPlus {
    using MS = MonoidMaxIndex<T, inf, smaller_index>;
    using MF = MonoidPlus<T>;
    using S = typename MS::value_type;
    using F = typename MF::value_type;
    static constexpr S mapping(const F f, const S x, const int size) {
        if (f == MF::identity()) {
            return {x.v, x.i};
        }
        return {x.v + f, x.i};
    }
};
#line 2 "algebra/acted_monoid/acted_monoid_min_index_plus.hpp"

#line 2 "algebra/monoid/monoid_min_index.hpp"

#line 4 "algebra/monoid/monoid_min_index.hpp"

template <class T, T inf, bool smaller_index> struct MonoidMinIndex {
    using value_type = ValueIndex<T>;
    static constexpr value_type operation(const value_type& a,
                                          const value_type& b) {
        if (a.v < b.v) return a;
        if (a.v > b.v) return b;
        bool is_small = smaller_index ? (a.i < b.i) : (a.i >= b.i);
        return is_small ? a : b;
    }
    static constexpr value_type identity() noexcept { return {inf, -1}; }
    static constexpr bool commutative = true;
};
#line 5 "algebra/acted_monoid/acted_monoid_min_index_plus.hpp"

template <class T, T inf, bool smaller_index> struct ActedMonoidMinIndexPlus {
    using MS = MonoidMinIndex<T, inf, smaller_index>;
    using MF = MonoidPlus<T>;
    using S = typename MS::value_type;
    using F = typename MF::value_type;
    static constexpr S mapping(const F f, const S x, const int size) {
        if (f == MF::identity()) {
            return {x.v, x.i};
        }
        return {x.v + f, x.i};
    }
};
#line 2 "segment_tree/lazy_segment_tree.hpp"

#line 2 "misc/bit_ceil.hpp"

#include <cassert>

#if __cplusplus >= 202002L
#include <bit>
#endif

// bit_ceil
// (0, 1, 2, 3, 4) -> (1, 1, 2, 4, 4)
#if __cplusplus >= 202002L
using std::bit_ceil;
#else
unsigned int bit_ceil(unsigned int x) {
    unsigned int p = 1;
    while (p < x) p *= 2;
    return p;
}
unsigned long long int bit_ceil(unsigned long long int x) {
    unsigned long long int p = 1;
    while (p < x) p *= 2;
    return p;
}
#endif
int bit_ceil(int x) {
    assert(x >= 0);
    return bit_ceil((unsigned int)(x));
}
long long int bit_ceil(long long int x) {
    assert(x >= 0);
    return bit_ceil((unsigned long long int)(x));
}
#line 2 "misc/countr_zero.hpp"

#if __cplusplus >= 202002L
#include <bit>
#endif

// countr_zero
// (000, 001, 010, 011, 100) -> (32, 0, 1, 0, 2)
#if __cplusplus >= 202002L
using std::countr_zero;
#else
int countr_zero(unsigned int x) {
    return x == 0 ? 32 : __builtin_ctz(x);
}
int countr_zero(unsigned long long int x) {
    return x == 0 ? 64 : __builtin_ctzll(x);
}
#endif
int countr_zero(int x) { return countr_zero((unsigned int)(x)); }
int countr_zero(long long int x) {
    return countr_zero((unsigned long long int)(x));
}
#line 2 "misc/topbit.hpp"

#line 2 "misc/countl_zero.hpp"

#if __cplusplus >= 202002L
#include <bit>
#endif

// countl_zero
// (000, 001, 010, 011, 100) -> (32, 31, 30, 30, 29)
#if __cplusplus >= 202002L
using std::countl_zero;
#else
int countl_zero(unsigned int x) {
    return x == 0 ? 32 : __builtin_clz(x);
}
int countl_zero(unsigned long long int x) {
    return x == 0 ? 64 : __builtin_clzll(x);
}
#endif
int countl_zero(int x) { return countl_zero((unsigned int)(x)); }
int countl_zero(long long int x) {
    return countl_zero((unsigned long long int)(x));
}
#line 4 "misc/topbit.hpp"

// topbit
// (000, 001, 010, 011, 100) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return 31 - countl_zero(x); }
int topbit(unsigned int x) { return 31 - countl_zero(x); }
int topbit(long long int x) { return 63 - countl_zero(x); }
int topbit(unsigned long long int x) { return 63 - countl_zero(x); }
#line 6 "segment_tree/lazy_segment_tree.hpp"

#line 8 "segment_tree/lazy_segment_tree.hpp"
#include <vector>

// Lazy Segment Tree
template <class AM> struct LazySegmentTree {
  public:
    using MS = typename AM::MS;
    using MF = typename AM::MF;
    using S = typename MS::value_type;
    using F = typename MF::value_type;

    LazySegmentTree() = default;

    explicit LazySegmentTree(int n)
        : LazySegmentTree(std::vector<S>(n, MS::identity())) {}

    explicit LazySegmentTree(const std::vector<S>& v) : n((int)(v.size())) {
        size = bit_ceil(n);
        log = countr_zero(size);
        d = std::vector<S>(size << 1, MS::identity());
        lz = std::vector<F>(size, MF::identity());
        for (int i = 0; i < n; i++) d[i + size] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }

    void set(int p, const S& x) {
        assert(0 <= p and 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);
    }

    void add(int p, const S& x) {
        assert(0 <= p and p < n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = MS::operation(d[p], x);
        for (int i = 1; i <= log; i++) update(p >> i);
    }

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

    S get(int p) {
        assert(0 <= p and 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 and l <= r and r <= n);
        if (l == r) return MS::identity();

        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 = MS::identity(), smr = MS::identity();
        while (l < r) {
            if (l & 1) sml = MS::operation(sml, d[l++]);
            if (r & 1) smr = MS::operation(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }
        return MS::operation(sml, smr);
    }

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

    void apply(int p, const F& f) {
        assert(0 <= p and p < n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = AM::mapping(f, d[p], 1);
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    void apply(int l, int r, const F& f) {
        assert(0 <= l and l <= r and 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 <class G> int max_right(int l, G& g) {
        assert(0 <= l and l <= n);
        assert(g(MS::identity()));
        if (l == n) return n;
        l += size;
        for (int i = log; i >= 1; i--) push(l >> i);
        S sm = MS::identity();
        do {
            while ((l & 1) == 0) l >>= 1;
            if (!g(MS::operation(sm, d[l]))) {
                while (l < size) {
                    push(l);
                    l <<= 1;
                    if (g(MS::operation(sm, d[l]))) {
                        sm = MS::operation(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = MS::operation(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return n;
    }

    template <class G> int min_left(int r, G& g) {
        assert(0 <= r and r <= n);
        assert(g(MS::identity()));
        if (r == 0) return 0;
        r += size;
        for (int i = log; i >= 1; i--) push((r - 1) >> i);
        S sm = MS::identity();
        do {
            r--;
            while (r > 1 and (r & 1)) r >>= 1;
            if (!g(MS::operation(d[r], sm))) {
                while (r < size) {
                    push(r);
                    r = (r << 1) | 1;
                    if (g(MS::operation(d[r], sm))) {
                        sm = MS::operation(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = MS::operation(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

    std::vector<S> make_vector() {
        std::vector<S> vec(n);
        for (int i = 0; i < n; i++) vec[i] = get(i);
        return vec;
    }

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

    inline void update(int k) {
        d[k] = MS::operation(d[k << 1], d[(k << 1) | 1]);
    }

    void all_apply(int k, const F& f) {
        d[k] = AM::mapping(f, d[k], 1 << (log - topbit(k)));
        // MF::operation(f, g), g(f(x))
        if (k < size) lz[k] = MF::operation(lz[k], f);
    }

    void push(int k) {
        all_apply(k << 1, lz[k]);
        all_apply((k << 1) | 1, lz[k]);
        lz[k] = MF::identity();
    }
};
#line 9 "segment_tree/test/lazy_segment_tree_min_index_plus.test.cpp"

constexpr int INF = std::numeric_limits<int>::max();

void test1_basic() {
    using AMMin = ActedMonoidMinIndexPlus<int, INF, true>;
    assert((AMMin::MS::identity().v == INF));
    assert((AMMin::MS::identity().i == -1));
    assert((AMMin::MS::commutative == true));
    assert((AMMin::MF::identity() == 0));
    assert((AMMin::MF::commutative == true));

    using AMMax = ActedMonoidMaxIndexPlus<int, INF, true>;
    assert((AMMax::MS::identity().v == -INF));
    assert((AMMax::MS::identity().i == -1));
    assert((AMMax::MS::commutative == true));
    assert((AMMax::MF::identity() == 0));
    assert((AMMax::MF::commutative == true));
}

void test2_query() {
    // a = {3, 1, 4, 1, 5}
    std::vector<ValueIndex<int>> a_min = {
        {3, 0}, {1, 1}, {4, 2}, {1, 3}, {5, 4}};
    std::vector<ValueIndex<int>> a_max = {
        {-3, 0}, {-1, 1}, {-4, 2}, {-1, 3}, {-5, 4}};
    LazySegmentTree<ActedMonoidMinIndexPlus<int, INF, true>> segmin(a_min);
    LazySegmentTree<ActedMonoidMaxIndexPlus<int, INF, true>> segmax(a_max);

    // []
    assert(segmin.prod(0, 0).v == INF);
    assert(segmin.prod(0, 0).i == -1);
    assert(segmax.prod(0, 0).v == -INF);
    assert(segmax.prod(0, 0).i == -1);
    // [3, 1]
    assert(segmin.prod(0, 2).v == 1);
    assert(segmin.prod(0, 2).i == 1);
    assert(segmax.prod(0, 2).v == -1);
    assert(segmax.prod(0, 2).i == 1);

    // [3, 1, 4, 1, 5]
    assert(segmin.prod(0, 5).v == 1);
    assert(segmin.prod(0, 5).i == 1);  // left = true
    assert(segmax.prod(0, 5).v == -1);
    assert(segmax.prod(0, 5).i == 1);  // left = true

    // apply +10 to [0, 3)
    // a = {13, 11, 14, 1, 5}
    segmin.apply(0, 3, 10);
    segmax.apply(0, 3, -10);
    assert(segmin.prod(0, 5).v == 1);
    assert(segmin.prod(0, 5).i == 3);
    assert(segmax.prod(0, 5).v == -1);
    assert(segmax.prod(0, 5).i == 3);

    // apply -20 to [2, 5)
    segmin.apply(2, 5, -20);
    segmax.apply(2, 5, 20);
    // a = {13, 11, -6, -19, -15}
    assert(segmin.prod(0, 5).v == -19);
    assert(segmin.prod(0, 5).i == 3);
    assert(segmax.prod(0, 5).v == 19);
    assert(segmax.prod(0, 5).i == 3);
}

void test3_smaller_index() {
    std::vector<ValueIndex<int>> a_min = {{1, 0}, {1, 1}};
    std::vector<ValueIndex<int>> a_max = {{1, 0}, {1, 1}};
    LazySegmentTree<ActedMonoidMinIndexPlus<int, INF, true>> segmin(a_min);
    LazySegmentTree<ActedMonoidMaxIndexPlus<int, INF, true>> segmax(a_max);
    assert(segmin.all_prod().i == 0);
    assert(segmax.all_prod().i == 0);
}

void test4_not_smaller_index() {
    std::vector<ValueIndex<int>> a_min = {{1, 0}, {1, 1}};
    std::vector<ValueIndex<int>> a_max = {{1, 0}, {1, 1}};
    LazySegmentTree<ActedMonoidMinIndexPlus<int, INF, false>> segmin(a_min);
    LazySegmentTree<ActedMonoidMaxIndexPlus<int, INF, false>> segmax(a_max);
    assert(segmin.all_prod().i == 1);
    assert(segmax.all_prod().i == 1);
}

int main() {
    test1_basic();
    test2_query();
    test3_smaller_index();
    test4_not_smaller_index();
    int a, b;
    std::cin >> a >> b;
    std::cout << a + b << '\n';
    return 0;
}
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