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bit/test/point_add_subset_sum_test.cpp
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- Last update: 2026-07-14 21:24:54+09:00
- Link: https://onlinejudge.u-aizu.ac.jp/courses/lesson/2/ITP1/1/ITP1_1_A
Depends on
- bit/point_add_subset_sum.hpp
data_structure/operations.hpp
- number_theory/mod_int.hpp
- number_theory/utils.hpp
- template/random.hpp
- template/template.hpp
Code
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/lesson/2/ITP1/1/ITP1_1_A"
#define FAST_IO
#define FIX_SEED
#include "../../bit/point_add_subset_sum.hpp"
#include "../../number_theory/mod_int.hpp"
#include "../../data_structure/operations.hpp"
#include "../../template/template.hpp"
using M = ModInt<998244353>;
void test() {
constexpr i32 ITER = 100;
REP(_, ITER) {
i32 l = uniform(0, 15);
PointAddSubsetSum<Add<M>> ds(l);
V<M> arr(1 << l);
i32 q = 1000;
REP(qi, q) {
if (uniform(2)) {
u32 idx = uniform(1 << l);
M val = M(uniform(M::get_mod()));
arr[idx] += val;
ds.add(idx, val);
} else {
u32 idx = uniform(1 << l);
M right = arr[0];
for (u32 i = idx; i; i = (i - 1) & idx) {
right += arr[i];
}
assert(right == ds.get(idx));
}
}
}
}
int main() {
test();
cout << "Hello World\n";
}#line 1 "bit/test/point_add_subset_sum_test.cpp"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/lesson/2/ITP1/1/ITP1_1_A"
#define FAST_IO
#define FIX_SEED
#line 2 "bit/point_add_subset_sum.hpp"
#include <algorithm>
#include <array>
#include <cassert>
#include <vector>
#line 2 "template/random.hpp"
#include <chrono>
#include <random>
#if defined(LOCAL) || defined(FIX_SEED)
std::mt19937_64 mt(123456789);
#else
std::mt19937_64 mt(std::chrono::steady_clock::now().time_since_epoch().count());
#endif
template <typename T>
T uniform(T l, T r) {
return std::uniform_int_distribution<T>(l, r - 1)(mt);
}
template <typename T>
T uniform(T n) {
return std::uniform_int_distribution<T>(0, n - 1)(mt);
}
#line 7 "bit/point_add_subset_sum.hpp"
template <typename CommutativeMonoid>
class PointAddSubsetSum {
public:
using Value = typename CommutativeMonoid::Value;
private:
unsigned l, even;
std::array<unsigned, 4> mask;
std::vector<Value> arr;
public:
PointAddSubsetSum(unsigned l_) : l((l_ + 1) / 2 * 2), even(0), mask(), arr(1 << l, CommutativeMonoid::id()) {
std::fill(mask.begin(), mask.end(), 0);
for (unsigned i = 0; i < l; i += 2) {
mask[uniform(4)] |= 1u << i;
even |= 1u << i;
}
}
void read_queries(const std::vector<unsigned> &add, const std::vector<unsigned> &get) {
auto eval = [&] {
long long cost = 0;
for (unsigned elem : add) {
unsigned lo = elem & even;
unsigned hi = (elem >> 1) & even;
unsigned d0 = ~lo & ~hi & even;
unsigned d1 = lo & ~hi;
unsigned d2 = ~lo & hi;
unsigned tot = (d0 & (mask[0] | mask[1] | mask[2])) | (d1 & (mask[1] | mask[2] | mask[3])) |
(d2 & (mask[0] | mask[2] | mask[3]));
cost += 1LL << __builtin_popcount(tot);
}
for (unsigned elem : get) {
unsigned lo = elem & even;
unsigned hi = (elem >> 1) & even;
unsigned d1 = lo & ~hi;
unsigned d2 = ~lo & hi;
unsigned d3 = lo & hi;
unsigned tot = (d1 & (mask[1] | mask[2] | mask[3])) | (d2 & (mask[0] | mask[2] | mask[3])) |
(d3 & (mask[0] | mask[1] | mask[3]));
cost += 1LL << __builtin_popcount(tot);
}
return cost;
};
fill(ALL(mask), 0);
for (unsigned i = 0; i < l; i += 2) {
long long c[4];
for (int j = 0; j < 4; ++j) {
mask[j] ^= 1u << (2 * i);
c[j] = eval();
mask[j] ^= 1u << (2 * i);
}
int idx = std::min_element(c, c + 4) - c;
mask[idx] ^= 1u << (2 * i);
}
}
void add(unsigned idx, Value v) {
unsigned lo = idx & even;
unsigned hi = (idx >> 1) & even;
unsigned d0 = ~lo & ~hi & even;
unsigned d1 = lo & ~hi;
unsigned d2 = ~lo & hi;
unsigned add1 = (mask[0] & (d0 | d2)) | ((mask[2] | mask[3]) & d2);
unsigned add2 = (mask[1] & (d0 | d1)) | ((mask[2] | mask[3]) & d1);
unsigned add3 = mask[2] & d0;
unsigned sub = add1 | (add2 << 1);
for (unsigned st = add3; st; st = (st - 1) & add3) {
unsigned x = idx ^ st ^ (st << 1);
for (unsigned st2 = sub; st2; st2 = (st2 - 1) & sub) {
arr[x ^ st2] = CommutativeMonoid::op(arr[x ^ st2], v);
}
arr[x] = CommutativeMonoid::op(arr[x], v);
}
{
for (unsigned st2 = sub; st2; st2 = (st2 - 1) & sub) {
arr[idx ^ st2] = CommutativeMonoid::op(arr[idx ^ st2], v);
}
arr[idx] = CommutativeMonoid::op(arr[idx], v);
}
}
Value get(unsigned idx) const {
unsigned lo = idx & even;
unsigned hi = (idx >> 1) & even;
unsigned d1 = lo & ~hi;
unsigned d2 = ~lo & hi;
unsigned d3 = lo & hi;
unsigned add1 = (mask[1] & (d1 | d3)) | ((mask[2] | mask[3]) & d1);
unsigned add2 = (mask[0] & (d2 | d3)) | ((mask[2] | mask[3]) & d2);
unsigned add3 = mask[3] & d3;
unsigned sub = add1 | (add2 << 1);
Value ans = CommutativeMonoid::id();
for (unsigned st = add3; st; st = (st - 1) & add3) {
unsigned x = idx ^ st ^ (st << 1);
for (unsigned st2 = sub; st2; st2 = (st2 - 1) & sub) {
ans = CommutativeMonoid::op(ans, arr[x ^ st2]);
}
ans = CommutativeMonoid::op(ans, arr[x]);
}
{
for (unsigned st2 = sub; st2; st2 = (st2 - 1) & sub) {
ans = CommutativeMonoid::op(ans, arr[idx ^ st2]);
}
ans = CommutativeMonoid::op(ans, arr[idx]);
}
return ans;
}
};
#line 2 "number_theory/mod_int.hpp"
#line 4 "number_theory/mod_int.hpp"
#include <iostream>
#include <type_traits>
#line 2 "number_theory/utils.hpp"
#include <utility>
constexpr bool is_prime(unsigned n) {
if (n == 0 || n == 1) {
return false;
}
for (unsigned i = 2; i * i <= n; ++i) {
if (n % i == 0) {
return false;
}
}
return true;
}
constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) {
unsigned ret = 1, self = x;
while (y != 0) {
if (y & 1) {
ret = (unsigned)((unsigned long long)ret * self % mod);
}
self = (unsigned)((unsigned long long)self * self % mod);
y /= 2;
}
return ret;
}
template <unsigned mod>
constexpr unsigned primitive_root() {
static_assert(is_prime(mod), "`mod` must be a prime number.");
if (mod == 2) {
return 1;
}
unsigned primes[32] = {};
int it = 0;
{
unsigned m = mod - 1;
for (unsigned i = 2; i * i <= m; ++i) {
if (m % i == 0) {
primes[it++] = i;
while (m % i == 0) {
m /= i;
}
}
}
if (m != 1) {
primes[it++] = m;
}
}
for (unsigned i = 2; i < mod; ++i) {
bool ok = true;
for (int j = 0; j < it; ++j) {
if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {
ok = false;
break;
}
}
if (ok) return i;
}
return 0;
}
// y >= 1
template <typename T>
constexpr T safe_mod(T x, T y) {
x %= y;
if (x < 0) {
x += y;
}
return x;
}
// y != 0
template <typename T>
constexpr T floor_div(T x, T y) {
if (y < 0) {
x *= -1;
y *= -1;
}
if (x >= 0) {
return x / y;
} else {
return -((-x + y - 1) / y);
}
}
// y != 0
template <typename T>
constexpr T ceil_div(T x, T y) {
if (y < 0) {
x *= -1;
y *= -1;
}
if (x >= 0) {
return (x + y - 1) / y;
} else {
return -(-x / y);
}
}
// b >= 1
// returns (g, x) s.t. g = gcd(a, b), a * x = g (mod b), 0 <= x < b / g
// from ACL
template <typename T>
std::pair<T, T> extgcd(T a, T b) {
a = safe_mod(a, b);
T s = b, t = a, m0 = 0, m1 = 1;
while (t) {
T u = s / t;
s -= t * u;
m0 -= m1 * u;
std::swap(s, t);
std::swap(m0, m1);
}
if (m0 < 0) {
m0 += b / s;
}
return std::pair<T, T>(s, m0);
}
// b >= 1
// returns (g, x, y) s.t. g = gcd(a, b), a * x + b * y = g, 0 <= x < b / g, |y| < max(2, |a| / g)
template <typename T>
std::tuple<T, T, T> extgcd2(T a, T b) {
T _a = safe_mod(a, b);
T quot = (a - _a) / b;
T x00 = 0, x01 = 1, y0 = b;
T x10 = 1, x11 = -quot, y1 = _a;
while (y1) {
T u = y0 / y1;
x00 -= u * x10;
x01 -= u * x11;
y0 -= u * y1;
std::swap(x00, x10);
std::swap(x01, x11);
std::swap(y0, y1);
}
if (x00 < 0) {
x00 += b / y0;
x01 -= a / y0;
}
return std::tuple<T, T, T>(y0, x00, x01);
}
// gcd(x, m) == 1
template <typename T>
T inv_mod(T x, T m) {
return extgcd(x, m).second;
}
#line 7 "number_theory/mod_int.hpp"
template <unsigned mod>
struct ModInt {
static_assert(mod != 0, "`mod` must not be equal to 0.");
static_assert(mod < (1u << 31),
"`mod` must be less than (1u << 31) = 2147483648.");
unsigned val;
static constexpr unsigned get_mod() { return mod; }
constexpr ModInt() : val(0) {}
template <typename T, std::enable_if_t<std::is_signed_v<T>> * = nullptr>
constexpr ModInt(T x)
: val((unsigned)((long long)x % (long long)mod + (x < 0 ? mod : 0))) {}
template <typename T, std::enable_if_t<std::is_unsigned_v<T>> * = nullptr>
constexpr ModInt(T x) : val((unsigned)(x % mod)) {}
static constexpr ModInt raw(unsigned x) {
ModInt<mod> ret;
ret.val = x;
return ret;
}
constexpr unsigned get_val() const { return val; }
constexpr ModInt operator+() const { return *this; }
constexpr ModInt operator-() const { return ModInt<mod>(0u) - *this; }
constexpr ModInt &operator+=(const ModInt &rhs) {
val += rhs.val;
if (val >= mod) val -= mod;
return *this;
}
constexpr ModInt &operator-=(const ModInt &rhs) {
val -= rhs.val;
if (val >= mod) val += mod;
return *this;
}
constexpr ModInt &operator*=(const ModInt &rhs) {
val = (unsigned long long)val * rhs.val % mod;
return *this;
}
constexpr ModInt &operator/=(const ModInt &rhs) {
val = (unsigned long long)val * rhs.inv().val % mod;
return *this;
}
friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) += rhs;
}
friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) -= rhs;
}
friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) *= rhs;
}
friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) /= rhs;
}
constexpr ModInt pow(unsigned long long x) const {
ModInt<mod> ret = ModInt<mod>::raw(1);
ModInt<mod> self = *this;
while (x != 0) {
if (x & 1) ret *= self;
self *= self;
x >>= 1;
}
return ret;
}
constexpr ModInt inv() const {
static_assert(is_prime(mod), "`mod` must be a prime number.");
assert(val != 0);
return this->pow(mod - 2);
}
friend std::istream &operator>>(std::istream &is, ModInt<mod> &x) {
long long val;
is >> val;
x.val = val % mod + (val < 0 ? mod : 0);
return is;
}
friend std::ostream &operator<<(std::ostream &os, const ModInt<mod> &x) {
os << x.val;
return os;
}
friend bool operator==(const ModInt &lhs, const ModInt &rhs) {
return lhs.val == rhs.val;
}
friend bool operator!=(const ModInt &lhs, const ModInt &rhs) {
return lhs.val != rhs.val;
}
};
template <unsigned mod>
void debug(ModInt<mod> x) {
std::cerr << x.val;
}
#line 2 "data_structure/operations.hpp"
#line 4 "data_structure/operations.hpp"
#include <limits>
#line 6 "data_structure/operations.hpp"
template <typename T>
struct Add {
using Value = T;
static Value id() { return T(0); }
static Value op(const Value &lhs, const Value &rhs) { return lhs + rhs; }
static Value inv(const Value &x) { return -x; }
};
template <typename T>
struct Mul {
using Value = T;
static Value id() { return Value(1); }
static Value op(const Value &lhs, const Value &rhs) { return lhs * rhs; }
static Value inv(const Value &x) { return Value(1) / x; }
};
template <typename T>
struct Min {
static_assert(std::numeric_limits<T>::is_specialized);
using Value = T;
static Value id() { return std::numeric_limits<T>::max(); }
static Value op(const Value &lhs, const Value &rhs) {
return std::min(lhs, rhs);
}
};
template <typename T>
struct Max {
static_assert(std::numeric_limits<T>::is_specialized);
using Value = T;
static Value id() { return std::numeric_limits<Value>::min(); }
static Value op(const Value &lhs, const Value &rhs) {
return std::max(lhs, rhs);
}
};
template <typename T>
struct Xor {
using Value = T;
static Value id() { return T(0); }
static Value op(const Value &lhs, const Value &rhs) { return lhs ^ rhs; }
static Value inv(const Value &x) { return x; }
};
template <typename Monoid>
struct Reversible {
using Value = std::pair<typename Monoid::Value, typename Monoid::Value>;
static Value id() { return Value(Monoid::id(), Monoid::id()); }
static Value op(const Value &v1, const Value &v2) {
return Value(Monoid::op(v1.first, v2.first),
Monoid::op(v2.second, v1.second));
}
};
#line 2 "template/template.hpp"
#include <bits/stdc++.h>
#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER2(i, n) for (i32 i = (i32)(n)-1; i >= 0; --i)
#define PER3(i, m, n) for (i32 i = (i32)(n)-1; i >= (i32)(m); --i)
#define PER(...) OVERRIDE(__VA_ARGS__, PER3, PER2)(__VA_ARGS__)
#define ALL(x) begin(x), end(x)
#define LEN(x) (i32)(x.size())
using namespace std;
using u32 = unsigned int;
using u64 = unsigned long long;
using i32 = signed int;
using i64 = signed long long;
using f64 = double;
using f80 = long double;
using pi = pair<i32, i32>;
using pl = pair<i64, i64>;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = V<V<T>>;
template <typename T>
using VVV = V<V<V<T>>>;
template <typename T>
using VVVV = V<V<V<V<T>>>>;
template <typename T>
using PQR = priority_queue<T, V<T>, greater<T>>;
template <typename T>
bool chmin(T &x, const T &y) {
if (x > y) {
x = y;
return true;
}
return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
if (x < y) {
x = y;
return true;
}
return false;
}
template <typename T>
i32 lob(const V<T> &arr, const T &v) {
return (i32)(lower_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
i32 upb(const V<T> &arr, const T &v) {
return (i32)(upper_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
V<i32> argsort(const V<T> &arr) {
V<i32> ret(arr.size());
iota(ALL(ret), 0);
sort(ALL(ret), [&](i32 i, i32 j) -> bool {
if (arr[i] == arr[j]) {
return i < j;
} else {
return arr[i] < arr[j];
}
});
return ret;
}
#ifdef INT128
using u128 = __uint128_t;
using i128 = __int128_t;
#endif
[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
SetUpIO() {
#ifdef FAST_IO
ios::sync_with_stdio(false);
cin.tie(nullptr);
#endif
cout << fixed << setprecision(15);
}
} set_up_io;
void scan(char &x) { cin >> x; }
void scan(u32 &x) { cin >> x; }
void scan(u64 &x) { cin >> x; }
void scan(i32 &x) { cin >> x; }
void scan(i64 &x) { cin >> x; }
void scan(f64 &x) { cin >> x; }
void scan(string &x) { cin >> x; }
template <typename T>
void scan(V<T> &x) {
for (T &ele : x) {
scan(ele);
}
}
void read() {}
template <typename Head, typename... Tail>
void read(Head &head, Tail &...tail) {
scan(head);
read(tail...);
}
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__);
#define U32(...) \
u32 __VA_ARGS__; \
read(__VA_ARGS__);
#define U64(...) \
u64 __VA_ARGS__; \
read(__VA_ARGS__);
#define I32(...) \
i32 __VA_ARGS__; \
read(__VA_ARGS__);
#define I64(...) \
i64 __VA_ARGS__; \
read(__VA_ARGS__);
#define F64(...) \
f64 __VA_ARGS__; \
read(__VA_ARGS__);
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__);
#define VEC(type, name, size) \
V<type> name(size); \
read(name);
#define VVEC(type, name, size1, size2) \
VV<type> name(size1, V<type>(size2)); \
read(name);
#line 9 "bit/test/point_add_subset_sum_test.cpp"
using M = ModInt<998244353>;
void test() {
constexpr i32 ITER = 100;
REP(_, ITER) {
i32 l = uniform(0, 15);
PointAddSubsetSum<Add<M>> ds(l);
V<M> arr(1 << l);
i32 q = 1000;
REP(qi, q) {
if (uniform(2)) {
u32 idx = uniform(1 << l);
M val = M(uniform(M::get_mod()));
arr[idx] += val;
ds.add(idx, val);
} else {
u32 idx = uniform(1 << l);
M right = arr[0];
for (u32 i = idx; i; i = (i - 1) & idx) {
right += arr[i];
}
assert(right == ds.get(idx));
}
}
}
}
int main() {
test();
cout << "Hello World\n";
}