結果
| 問題 | No.1774 Love Triangle (Hard) |
| ユーザー |
👑  hitonanode
|
| 提出日時 | 2021-09-23 11:13:16 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 7,327 ms / 8,000 ms |
| コード長 | 26,865 bytes |
| コンパイル時間 | 3,879 ms |
| コンパイル使用メモリ | 220,136 KB |
| 実行使用メモリ | 41,972 KB |
| 最終ジャッジ日時 | 2023-10-09 22:41:19 |
| 合計ジャッジ時間 | 506,306 ms |
|
ジャッジサーバーID （参考情報） |
judge11 / judge12 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
4,352 KB |
| testcase_01 | AC | 2 ms
4,376 KB |
| testcase_02 | AC | 4 ms
4,348 KB |
| testcase_03 | AC | 6 ms
4,352 KB |
| testcase_04 | AC | 4 ms
4,352 KB |
| testcase_05 | AC | 5 ms
4,348 KB |
| testcase_06 | AC | 2 ms
4,372 KB |
| testcase_07 | AC | 60 ms
32,144 KB |
| testcase_08 | AC | 2 ms
4,348 KB |
| testcase_09 | AC | 2 ms
4,348 KB |
| testcase_10 | AC | 1 ms
4,352 KB |
| testcase_11 | AC | 61 ms
32,184 KB |
| testcase_12 | AC | 4,466 ms
38,424 KB |
| testcase_13 | AC | 3,120 ms
37,036 KB |
| testcase_14 | AC | 165 ms
11,284 KB |
| testcase_15 | AC | 2,199 ms
36,832 KB |
| testcase_16 | AC | 549 ms
12,388 KB |
| testcase_17 | AC | 46 ms
4,372 KB |
| testcase_18 | AC | 2,570 ms
23,192 KB |
| testcase_19 | AC | 137 ms
18,664 KB |
| testcase_20 | AC | 232 ms
4,772 KB |
| testcase_21 | AC | 132 ms
4,372 KB |
| testcase_22 | AC | 6,473 ms
40,540 KB |
| testcase_23 | AC | 6,505 ms
40,828 KB |
| testcase_24 | AC | 6,679 ms
40,992 KB |
| testcase_25 | AC | 6,494 ms
40,704 KB |
| testcase_26 | AC | 6,720 ms
27,316 KB |
| testcase_27 | AC | 6,624 ms
40,620 KB |
| testcase_28 | AC | 6,748 ms
40,652 KB |
| testcase_29 | AC | 6,966 ms
41,860 KB |
| testcase_30 | AC | 6,795 ms
40,772 KB |
| testcase_31 | AC | 6,768 ms
40,724 KB |
| testcase_32 | AC | 6,549 ms
40,724 KB |
| testcase_33 | AC | 6,775 ms
40,964 KB |
| testcase_34 | AC | 6,782 ms
40,632 KB |
| testcase_35 | AC | 6,802 ms
41,848 KB |
| testcase_36 | AC | 6,576 ms
40,608 KB |
| testcase_37 | AC | 6,865 ms
41,680 KB |
| testcase_38 | AC | 6,522 ms
41,732 KB |
| testcase_39 | AC | 6,610 ms
40,612 KB |
| testcase_40 | AC | 6,740 ms
41,936 KB |
| testcase_41 | AC | 6,677 ms
40,988 KB |
| testcase_42 | AC | 6,726 ms
40,692 KB |
| testcase_43 | AC | 6,843 ms
41,008 KB |
| testcase_44 | AC | 6,848 ms
41,740 KB |
| testcase_45 | AC | 6,965 ms
40,732 KB |
| testcase_46 | AC | 6,812 ms
41,864 KB |
| testcase_47 | AC | 6,839 ms
41,004 KB |
| testcase_48 | AC | 6,860 ms
41,096 KB |
| testcase_49 | AC | 6,892 ms
16,184 KB |
| testcase_50 | AC | 6,832 ms
40,848 KB |
| testcase_51 | AC | 6,758 ms
40,868 KB |
| testcase_52 | AC | 6,713 ms
41,880 KB |
| testcase_53 | AC | 6,848 ms
41,876 KB |
| testcase_54 | AC | 6,837 ms
27,628 KB |
| testcase_55 | AC | 7,027 ms
41,848 KB |
| testcase_56 | AC | 7,019 ms
41,876 KB |
| testcase_57 | AC | 6,824 ms
41,956 KB |
| testcase_58 | AC | 6,785 ms
41,972 KB |
| testcase_59 | AC | 6,808 ms
40,684 KB |
| testcase_60 | AC | 6,822 ms
27,520 KB |
| testcase_61 | AC | 6,843 ms
41,776 KB |
| testcase_62 | AC | 6,747 ms
41,892 KB |
| testcase_63 | AC | 6,879 ms
40,804 KB |
| testcase_64 | AC | 6,874 ms
40,620 KB |
| testcase_65 | AC | 7,327 ms
41,844 KB |
| testcase_66 | AC | 6,867 ms
41,884 KB |
| testcase_67 | AC | 6,684 ms
40,684 KB |
| testcase_68 | AC | 7,160 ms
41,948 KB |
| testcase_69 | AC | 7,079 ms
40,752 KB |
| testcase_70 | AC | 6,850 ms
41,672 KB |
| testcase_71 | AC | 6,907 ms
40,944 KB |
| testcase_72 | AC | 6,937 ms
40,936 KB |
| testcase_73 | AC | 6,983 ms
27,372 KB |
| testcase_74 | AC | 6,804 ms
40,768 KB |
| testcase_75 | AC | 6,991 ms
40,756 KB |
| testcase_76 | AC | 6,980 ms
40,712 KB |
| testcase_77 | AC | 7,108 ms
41,952 KB |
| testcase_78 | AC | 7,138 ms
40,852 KB |
| testcase_79 | AC | 6,764 ms
14,724 KB |
| testcase_80 | AC | 7,117 ms
41,892 KB |
| testcase_81 | AC | 7,115 ms
27,644 KB |
| testcase_82 | AC | 6,874 ms
40,952 KB |
| testcase_83 | AC | 6,830 ms
40,616 KB |
| testcase_84 | AC | 6,775 ms
41,488 KB |
| testcase_85 | AC | 6,844 ms
28,128 KB |
| testcase_86 | AC | 6,855 ms
41,744 KB |
| testcase_87 | AC | 7,058 ms
40,920 KB |
| testcase_88 | AC | 6,745 ms
40,708 KB |
| testcase_89 | AC | 6,725 ms
40,564 KB |
| testcase_90 | AC | 6,687 ms
26,580 KB |
| testcase_91 | AC | 6,414 ms
41,812 KB |
| testcase_92 | AC | 6,430 ms
40,500 KB |
ソースコード
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <typename T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl
#define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr)
#else
#define dbg(x) (x)
#define dbgif(cond, x) 0
#endif
template <int md> struct ModInt {
#if __cplusplus >= 201402L
#define MDCONST constexpr
#else
#define MDCONST
#endif
using lint = long long;
MDCONST static int mod() { return md; }
static int get_primitive_root() {
static int primitive_root = 0;
if (!primitive_root) {
primitive_root = [&]() {
std::set<int> fac;
int v = md - 1;
for (lint i = 2; i * i <= v; i++)
while (v % i == 0) fac.insert(i), v /= i;
if (v > 1) fac.insert(v);
for (int g = 1; g < md; g++) {
bool ok = true;
for (auto i : fac)
if (ModInt(g).pow((md - 1) / i) == 1) {
ok = false;
break;
}
if (ok) return g;
}
return -1;
}();
}
return primitive_root;
}
int val;
MDCONST ModInt() : val(0) {}
MDCONST ModInt &_setval(lint v) { return val = (v >= md ? v - md : v), *this; }
MDCONST ModInt(lint v) { _setval(v % md + md); }
MDCONST explicit operator bool() const { return val != 0; }
MDCONST ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); }
MDCONST ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + md); }
MDCONST ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % md); }
MDCONST ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % md); }
MDCONST ModInt operator-() const { return ModInt()._setval(md - val); }
MDCONST ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
MDCONST ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
MDCONST ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
MDCONST ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
friend MDCONST ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % md + x.val); }
friend MDCONST ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % md - x.val + md); }
friend MDCONST ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % md * x.val % md); }
friend MDCONST ModInt operator/(lint a, const ModInt &x) {
return ModInt()._setval(a % md * x.inv() % md);
}
MDCONST bool operator==(const ModInt &x) const { return val == x.val; }
MDCONST bool operator!=(const ModInt &x) const { return val != x.val; }
MDCONST bool operator<(const ModInt &x) const { return val < x.val; } // To use std::map<ModInt, T>
friend std::istream &operator>>(std::istream &is, ModInt &x) {
lint t;
return is >> t, x = ModInt(t), is;
}
MDCONST friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { return os << x.val; }
MDCONST ModInt pow(lint n) const {
ModInt ans = 1, tmp = *this;
while (n) {
if (n & 1) ans *= tmp;
tmp *= tmp, n >>= 1;
}
return ans;
}
static std::vector<ModInt> facs, facinvs, invs;
MDCONST static void _precalculation(int N) {
int l0 = facs.size();
if (N > md) N = md;
if (N <= l0) return;
facs.resize(N), facinvs.resize(N), invs.resize(N);
for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i;
facinvs[N - 1] = facs.back().pow(md - 2);
for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1);
for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1];
}
MDCONST lint inv() const {
if (this->val < std::min(md >> 1, 1 << 21)) {
while (this->val >= int(facs.size())) _precalculation(facs.size() * 2);
return invs[this->val].val;
} else {
return this->pow(md - 2).val;
}
}
MDCONST ModInt fac() const {
while (this->val >= int(facs.size())) _precalculation(facs.size() * 2);
return facs[this->val];
}
MDCONST ModInt facinv() const {
while (this->val >= int(facs.size())) _precalculation(facs.size() * 2);
return facinvs[this->val];
}
MDCONST ModInt doublefac() const {
lint k = (this->val + 1) / 2;
return (this->val & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac())
: ModInt(k).fac() * ModInt(2).pow(k);
}
MDCONST ModInt nCr(const ModInt &r) const {
return (this->val < r.val) ? 0 : this->fac() * (*this - r).facinv() * r.facinv();
}
MDCONST ModInt nPr(const ModInt &r) const {
return (this->val < r.val) ? 0 : this->fac() * (*this - r).facinv();
}
ModInt sqrt() const {
if (val == 0) return 0;
if (md == 2) return val;
if (pow((md - 1) / 2) != 1) return 0;
ModInt b = 1;
while (b.pow((md - 1) / 2) == 1) b += 1;
int e = 0, m = md - 1;
while (m % 2 == 0) m >>= 1, e++;
ModInt x = pow((m - 1) / 2), y = (*this) * x * x;
x *= (*this);
ModInt z = b.pow(m);
while (y != 1) {
int j = 0;
ModInt t = y;
while (t != 1) j++, t *= t;
z = z.pow(1LL << (e - j - 1));
x *= z, z *= z, y *= z;
e = j;
}
return ModInt(std::min(x.val, md - x.val));
}
};
template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0};
// using mint = ModInt<1000000007>;
using mint = ModInt<998244853>;
template <typename T> struct matrix {
int H, W;
std::vector<T> elem;
typename std::vector<T>::iterator operator[](int i) { return elem.begin() + i * W; }
inline T &at(int i, int j) { return elem[i * W + j]; }
inline T get(int i, int j) const { return elem[i * W + j]; }
int height() const { return H; }
int width() const { return W; }
std::vector<std::vector<T>> vecvec() const {
std::vector<std::vector<T>> ret(H);
for (int i = 0; i < H; i++) {
std::copy(elem.begin() + i * W, elem.begin() + (i + 1) * W, std::back_inserter(ret[i]));
}
return ret;
}
operator std::vector<std::vector<T>>() const { return vecvec(); }
matrix() = default;
matrix(int H, int W) : H(H), W(W), elem(H * W) {}
matrix(const std::vector<std::vector<T>> &d) : H(d.size()), W(d.size() ? d[0].size() : 0) {
for (auto &raw : d) std::copy(raw.begin(), raw.end(), std::back_inserter(elem));
}
static matrix Identity(int N) {
matrix ret(N, N);
for (int i = 0; i < N; i++) ret.at(i, i) = 1;
return ret;
}
matrix operator-() const {
matrix ret(H, W);
for (int i = 0; i < H * W; i++) ret.elem[i] = -elem[i];
return ret;
}
matrix operator*(const T &v) const {
matrix ret = *this;
for (auto &x : ret.elem) x *= v;
return ret;
}
matrix operator/(const T &v) const {
matrix ret = *this;
const T vinv = T(1) / v;
for (auto &x : ret.elem) x *= vinv;
return ret;
}
matrix operator+(const matrix &r) const {
matrix ret = *this;
for (int i = 0; i < H * W; i++) ret.elem[i] += r.elem[i];
return ret;
}
matrix operator-(const matrix &r) const {
matrix ret = *this;
for (int i = 0; i < H * W; i++) ret.elem[i] -= r.elem[i];
return ret;
}
matrix operator*(const matrix &r) const {
matrix ret(H, r.W);
for (int i = 0; i < H; i++) {
for (int k = 0; k < W; k++) {
for (int j = 0; j < r.W; j++) ret.at(i, j) += this->get(i, k) * r.get(k, j);
}
}
return ret;
}
matrix &operator*=(const T &v) { return *this = *this * v; }
matrix &operator/=(const T &v) { return *this = *this / v; }
matrix &operator+=(const matrix &r) { return *this = *this + r; }
matrix &operator-=(const matrix &r) { return *this = *this - r; }
matrix &operator*=(const matrix &r) { return *this = *this * r; }
bool operator==(const matrix &r) const { return H == r.H and W == r.W and elem == r.elem; }
bool operator!=(const matrix &r) const { return H != r.H or W != r.W or elem != r.elem; }
bool operator<(const matrix &r) const { return elem < r.elem; }
matrix pow(int64_t n) const {
matrix ret = Identity(H);
bool ret_is_id = true;
if (n == 0) return ret;
for (int i = 63 - __builtin_clzll(n); i >= 0; i--) {
if (!ret_is_id) ret *= ret;
if ((n >> i) & 1) ret *= (*this), ret_is_id = false;
}
return ret;
}
std::vector<T> pow_vec(int64_t n, std::vector<T> vec) const {
matrix x = *this;
while (n) {
if (n & 1) vec = x * vec;
x *= x;
n >>= 1;
}
return vec;
};
matrix transpose() const {
matrix ret(W, H);
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) ret.at(j, i) = this->get(i, j);
}
return ret;
}
// Gauss-Jordan elimination
// - Require inverse for every non-zero element
// - Complexity: O(H^2 W)
template <typename T2, typename std::enable_if<std::is_floating_point<T2>::value>::type * = nullptr>
static int choose_pivot(const matrix<T2> &mtr, int h, int c) noexcept {
int piv = -1;
for (int j = h; j < mtr.H; j++) {
if (mtr.get(j, c) and (piv < 0 or std::abs(mtr.get(j, c)) > std::abs(mtr.get(piv, c)))) piv = j;
}
return piv;
}
template <typename T2, typename std::enable_if<!std::is_floating_point<T2>::value>::type * = nullptr>
static int choose_pivot(const matrix<T2> &mtr, int h, int c) noexcept {
for (int j = h; j < mtr.H; j++) {
if (mtr.get(j, c)) return j;
}
return -1;
}
matrix gauss_jordan() const {
int c = 0;
matrix mtr(*this);
std::vector<int> ws;
ws.reserve(W);
for (int h = 0; h < H; h++) {
if (c == W) break;
int piv = choose_pivot(mtr, h, c);
if (piv == -1) {
c++;
h--;
continue;
}
if (h != piv) {
for (int w = 0; w < W; w++) {
std::swap(mtr[piv][w], mtr[h][w]);
mtr.at(piv, w) *= -1; // To preserve sign of determinant
}
}
ws.clear();
for (int w = c; w < W; w++) {
if (mtr.at(h, w) != 0) ws.emplace_back(w);
}
const T hcinv = T(1) / mtr.at(h, c);
for (int hh = 0; hh < H; hh++)
if (hh != h) {
const T coeff = mtr.at(hh, c) * hcinv;
for (auto w : ws) mtr.at(hh, w) -= mtr.at(h, w) * coeff;
mtr.at(hh, c) = 0;
}
c++;
}
return mtr;
}
int rank_of_gauss_jordan() const {
for (int i = H * W - 1; i >= 0; i--) {
if (elem[i]) return i / W + 1;
}
return 0;
}
T determinant_of_upper_triangle() const {
T ret = 1;
for (int i = 0; i < H; i++) ret *= get(i, i);
return ret;
}
int inverse() {
assert(H == W);
std::vector<std::vector<T>> ret = Identity(H), tmp = *this;
int rank = 0;
for (int i = 0; i < H; i++) {
int ti = i;
while (ti < H and tmp[ti][i] == 0) ti++;
if (ti == H) {
continue;
} else {
rank++;
}
ret[i].swap(ret[ti]), tmp[i].swap(tmp[ti]);
T inv = T(1) / tmp[i][i];
for (int j = 0; j < W; j++) ret[i][j] *= inv;
for (int j = i + 1; j < W; j++) tmp[i][j] *= inv;
for (int h = 0; h < H; h++) {
if (i == h) continue;
const T c = -tmp[h][i];
for (int j = 0; j < W; j++) ret[h][j] += ret[i][j] * c;
for (int j = i + 1; j < W; j++) tmp[h][j] += tmp[i][j] * c;
}
}
*this = ret;
return rank;
}
friend std::vector<T> operator*(const matrix &m, const std::vector<T> &v) {
assert(m.W == int(v.size()));
std::vector<T> ret(m.H);
for (int i = 0; i < m.H; i++) {
for (int j = 0; j < m.W; j++) ret[i] += m.get(i, j) * v[j];
}
return ret;
}
friend std::vector<T> operator*(const std::vector<T> &v, const matrix &m) {
assert(int(v.size()) == m.H);
std::vector<T> ret(m.W);
for (int i = 0; i < m.H; i++) {
for (int j = 0; j < m.W; j++) ret[j] += v[i] * m.get(i, j);
}
return ret;
}
std::vector<T> prod(const std::vector<T> &v) const { return (*this) * v; }
std::vector<T> prod_left(const std::vector<T> &v) const { return v * (*this); }
friend std::ostream &operator<<(std::ostream &os, const matrix &x) {
os << "[(" << x.H << " * " << x.W << " matrix)";
os << "\n[column sums: ";
for (int j = 0; j < x.W; j++) {
T s = 0;
for (int i = 0; i < x.H; i++) s += x.get(i, j);
os << s << ",";
}
os << "]";
for (int i = 0; i < x.H; i++) {
os << "\n[";
for (int j = 0; j < x.W; j++) os << x.get(i, j) << ",";
os << "]";
}
os << "]\n";
return os;
}
friend std::istream &operator>>(std::istream &is, matrix &x) {
for (auto &v : x.elem) is >> v;
return is;
}
};
template <class ModInt>
std::vector<int>
linear_matroid_parity(const std::vector<std::pair<std::vector<ModInt>, std::vector<ModInt>>> &bcs) {
if (bcs.empty()) return {};
const int r = bcs[0].first.size(), m = bcs.size(), r2 = (r + 1) / 2;
std::mt19937 mt(std::chrono::steady_clock::now().time_since_epoch().count());
std::uniform_int_distribution<int> d(0, ModInt::mod() - 1);
auto gen_random_vector = [&]() -> std::vector<ModInt> {
std::vector<ModInt> v(r2 * 2);
for (int i = 0; i < r2 * 2; i++) v[i] = d(mt);
return v;
};
std::vector<ModInt> x(m);
using Vec = std::vector<ModInt>;
std::vector<std::pair<Vec, Vec>> bcadd(r2 * 2);
matrix<ModInt> Y, Yinv; // r2 * r2 matrices
int rankY = -1;
while (rankY < r2 * 2) {
Y = matrix<ModInt>(r2 * 2, r2 * 2);
for (int i = 0; i < m; i++) {
x[i] = d(mt);
const auto &b = bcs[i].first, &c = bcs[i].second;
for (int j = 0; j < r; j++) {
for (int k = 0; k < r; k++) Y[j][k] += x[i] * (b[j] * c[k] - c[j] * b[k]);
}
}
for (auto &[b, c] : bcadd) {
b = gen_random_vector(), c = gen_random_vector();
for (int j = 0; j < r2 * 2; j++) {
for (int k = 0; k < r2 * 2; k++) Y[j][k] += b[j] * c[k] - c[j] * b[k];
}
}
Yinv = Y;
rankY = Yinv.inverse();
}
// dbg(Yinv);
std::vector<std::vector<ModInt>> tmpmat(r2 * 2, std::vector<ModInt>(r2 * 2));
// dbg(xadd);
// dbg(Y);
int additional_dim = bcadd.size();
for (auto &[b, c] : bcadd) {
std::vector<ModInt> Yib = Yinv * b, Yic = Yinv * c;
ModInt bYic = std::inner_product(b.begin(), b.end(), Yic.begin(), ModInt(0));
const ModInt v = 1 + bYic;
if (v == 0) {
// これを消すとランクが落ちてしまう
continue;
} else {
additional_dim--;
const auto coeff = 1 / v;
for (int j = 0; j < r2 * 2; j++) {
for (int k = 0; k < r2 * 2; k++) {
tmpmat[j][k] = Yib[j] * Yic[k] - Yic[j] * Yib[k];
}
}
for (int j = 0; j < r2 * 2; j++) {
for (int k = 0; k < r2 * 2; k++) Yinv[j][k] -= tmpmat[j][k] * coeff;
}
}
}
// dbg(r2);
// dbg(additional_dim);
std::vector<int> ret(m);
for (int i = m - 1; i >= 0; i--) {
ret[i] = r2 - additional_dim;
auto b = bcs[i].first, c = bcs[i].second;
b.resize(r2 * 2, 0), c.resize(r2 * 2, 0);
std::vector<ModInt> Yib = Yinv * b, Yic = Yinv * c;
ModInt bYic = std::inner_product(b.begin(), b.end(), Yic.begin(), ModInt(0));
ModInt v = 1 + x[i] * bYic;
if (v == 0) {
// これを消すとランクが落ちてしまう
additional_dim++;
{
auto b = gen_random_vector(), c = gen_random_vector();
std::vector<ModInt> Yib = Yinv * b, Yic = Yinv * c;
ModInt bYic = std::inner_product(b.begin(), b.end(), Yic.begin(), ModInt(0));
const ModInt v = 1 + bYic;
const auto coeff = 1 / v;
for (int j = 0; j < r2 * 2; j++) {
for (int k = 0; k < r2 * 2; k++) tmpmat[j][k] = Yib[j] * Yic[k] - Yic[j] * Yib[k];
}
for (int j = 0; j < r2 * 2; j++) {
for (int k = 0; k < r2 * 2; k++) Yinv[j][k] -= tmpmat[j][k] * coeff;
}
}
Yib = Yinv * b, Yic = Yinv * c;
bYic = std::inner_product(b.begin(), b.end(), Yic.begin(), ModInt(0));
v = 1 + x[i] * bYic;
}
const auto coeff = x[i] / v;
for (int j = 0; j < r2 * 2; j++) {
for (int k = 0; k < r2 * 2; k++) {
tmpmat[j][k] = Yib[j] * Yic[k] - Yic[j] * Yib[k];
}
}
for (int j = 0; j < r2 * 2; j++) {
for (int k = 0; k < r2 * 2; k++) Yinv[j][k] -= tmpmat[j][k] * coeff;
}
// dbg(additional_dim);
}
return ret;
}
struct rand_int_ {
using lint = long long;
mt19937 mt;
rand_int_() : mt(chrono::steady_clock::now().time_since_epoch().count()) {}
lint operator()(lint x) { return this->operator()(0, x); } // [0, x)
lint operator()(lint l, lint r) {
uniform_int_distribution<lint> d(l, r - 1);
return d(mt);
}
} rnd;
// UnionFind Tree (0-indexed), based on size of each disjoint set
struct UnionFind {
std::vector<int> par, cou;
UnionFind(int N = 0) : par(N), cou(N, 1) { iota(par.begin(), par.end(), 0); }
int find(int x) { return (par[x] == x) ? x : (par[x] = find(par[x])); }
bool unite(int x, int y) {
x = find(x), y = find(y);
if (x == y) return false;
if (cou[x] < cou[y]) std::swap(x, y);
par[y] = x, cou[x] += cou[y];
return true;
}
int count(int x) { return cou[find(x)]; }
bool same(int x, int y) { return find(x) == find(y); }
};
vector<int> guchoku(int N, vector<pair<pint, pint>> bcs) {
const int M = bcs.size();
vector<int> ret(M);
FOR(s, 1, 1 << M) {
bool good = true;
UnionFind uf(N);
int last = -1;
REP(e, M) {
if (!((s >> e) & 1)) continue;
chmax(last, e);
auto [ab, cd] = bcs[e];
auto [a, b] = ab;
auto [c, d] = cd;
if (!uf.unite(a, b)) good = false;
if (!uf.unite(c, d)) good = false;
if (!good) break;
}
if (good) {
chmax(ret[last], __builtin_popcount(s));
}
}
REP(i, M - 1) chmax(ret[i + 1], ret[i]);
return ret;
}
vector<int> solve(int N, vector<pair<pint, pint>> bcs) {
vector<pair<vector<mint>, vector<mint>>> vs;
for (auto [ab, cd] : bcs) {
auto [a, b] = ab;
auto [c, d] = cd;
vector<mint> B(N), C(N);
B.at(a) += 1;
B.at(b) -= 1;
C.at(c) += 1;
C.at(d) -= 1;
vs.emplace_back(B, C);
}
auto ret1 = linear_matroid_parity<mint>(vs);
// REP(t, 1) {
// auto ret2 = linear_matroid_parity<mint>(vs);
// REP(i, ret2.size()) chmax(ret1[i], ret2[i]);
// }
return ret1;
}
void main_() {
// int Nmax, Mmax;
// cin >> Nmax >> Mmax;
const int N = 200, M = 500;
vector<mint> b0{0, 0, 0, 0};
vector<mint> c0{0, 0, 1, -1};
vector<mint> d0{1, -1, 0, 0};
dbg(linear_matroid_parity<mint>({{c0, b0}, {c0, d0}}));
dbg(linear_matroid_parity<mint>({{c0, d0}}));
for (long long ntry = 1;; ntry++) {
auto START = std::chrono::system_clock::now();
// int N = rnd(2, Nmax + 1);
// int M = rnd(2, Mmax + 1);
vector<pair<pint, pint>> edge_pairs;
REP(e, M) { edge_pairs.emplace_back(pint(rnd(min(20, N)), rnd(N)), pint(rnd(min(20, N)), rnd(N))); }
auto s = solve(N, edge_pairs);
int64_t spent_ms = std::chrono::duration_cast<std::chrono::milliseconds>(std::chrono::system_clock::now() - START).count();
dbg(spent_ms);
dbg(s);
// auto g = guchoku(N, edge_pairs);
// if (s != g) {
// dbg(N);
// dbg(edge_pairs);
// // dbg(g);
// dbg(s);
// }
if (__builtin_popcountll(ntry) == 1) { dbg(ntry); }
}
}
int main() {
int N, M;
cin >> N >> M;
vector<pair<pint, pint>> edges;
while (M--) {
int u, v, w;
cin >> u >> v >> w;
u--, v--, w--;
edges.push_back({{u, w}, {v, w}});
}
auto ret = solve(N, edges);
for (auto x : ret) cout << x << '\n';
}