結果
| 問題 | No.1502 Many Simple Additions |
| ユーザー |
 hitonanode
|
| 提出日時 | 2021-05-08 02:12:55 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 56 ms / 2,000 ms |
| コード長 | 13,710 bytes |
| コンパイル時間 | 1,776 ms |
| コンパイル使用メモリ | 148,972 KB |
| 最終ジャッジ日時 | 2025-01-21 09:06:30 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 5 |
| other | AC * 39 |
ソースコード
#include <algorithm>#include <array>#include <bitset>#include <cassert>#include <chrono>#include <cmath>#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 <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) { if (m < q) {m = q; return true;} else return false; }template <typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return 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::lower_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 >= 201703Ltemplate <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); returnis; }template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { std::apply([&os](auto &&... args) { ((os << args << ','), ...);},tpl); return os; }#endiftemplate <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_LOCALconst 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#else#define dbg(x) (x)#endiftemplate <int mod> struct ModInt {#if __cplusplus >= 201402L#define MDCONST constexpr#else#define MDCONST#endifusing lint = long long;MDCONST static int get_mod() { return mod; }static int get_primitive_root() {static int primitive_root = 0;if (!primitive_root) {primitive_root = [&]() {std::set<int> fac;int v = mod - 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 < mod; g++) {bool ok = true;for (auto i : fac)if (ModInt(g).pow((mod - 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 >= mod ? v - mod : v), *this; }MDCONST ModInt(lint v) { _setval(v % mod + mod); }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 + mod); }MDCONST ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % mod); }MDCONST ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % mod); }MDCONST ModInt operator-() const { return ModInt()._setval(mod - 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 % mod + x.val); }friend MDCONST ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % mod - x.val + mod); }friend MDCONST ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.val % mod); }friend MDCONST ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.inv() % mod); }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 {lint ans = 1, tmp = this->val;while (n) {if (n & 1) ans = ans * tmp % mod;tmp = tmp * tmp % mod, n /= 2;}return ans;}static std::vector<long long> facs, invs;MDCONST static void _precalculation(int N) {int l0 = facs.size();if (N <= l0) return;facs.resize(N), invs.resize(N);for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i % mod;long long facinv = ModInt(facs.back()).pow(mod - 2).val;for (int i = N - 1; i >= l0; i--) {invs[i] = facinv * facs[i - 1] % mod;facinv = facinv * i % mod;}}MDCONST lint inv() const {if (this->val < std::min(mod >> 1, 1 << 21)) {while (this->val >= int(facs.size())) _precalculation(facs.size() * 2);return invs[this->val];} else {return this->pow(mod - 2).val;}}MDCONST ModInt fac() const {while (this->val >= int(facs.size())) _precalculation(facs.size() * 2);return facs[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).fac() * r.fac());}ModInt sqrt() const {if (val == 0) return 0;if (mod == 2) return val;if (pow((mod - 1) / 2) != 1) return 0;ModInt b = 1;while (b.pow((mod - 1) / 2) == 1) b += 1;int e = 0, m = mod - 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, mod - x.val));}};template <int mod> std::vector<long long> ModInt<mod>::facs = {1};template <int mod> std::vector<long long> ModInt<mod>::invs = {0};using mint = ModInt<1000000007>;// Weighted UnionFindtemplate <typename T> struct WeightedUnionFind {std::vector<int> par, sz;std::vector<T> pot;WeightedUnionFind(int N = 0) : par(N), sz(N, 1), pot(N) { std::iota(par.begin(), par.end(), 0); }int find(int x) {if (par[x] != x) {int r = find(par[x]);pot[x] = pot[x] + pot[par[x]], par[x] = r;}return par[x];}bool unite(int s, int t, T rel_diff) {// Relate s and t by t = s + rel_diff// Return false iff contradiction happens.rel_diff = rel_diff + weight(s) + (-weight(t));if ((s = find(s)) == (t = find(t))) return rel_diff == 0;if (sz[s] < sz[t]) std::swap(s, t), rel_diff = -rel_diff;par[t] = s, sz[s] += sz[t], pot[t] = rel_diff;return true;}T weight(int x) {find(x);return pot[x];}T diff(int s, int t) { return weight(t) + (-weight(s)); }int count(int x) { return sz[find(x)]; }bool same(int s, int t) { return find(s) == find(t); }};// UnionFind Tree (0-indexed), based on size of each disjoint setstruct 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); }};void bad() {puts("0");exit(0);}int main() {int N, M, K;cin >> N >> M >> K;WeightedUnionFind<lint> uf(N * 2);UnionFind uf0(N);while (M--) {lint x, y, z;cin >> x >> y >> z;x--, y--;if (!uf.unite(y + N, x, z)) bad();if (!uf.unite(x + N, y, z)) bad();uf0.unite(x, y);}vector<vector<int>> mp(N);REP(i, N) mp[uf0.find(i)].push_back(i);mint ret0 = 1, ret1 = 0;constexpr lint INF = 1LL << 60;for (const auto &vs : mp) if (vs.size()) {int r = vs[0];if (uf.same(r, r + N)) {for (auto v : vs) {auto d2 = uf.diff(v + N, v), d = d2 / 2;if (d2 % 2 or d > K or d <= 0) bad();if (d == K) {ret1 += ret0;ret0 = 0;}}continue;}lint lo = 1, hi = K;lint dmin = 0, dmax = 0;lint invmin = INF, invmax = -INF;for (auto x : vs) {if (uf.same(r, x)) {chmin(dmin, uf.diff(r, x));chmax(dmax, uf.diff(r, x));} else {chmin(invmin, uf.diff(x + N, r));chmax(invmax, uf.diff(x + N, r));}chmax(lo, 1 - dmin);chmin(hi, K - dmax);chmax(lo, invmax - K);chmin(hi, invmin - 1);}if (lo > hi) bad();lint w = hi - lo + 1;ret1 *= w;int b1 = (hi + dmax == K);int b2 = (-lo + invmax == K);if (b1 and b2 and lo == hi) b2--;ret1 += ret0 * (b1 + b2);ret0 *= (w - (b1 + b2));}cout << ret1 << '\n';}