結果
| 問題 | No.1815 K色問題 |
| ユーザー |
 FF256grhy
|
| 提出日時 | 2022-01-27 12:54:13 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 10,993 bytes |
| コンパイル時間 | 3,018 ms |
| コンパイル使用メモリ | 223,888 KB |
| 実行使用メモリ | 13,224 KB |
| 最終ジャッジ日時 | 2024-09-29 22:40:32 |
| 合計ジャッジ時間 | 9,670 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge1 |
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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
12,072 KB |
| testcase_01 | AC | 2 ms
5,248 KB |
| testcase_02 | AC | 2 ms
5,248 KB |
| testcase_03 | AC | 2 ms
5,248 KB |
| testcase_04 | AC | 2 ms
5,248 KB |
| testcase_05 | AC | 2 ms
5,248 KB |
| testcase_06 | AC | 74 ms
6,272 KB |
| testcase_07 | AC | 17 ms
5,248 KB |
| testcase_08 | TLE | - |
| testcase_09 | AC | 18 ms
6,816 KB |
| testcase_10 | AC | 26 ms
6,816 KB |
| testcase_11 | AC | 724 ms
6,816 KB |
| testcase_12 | AC | 2 ms
6,816 KB |
| testcase_13 | AC | 2 ms
6,816 KB |
| testcase_14 | TLE | - |
| testcase_15 | -- | - |
ソースコード
#include <bits/stdc++.h>
using namespace std;
#define incII(i, l, r) for(decay_t<decltype(r)> i = (l) ; i <= (r); i++)
#define incIX(i, l, r) for(decay_t<decltype(r)> i = (l) ; i < (r); i++)
#define incXI(i, l, r) for(decay_t<decltype(r)> i = (l) + 1; i <= (r); i++)
#define incXX(i, l, r) for(decay_t<decltype(r)> i = (l) + 1; i < (r); i++)
#define decII(i, l, r) for(decay_t<decltype(r)> i = (r) ; i >= (l); i--)
#define decIX(i, l, r) for(decay_t<decltype(r)> i = (r) - 1; i >= (l); i--)
#define decXI(i, l, r) for(decay_t<decltype(r)> i = (r) ; i > (l); i--)
#define decXX(i, l, r) for(decay_t<decltype(r)> i = (r) - 1; i > (l); i--)
#define inc(i, n) incIX(i, 0, n)
#define dec(i, n) decIX(i, 0, n)
#define inc1(i, n) incII(i, 1, n)
#define dec1(i, n) decII(i, 1, n)
auto inII = [](auto a, auto l, auto r) -> bool { return (l <= a && a <= r); };
auto inIX = [](auto a, auto l, auto r) -> bool { return (l <= a && a < r); };
auto inXI = [](auto a, auto l, auto r) -> bool { return (l < a && a <= r); };
auto inXX = [](auto a, auto l, auto r) -> bool { return (l < a && a < r); };
auto setmin = [](auto & a, auto b) -> bool { return (b < a ? a = b, true : false); };
auto setmax = [](auto & a, auto b) -> bool { return (b > a ? a = b, true : false); };
auto setmineq = [](auto & a, auto b) -> bool { return (b <= a ? a = b, true : false); };
auto setmaxeq = [](auto & a, auto b) -> bool { return (b >= a ? a = b, true : false); };
using LL = long long int;
using LD = long double;
#define PB push_back
#define EB emplace_back
#define MP make_pair
#define MT make_tuple
#define FI first
#define SE second
#define FR front()
#define BA back()
#define ALL(a) begin(a), end(a)
#define RALL(a) rbegin(a), rend(a)
#define RV(a) reverse(ALL(a))
#define ST(a) sort(ALL(a))
#define RST(a) sort(RALL(a))
#define SC static_cast
#define SI(a) SC<int>(a.size())
#define SL(a) SC<LL>(a.size())
#define RF(e, ...) for(auto && e: __VA_ARGS__)
#define SF(a, ...) for(auto && [__VA_ARGS__]: a)
#define until(e) while(not(e))
#define if_not(e) if(not(e))
#define ef else if
#define UR assert(false)
auto * IS = & cin;
auto * OS = & cout;
template<typename ... A> void in(A & ... a) { (* IS >> ... >> a); }
#define IN(...) __VA_ARGS__; in(__VA_ARGS__)
struct OS_init { OS_init() { * OS << boolalpha << fixed << setprecision(20); } } os_init_;
void out_([[maybe_unused]] string const & s) { }
template<typename A > void out_([[maybe_unused]] string const & s, A const & a) { * OS << a; }
template<typename A, typename ... B> void out_( string const & s, A const & a, B const & ... b) { * OS << a << s; out_(s, b ...); }
auto outF = [](array<string, 3> const & s, auto const & ... a) { * OS << s[0]; out_(s[1], a ...); * OS << s[2] << flush; };
auto outN = [](auto const & ... a) { outF({ "", "" , "" }, a ...); };
auto outS = [](auto const & ... a) { outF({ "", " " , " " }, a ...); };
auto outL = [](auto const & ... a) { outF({ "", "\n", "\n" }, a ...); };
auto outSN = [](auto const & ... a) { outF({ "", " " , "" }, a ...); };
auto outNL = [](auto const & ... a) { outF({ "", "" , "\n" }, a ...); };
auto outSL = [](auto const & ... a) { outF({ "", " " , "\n" }, a ...); };
auto outD = [](auto const & ... a) { outF({ "[ ", " : " , " ]\n" }, a ...); };
auto out = outSL;
template<typename A > void disp_(A const & a) { * OS << a; }
template<typename A, typename ... T> void disp_(A const & a, string const & s, T const & ... t) { string ss; for(auto && e: a) { * OS << ss; ss = s; disp_(e, t ...); } }
auto dispI = [](auto const & a, auto const & s, auto const & ... t) { disp_(a, t ...); * OS << s << flush; };
auto dispT = [](auto const & a, auto const & s, auto const & ... t) { for(auto && e: a) { disp_(e, t ...); * OS << s; } * OS << flush; };
auto dispL = [](auto const & a, auto const & ... t) { dispT(a, "\n", t ...); };
template<typename A> istream & operator>>(istream & is, vector<A> & v) { for(auto && e: v) { is >> e; } return is; }
template<typename A> ostream & operator<<(ostream & os, vector<A> const & v) { string ss; for(auto && e: v) { os << ss << e; ss = " "; } return os; }
template<typename A > auto make_v(A a) { return a; }
template<typename A, typename ... M> auto make_v(A a, int n, M ... m) { return vector(n, make_v(a, m ...)); }
template<typename A, typename ... N> auto read_v(N ... n) { auto a = make_v(A { }, n ...); in(a); return a; }
template<typename A, size_t N> istream & operator>>(istream & is, array<A, N> & a) { for(auto && e: a) { is >> e; } return is; }
template<typename A, size_t N> ostream & operator<<(ostream & os, array<A, N> const & a) { string ss; for(auto && e: a) { os << ss << e; ss = " "; } return os; }
template<typename A, typename B> istream & operator>>(istream & is, pair<A, B> & p) { return is >> p.first >> p.second; }
template<typename A, typename B> ostream & operator<<(ostream & os, pair<A, B> const & p) { return os << p.first << " " << p.second; }
template<int I = 0, typename T> void tin_ (istream & is, T & t) { if constexpr(I < tuple_size<T>::value) { is >> get<I>(t); tin_<I + 1>(is, t); } }
template<int I = 0, typename T> void tout_(ostream & os, T const & t) { if constexpr(I < tuple_size<T>::value) { if(I != 0) { os << " "; } os << get<I>(t); tout_<I + 1>(os, t); } }
template<typename ... A> istream & operator>>(istream & is, tuple<A ...> & t) { tin_ (is, t); return is; }
template<typename ... A> ostream & operator<<(ostream & os, tuple<A ...> const & t) { tout_(os, t); return os; }
// ---- ----
template<typename T, T(* PLUS)(T, T), T(* MULT)(T, T), T(* ZERO)(), T(* UNIT)()> struct Matrix_ {
int h, w;
vector<vector<T>> v;
explicit Matrix_(int h = 1): h(h), w(h), v(h, vector<T>(w, ZERO())) { }
explicit Matrix_(int h, int w): h(h), w(w), v(h, vector<T>(w, ZERO())) { }
Matrix_(vector<vector<T>> const & v): h(SI(v)), w(SI(v[0])), v(v) {
inc(i, h) { assert(SI(v[i]) == w); }
}
vector<T> const & operator[](int i) const { return v.at(i); }
vector<T> & operator[](int i) { return v.at(i); }
static Matrix_ unit(int n) {
Matrix_ a(n);
inc(i, n) { a[i][i] = UNIT(); }
return a;
}
friend Matrix_ operator*(Matrix_ const & a, Matrix_ const & b) {
assert(a.w == b.h);
Matrix_ c(a.h, b.w);
inc(i, a.h) {
inc(j, b.w) {
inc(k, a.w) {
c[i][j] = PLUS(c[i][j], MULT(a[i][k], b[k][j]));
}
}
}
return c;
}
friend Matrix_ operator^(Matrix_ a, LL b) {
assert(a.h == a.w);
assert(b >= 0);
auto p = Matrix_::unit(a.h);
while(b) {
if(b & 1) { p *= a; }
a *= a;
b >>= 1;
}
return p;
}
friend Matrix_ & operator*=(Matrix_ & a, Matrix_ const & b) { return (a = a * b); }
friend Matrix_ & operator^=(Matrix_ & a, LL b) { return (a = a ^ b); }
friend Matrix_ & operator*=(Matrix_ & a, T b) {
inc(i, a.h) {
inc(j, a.w) {
a[i][j] = MULT(a[i][j], b);
}
}
return a;
}
friend Matrix_ operator*(Matrix_ a, T b) { return (a *= b); }
friend Matrix_ operator*(T b, Matrix_ a) { return (a *= b); }
friend ostream & operator<<(ostream & s, Matrix_ const & a) {
inc(i, a.h) { s << a[i] << endl; }
return s;
}
};
template<typename T> T PLUS(T a, T b) { return a + b; };
template<typename T> T MULT(T a, T b) { return a * b; };
template<typename T> T ZERO() { return 0; };
template<typename T> T UNIT() { return 1; };
template<typename T> using Matrix = Matrix_<T, PLUS<T>, MULT<T>, ZERO<T>, UNIT<T>>;
// ----
template<LL M> class ModInt {
private:
LL v;
pair<LL, LL> ext_gcd(LL a, LL b) {
if(b == 0) { assert(a == 1); return { 1, 0 }; }
auto p = ext_gcd(b, a % b);
return { p.SE, p.FI - (a / b) * p.SE };
}
public:
ModInt(LL vv = 0) { v = vv; if(abs(v) >= M) { v %= M; } if(v < 0) { v += M; } }
LL val() { return v; }
static LL mod() { return M; }
ModInt inv() { return ext_gcd(M, v).SE; }
ModInt exp(LL b) {
ModInt p = 1, a = v; if(b < 0) { a = a.inv(); b = -b; }
while(b) { if(b & 1) { p *= a; } a *= a; b >>= 1; }
return p;
}
friend bool operator< (ModInt a, ModInt b) { return (a.v < b.v); }
friend bool operator> (ModInt a, ModInt b) { return (a.v > b.v); }
friend bool operator<=(ModInt a, ModInt b) { return (a.v <= b.v); }
friend bool operator>=(ModInt a, ModInt b) { return (a.v >= b.v); }
friend bool operator==(ModInt a, ModInt b) { return (a.v == b.v); }
friend bool operator!=(ModInt a, ModInt b) { return (a.v != b.v); }
friend ModInt operator+ (ModInt a ) { return ModInt(+a.v); }
friend ModInt operator- (ModInt a ) { return ModInt(-a.v); }
friend ModInt operator+ (ModInt a, ModInt b) { return ModInt(a.v + b.v); }
friend ModInt operator- (ModInt a, ModInt b) { return ModInt(a.v - b.v); }
friend ModInt operator* (ModInt a, ModInt b) { return ModInt(a.v * b.v); }
friend ModInt operator/ (ModInt a, ModInt b) { return a * b.inv(); }
friend ModInt operator^ (ModInt a, LL b) { return a.exp(b); }
friend ModInt & operator+=(ModInt & a, ModInt b) { return (a = a + b); }
friend ModInt & operator-=(ModInt & a, ModInt b) { return (a = a - b); }
friend ModInt & operator*=(ModInt & a, ModInt b) { return (a = a * b); }
friend ModInt & operator/=(ModInt & a, ModInt b) { return (a = a / b); }
friend ModInt & operator^=(ModInt & a, LL b) { return (a = a ^ b); }
friend istream & operator>>(istream & s, ModInt & b) { s >> b.v; b = ModInt(b.v); return s; }
friend ostream & operator<<(ostream & s, ModInt b) { return (s << b.v); }
};
using MI = ModInt<1'000'000'007>;
// ----
template<typename T> struct Combination {
LL n;
vector<T> f, r;
Combination(LL n) : n(n) {
f = r = vector<T>(n + 1);
inc(i, n + 1) { f[i] = (i == 0 ? 1 : f[i - 1] * i ); }
dec(i, n + 1) { r[i] = (i == n ? f[n].inv() : r[i + 1] * (i + 1)); }
}
T P(LL a, LL b) {
assert(inII(a, 0, n) && inII(b, 0, n));
return (a < b ? 0 : f[a] * r[a - b]);
}
T C(LL a, LL b) {
assert(inII(a, 0, n) && inII(b, 0, n));
return (a < b ? 0 : f[a] * r[a - b] * r[b]);
}
T H(LL a, LL b) {
assert(inII(a, 0, n) && inII(b, 0, n) && inII(a + b - 1, -1, n));
return (a == 0 ? (b == 0 ? 1 : 0) : f[a + b - 1] * r[a - 1] * r[b]);
}
};
int main() {
auto f = [](int n, LL m, MI k) -> MI {
m--;
MI k1 = k - 1;
MI k2 = k - 2;
MI k3 = k - 3;
if(n == 1) { return k * (k1 ^ m); }
if(n == 2) { return k * k1 * ((k1 * k1 - k2) ^ m); }
Matrix<MI> v {{
{ k * k1 * k2, k * k1 }
}}, A {{
{ (k1 ^ 3) - 3 * k2 * k1 + 2 * k3, k2 * k1 - k3 },
{ (k1 ^ 3) - 2 * k2 * k1 - k1 * k1 + 2 * k2, k1 * k1 - k2 }
}}, w {{
{ 1 },
{ 1 }
}};
return (v * (A ^ m) * w)[0][0];
};
LL IN(n, m, k);
Combination<MI> c(k);
MI ans = 0;
incII(i, 0, k) { ans += (i % 2 == 0 ? +1 : -1) * c.C(k, i) * f(n, m, k - i); }
out(ans);
}