結果
| 問題 |
No.1815 K色問題
|
| ユーザー |
 Ricky_pon
|
| 提出日時 | 2022-03-14 19:28:26 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 148 ms / 2,000 ms |
| コード長 | 9,026 bytes |
| コンパイル時間 | 2,002 ms |
| コンパイル使用メモリ | 202,292 KB |
| 最終ジャッジ日時 | 2025-01-28 09:35:25 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 13 |
コンパイルメッセージ
main.cpp: In function ‘int main()’:
main.cpp:263:10: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
263 | scanf("%d%lld%d", &n, &m, &K);
| ~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
ソースコード
#include <bits/stdc++.h>
#include <atcoder/modint>
#include <atcoder/modint>
#include <vector>
template <class T>
struct Factorial {
int n;
std::vector<T> fact;
std::vector<T> revfact;
Factorial(int n) : n(n) {
fact.resize(n + 1);
revfact.resize(n + 1);
fact[0] = 1;
for (int i = 0; i < n; ++i) fact[i + 1] = fact[i] * (i + 1);
revfact[n] = fact[n].inv();
for (int i = n - 1; i >= 0; --i) revfact[i] = revfact[i + 1] * (i + 1);
}
T comb(int n, int r) {
if (n < r || r < 0) return 0;
return fact[n] * revfact[r] * revfact[n - r];
}
T perm(int n, int r) {
if (n < r || r < 0) return 0;
return fact[n] * revfact[n - r];
}
};
#include <assert.h>
#include <vector>
template <class T>
struct Matrix {
std::vector<std::vector<T>> a;
Matrix(int n, int m) : a(n, std::vector<T>(m, 0)) {}
Matrix(int n) : a(n, std::vector<T>(n, 0)) {}
int height() const { return a.size(); }
int width() const { return a[0].size(); }
inline const std::vector<T> &operator[](int i) const { return a[i]; }
inline std::vector<T> &operator[](int i) { return a[i]; }
static Matrix id(int n) {
Matrix res(n);
for (int i = 0; i < n; i++) res[i][i] = 1;
return res;
}
Matrix &operator*=(const Matrix &b) {
assert(width() == b.height());
std::vector<std::vector<T>> c(height(), std::vector<T>(b.width()));
for (int i = 0; i < height(); ++i) {
for (int k = 0; k < b.height(); ++k) {
for (int j = 0; j < b.width(); ++j) {
c[i][j] += a[i][k] * b[k][j];
}
}
}
a.swap(c);
return *this;
}
Matrix pow(long long n) const {
auto x = (*this), res = id(height());
while (n) {
if (n & 1) {
res *= x;
--n;
} else {
x *= x;
n >>= 1;
}
}
return res;
}
Matrix operator*(const Matrix &b) const { return Matrix(*this) *= b; }
std::vector<T> operator*(const std::vector<T> &v) {
assert(width() == (int)v.size());
std::vector<T> res(height(), 0);
for (int i = 0; i < height(); ++i) {
for (int j = 0; j < width(); ++j) {
res[i] += a[i][j] * v[j];
}
}
return res;
}
};
template <class T>
std::pair<int, bool> gauss_jordan(Matrix<T> &a) {
int rnk = 0;
bool swp = false;
for (int j = 0; j < a.width(); ++j) {
int pivot = -1;
for (int i = rnk; i < a.height(); ++i) {
if (a[i][j] != 0) {
pivot = i;
break;
}
}
if (pivot < 0) continue;
swap(a[pivot], a[rnk]);
if (pivot != rnk) swp ^= true;
for (int i = 0; i < a.height(); ++i) {
if (i != rnk && a[i][j] != 0) {
auto coef = a[i][j] / a[rnk][j];
for (int k = j; k < a.width(); ++k) {
a[i][k] -= a[rnk][k] * coef;
}
}
}
++rnk;
}
return {rnk, swp};
}
template <class T>
T determinant(Matrix<T> a) {
auto [rnk, swp] = gauss_jordan(a);
if (rnk < a.height()) return 0;
T res = 1;
for (int i = 0; i < a.height(); ++i) res *= a[i][i];
if (swp) res = -res;
return res;
}
template <class T>
std::pair<std::vector<T>, std::vector<std::vector<T>>>
system_of_linear_equations(Matrix<T> a, const std::vector<T> &b) {
assert(a.height() == (int)b.size());
Matrix<T> aug(a.height(), a.width() + 1);
for (int i = 0; i < a.height(); ++i) {
for (int j = 0; j < a.width(); ++j) {
aug[i][j] = a[i][j];
}
aug[i][a.width()] = b[i];
}
auto rnk = gauss_jordan(a).first, rnk_aug = gauss_jordan(aug).first;
std::vector<T> solution;
std::vector<std::vector<T>> kernel;
if (rnk < rnk_aug) return {solution, kernel};
solution.resize(a.width(), 0);
std::vector<bool> used(a.width(), false);
std::vector<int> pos(rnk);
for (int i = 0; i < rnk; ++i) {
for (int j = 0; j < a.width(); ++j) {
if (aug[i][j] != 0) {
solution[j] = aug[i][a.width()] / aug[i][j];
used[j] = true;
pos[i] = j;
break;
}
}
}
for (int j = 0; j < a.width(); ++j) {
if (!used[j]) {
std::vector<T> v(a.width(), 0);
v[j] = 1;
for (int i = 0; i < rnk; ++i) {
v[pos[i]] = -aug[i][j] / aug[i][pos[i]];
}
kernel.push_back(v);
}
}
return {solution, kernel};
}
#include <algorithm>
#include <cassert>
#include <vector>
template <class T>
bool chmax(T &a, const T &b) {
if (a < b) {
a = b;
return true;
}
return false;
}
template <class T>
bool chmin(T &a, const T &b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template <class T>
T div_floor(T a, T b) {
if (b < 0) a *= -1, b *= -1;
return a >= 0 ? a / b : (a + 1) / b - 1;
}
template <class T>
T div_ceil(T a, T b) {
if (b < 0) a *= -1, b *= -1;
return a > 0 ? (a - 1) / b + 1 : a / b;
}
template <typename T>
struct CoordComp {
std::vector<T> v;
bool sorted;
CoordComp() : sorted(false) {}
int size() { return v.size(); }
void add(T x) { v.push_back(x); }
void build() {
std::sort(v.begin(), v.end());
v.erase(std::unique(v.begin(), v.end()), v.end());
sorted = true;
}
int get_idx(T x) {
assert(sorted);
return lower_bound(v.begin(), v.end(), x) - v.begin();
}
T &operator[](int i) { return v[i]; }
};
#define For(i, a, b) for (int i = (int)(a); (i) < (int)(b); ++(i))
#define rFor(i, a, b) for (int i = (int)(a)-1; (i) >= (int)(b); --(i))
#define rep(i, n) For(i, 0, n)
#define rrep(i, n) rFor(i, n, 0)
#define fi first
#define se second
using namespace std;
using lint = long long;
using pii = pair<int, int>;
using pll = pair<lint, lint>;
using mint = atcoder::modint1000000007;
int main() {
int n, K;
lint m;
scanf("%d%lld%d", &n, &m, &K);
if (m * n < K) {
printf("%d\n", 0);
return 0;
}
if (K == 1) {
printf("%d\n", m * n == 1 ? 1 : 0);
return 0;
}
Factorial<mint> fc(K);
if (n == 1) {
mint ans = 0;
rep(i, K - 1) {
mint c = K - i;
mint tmp = fc.comb(K, i) * c * (c - 1).pow(m - 1);
if (i % 2 == 1)
ans -= tmp;
else
ans += tmp;
}
printf("%u\n", ans.val());
} else if (n == 2) {
mint ans = 0;
rep(i, K - 1) {
mint c = K - i;
mint b = (c - 1) * (c - 1) - (c - 2);
mint tmp = fc.comb(K, i) * c * (c - 1) * b.pow(m - 1);
if (i % 2 == 1)
ans -= tmp;
else
ans += tmp;
}
printf("%u\n", ans.val());
} else {
constexpr lint MOD = 1'000'000'007;
mint ans = 0;
rep(i, K - 1) {
lint c = K - i;
lint A00, A01 = 0, A10 = 0, A11 = 0;
A00 = ((c - 1) * (c - 1) - (c - 2) + MOD) % MOD;
if (c >= 3) {
A01 = ((c - 2) * (c - 1) - (c - 3) + MOD) % MOD;
A10 = ((c - 1) * (c - 1) * (c - 1) - 2 * (c - 2) * (c - 1) -
(c - 1) * (c - 1) + 2 * (c - 2) + MOD * MOD) %
MOD;
A11 = ((c - 1) * (c - 1) * (c - 1) - 3 * (c - 2) * (c - 1) +
2 * (c - 3) + MOD * MOD) %
MOD;
}
vector<lint> b = {(c * (c - 1)) % MOD,
(c * (c - 1) * (c - 2)) % MOD};
lint t = m - 1;
while (t) {
if (t & 1) {
lint nb0, nb1;
nb0 = (A00 * b[0] + A01 * b[1]) % MOD;
nb1 = (A10 * b[0] + A11 * b[1]) % MOD;
b[0] = nb0;
b[1] = nb1;
--t;
}
if (t > 0) {
lint nA00, nA01, nA10, nA11;
nA00 = (A00 * A00 + A01 * A10) % MOD;
nA01 = (A00 * A01 + A01 * A11) % MOD;
nA10 = (A10 * A00 + A11 * A10) % MOD;
nA11 = (A10 * A01 + A11 * A11) % MOD;
A00 = nA00;
A01 = nA01;
A10 = nA10;
A11 = nA11;
t >>= 1;
}
}
mint tmp = fc.comb(K, i) * ((b[0] + b[1]) % MOD);
if (i % 2 == 1)
ans -= tmp;
else
ans += tmp;
}
printf("%u\n", ans.val());
}
}