結果
| 問題 | No.1815 K色問題 |
| ユーザー |
 沙耶花
|
| 提出日時 | 2022-01-20 08:34:09 |
| 言語 | C++17(gcc12) (gcc 12.4.0 + boost 1.90.0) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 6,708 bytes |
| 記録 | |
| コンパイル時間 | 10,410 ms |
| コンパイル使用メモリ | 348,352 KB |
| 実行使用メモリ | 7,968 KB |
| 最終ジャッジ日時 | 2026-06-25 01:23:53 |
| 合計ジャッジ時間 | 15,324 ms |
|
ジャッジサーバーID （参考情報） |
judge1_0 / judge2_0 |
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| ファイルパターン | 結果 |
|---|---|
| sample | RE * 3 |
| other | RE * 13 |
コンパイルメッセージ
main.cpp:15:9: warning: #pragma once in main file
15 | #pragma once
| ^~~~
ソースコード
#include <stdio.h>
#include <bits/stdc++.h>
#include "testlib.h"
#include <atcoder/all>
using namespace atcoder;
using mint = modint1000000007;
using namespace std;
#define rep(i,n) for (int i = 0; i < (n); ++i)
#define Inf 1000000001
/*
https://nyaannyaan.github.io/library/matrix/matrix.hpp
*/
#pragma once
template <class T>
struct Matrix {
vector<vector<T> > A;
Matrix() = default;
Matrix(int n, int m) : A(n, vector<T>(m, T())) {}
Matrix(int n) : A(n, vector<T>(n, T())){};
int H() const { return A.size(); }
int W() const { return A[0].size(); }
int size() const { return A.size(); }
inline const vector<T> &operator[](int k) const { return A[k]; }
inline vector<T> &operator[](int k) { return A[k]; }
static Matrix I(int n) {
Matrix mat(n);
for (int i = 0; i < n; i++) mat[i][i] = 1;
return (mat);
}
Matrix &operator+=(const Matrix &B) {
int n = H(), m = W();
assert(n == B.H() && m == B.W());
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++) (*this)[i][j] += B[i][j];
return (*this);
}
Matrix &operator-=(const Matrix &B) {
int n = H(), m = W();
assert(n == B.H() && m == B.W());
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++) (*this)[i][j] -= B[i][j];
return (*this);
}
Matrix &operator*=(const Matrix &B) {
int n = H(), m = B.W(), p = W();
assert(p == B.H());
vector<vector<T> > C(n, vector<T>(m, T{}));
for (int i = 0; i < n; i++)
for (int k = 0; k < p; k++)
for (int j = 0; j < m; j++) C[i][j] += (*this)[i][k] * B[k][j];
A.swap(C);
return (*this);
}
Matrix &operator^=(long long k) {
Matrix B = Matrix::I(H());
while (k > 0) {
if (k & 1) B *= *this;
*this *= *this;
k >>= 1LL;
}
A.swap(B.A);
return (*this);
}
Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); }
Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); }
Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); }
Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); }
bool operator==(const Matrix &B) const {
assert(H() == B.H() && W() == B.W());
for (int i = 0; i < H(); i++)
for (int j = 0; j < W(); j++)
if (A[i][j] != B[i][j]) return false;
return true;
}
bool operator!=(const Matrix &B) const {
assert(H() == B.H() && W() == B.W());
for (int i = 0; i < H(); i++)
for (int j = 0; j < W(); j++)
if (A[i][j] != B[i][j]) return true;
return false;
}
friend ostream &operator<<(ostream &os, const Matrix &p) {
int n = p.H(), m = p.W();
for (int i = 0; i < n; i++) {
os << (i ? " " : "") << "[";
for (int j = 0; j < m; j++) {
os << p[i][j] << (j + 1 == m ? "]\n" : ",");
}
}
return (os);
}
T determinant() const {
Matrix B(*this);
assert(H() == W());
T ret = 1;
for (int i = 0; i < H(); i++) {
int idx = -1;
for (int j = i; j < W(); j++) {
if (B[j][i] != 0) {
idx = j;
break;
}
}
if (idx == -1) return 0;
if (i != idx) {
ret *= T(-1);
swap(B[i], B[idx]);
}
ret *= B[i][i];
T inv = T(1) / B[i][i];
for (int j = 0; j < W(); j++) {
B[i][j] *= inv;
}
for (int j = i + 1; j < H(); j++) {
T a = B[j][i];
if (a == 0) continue;
for (int k = i; k < W(); k++) {
B[j][k] -= B[i][k] * a;
}
}
}
return ret;
}
};
/**
* @brief 行列ライブラリ
*/
long long N,M,K;
vector<vector<int>> tt;
void check(vector<int> t){
rep(i,2){
rep(j,N-1){
if(t[i*N+j] == t[i*N+j+1])return;
}
}
rep(i,N){
if(t[i]==t[i+N])return;
}
tt.push_back(t);
}
void dfs(vector<int> &t,int cur){
if(t.size()==N*2){
check(t);
return;
}
rep(i,cur){
t.push_back(i);
dfs(t,cur);
t.pop_back();
}
t.push_back(cur);
cur++;
dfs(t,cur);
t.pop_back();
}
vector<int> trans(vector<int> t){
map<int,int> used;
rep(i,t.size()){
if(used.count(t[i])){
t[i] = used[t[i]];
}
else{
int tt = used.size();
used[t[i]] = tt;
t[i] = tt;
}
}
return t;
}
struct combi{
deque<mint> kaijou;
deque<mint> kaijou_;
combi(int n){
kaijou.push_back(1);
for(int i=1;i<=n;i++){
kaijou.push_back(kaijou[i-1]*i);
}
mint b=kaijou[n].inv();
kaijou_.push_front(b);
for(int i=1;i<=n;i++){
int k=n+1-i;
kaijou_.push_front(kaijou_[0]*k);
}
}
mint combination(int n,int r){
if(r>n)return 0;
mint a = kaijou[n]*kaijou_[r];
a *= kaijou_[n-r];
return a;
}
mint junretsu(int a,int b){
mint x = kaijou_[a]*kaijou_[b];
x *= kaijou[a+b];
return x;
}
mint catalan(int n){
return combination(2*n,n)/(n+1);
}
};
int main(){
cin>>N>>M>>K;
{
vector<int> t;
dfs(t,0);
}
sort(tt.begin(),tt.end());
vector<vector<int>> t;
rep(i,tt.size()){
vector<int> temp;
rep(j,N){
temp.push_back(tt[i][j]);
}
t.push_back(temp);
}
sort(t.begin(),t.end());
t.erase(unique(t.begin(),t.end()),t.end());
//cout<<tt.size()<<endl;
mint ans= 0;
combi C(400000);
vector<int> A(tt.size()),B(tt.size());
vector<vector<int>> Minus(tt.size());
rep(j,tt.size()){
int cnt = 0;
vector<bool> f(N*2,false);
vector<int> x,y;
rep(k,tt[j].size()){
if(k<N){
if(f[tt[j][k]]){
continue;
}
else{
cnt++;
f[tt[j][k]] = true;
}
x.push_back(tt[j][k]);
}
else{
if(f[tt[j][k]]){
}
else{
Minus[j].push_back(cnt);
cnt++;
f[tt[j][k]] = true;
}
y.push_back(tt[j][k]);
}
}
y = trans(y);
int d0 = distance(t.begin(),lower_bound(t.begin(),t.end(),x));
int d1 = distance(t.begin(),lower_bound(t.begin(),t.end(),y));
A[j]= d0;
B[j] = d1;
}
vector<vector<int>> Minus2(t.size());
rep(j,t.size()){
int cnt = 0;
vector<bool> f(N,false);
rep(k,t[j].size()){
if(f[t[j][k]]){
continue;
}
else{
Minus2[j].push_back(cnt);
cnt++;;
f[t[j][k]] = true;
}
}
}
rep(i,K){
Matrix<mint> mat(t.size(),t.size());;
//matrix<mint,op0,e0,op1,e1> mat(t.size(),t.size());
rep(j,tt.size()){
mint v = 1;
rep(k,Minus[j].size()){
v *= K-i-Minus[j][k];
}
mat[B[j]][A[j]] += v;
}
mat ^= M-1;
Matrix<mint> mat2(t.size(),1);
rep(j,t.size()){
mint v = 1;
rep(k,Minus2[j].size()){
v *= K-i-Minus2[j][k];
}
mat2[j][0] = v;
}
mat2 = mat * mat2;
mint sum = 0;
rep(j,t.size()){
sum += mat2[j][0];
}
sum *= C.combination(K,i);
if(i%2==1)sum *= -1;
ans += sum;
}
cout<<ans.val()<<endl;
return 0;
}