結果

問題 No.2267 群の公理
ユーザー 霊夢の3分ハッキング霊夢の3分ハッキング
提出日時 2023-11-26 13:13:18
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 3 ms / 2,000 ms
コード長 8,934 bytes
コンパイル時間 5,973 ms
コンパイル使用メモリ 295,272 KB
最終ジャッジ日時 2025-02-18 01:26:33
ジャッジサーバーID
(参考情報)
judge4 / judge5
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ファイルパターン 結果
other AC * 50
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ソースコード

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プレゼンテーションモードにする

#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using namespace atcoder;
#define rep(i,n) for(int i=0; i<n; i++)
#define ll long long
#define str string
#define vi vector<int>
#define vvi vector<vector<int>>
#define vl vector<ll>
#define vs vector<string>
int gi() {
int i;
cin >> i;
return i;
}
ll gl() {
ll l;
cin >> l;
return l;
}
double gd() {
double d;
cin >> d;
return d;
}
string gs() {
string s;
cin >> s;
return s;
}
vector<int> gia(int n) {
vector<int> A(n);
rep(i,n) {
cin >> A[i];
}
return A;
}
vector<ll> gla(int n) {
vector<ll> A(n);
rep(i,n) {
cin >> A[i];
}
return A;
}
vector<string> gsa(int n) {
vector<string> A(n);
rep(i,n) {
cin >> A[i];
}
return A;
}
vector<vector<int>> gsi2(int n, int m) {
vector<vector<int>> A(n, vector<int>(m));
rep(i,n) {
rep(j,m) {
cin >> A[i][j];
}
}
return A;
}
vector<vector<int>> readGraph(int n, int m, bool f=false) {
vector<vector<int>> G(n);
rep(i,m){
int a=gi();
int b=gi();
a--;
b--;
G[a].push_back(b);
if(!f){
G[b].push_back(a);
}
}
return G;
}
vector<vector<pair<ll,int>>> readGraphWithWeight(int n, int m, bool f=false) {
vector<vector<pair<ll,int>>> G(n);
rep(i,m){
int a=gi();
int b=gi();
ll c=gi();
a--;
b--;
pair<ll,int> p=make_pair(c,b);
G[a].push_back(p);
if(!f){
pair<ll,int> p2=make_pair(c,a);
G[b].push_back(p2);
}
}
return G;
}
void ov(vector<int> v) {
if((int)v.size()==0)return;
rep(i,(int)v.size()-1) {
cout << v[i] << ' ';
}
cout << v[v.size()-1] << endl;
}
//
bool isBipartite(vector<pair<ll,pair<int,int>>>& E, int N) {
dsu uf(N*2);
rep(i,E.size()) {
int a=E[i].second.first;
int b=E[i].second.second;
ll w=E[i].first;
uf.merge(a,b+N);
uf.merge(a+N,b);
}
rep(i,N) {
if(uf.same(i,i+N))return false;
}
return true;
}
vector<vl> matrixMulti(vector<vl>& A, vector<vl>& B) {
int AR=A.size();
int AC=A[0].size();
int BC=B[0].size();
vector<vl> ans(AR,vl(BC,0));
rep(i,AR) {
rep(j,BC) {
rep(k,AC) {
ans[i][k]+=A[i][j]*B[j][k];
}
}
}
return ans;
}
vector<vl> matrixPow(vector<vl>& A, int p) {
int q=p;
int cnt=0;
while(q>0) {
cnt++;
q=q>>1;
}
vector<vector<vl>> PAS;
PAS.push_back(A);
rep(i,cnt-1) {
PAS.push_back(matrixMulti(PAS[i],PAS[i]));
}
vector ans(A.size(),vl(A.size(),0));
rep(i,ans.size()) {
ans[i][i]=1;
}
rep(i,cnt) {
if((p>>i & 1) == 0)continue;
ans=matrixMulti(ans,PAS[i]);
}
return ans;
}
vector<string> split(const string &s, char delim) {
vector<string> elems;
string item;
for (char ch: s) {
if (ch == delim) {
if (!item.empty())
elems.push_back(item);
item.clear();
}
else {
item += ch;
}
}
if (!item.empty())
elems.push_back(item);
return elems;
}
// private
void recursive_comb(int *indexes, int s, int rest, std::function<void(int *)> f) {
if (rest == 0) {
f(indexes);
} else {
if (s < 0) return;
recursive_comb(indexes, s - 1, rest, f);
indexes[rest - 1] = s;
recursive_comb(indexes, s - 1, rest - 1, f);
}
}
// nCk
void foreach_comb(int n, int k, std::function<void(int *)> f) {
int indexes[k];
recursive_comb(indexes, n - 1, k, f);
}
vector<long long> fact, fact_inv, inv;
// nCk
void init_nCk(int SIZE, int mod) {
fact.resize(SIZE + 5);
fact_inv.resize(SIZE + 5);
inv.resize(SIZE + 5);
fact[0] = fact[1] = 1;
fact_inv[0] = fact_inv[1] = 1;
inv[1] = 1;
for (int i = 2; i < SIZE + 5; i++) {
fact[i] = fact[i - 1] * i % mod;
inv[i] = mod - inv[mod % i] * (mod / i) % mod;
fact_inv[i] = fact_inv[i - 1] * inv[i] % mod;
}
}
/* nCk :MOD( int_nCk )
:O(1)
*/
long long nCk(int n, int k, int mod) {
if(n<k)return 0;
return fact[n] * (fact_inv[k] * fact_inv[n - k] % mod) % mod;
}
int lis(vector<int> A) {
int MAX=INT_MAX;
vector<int> dp((int)A.size(), MAX);
rep(i, (int)A.size()) {
int a=A[i];
int mn=-1;
int mx=(int)A.size();
while(mx-mn>1){
int idx=(mx+mn)/2;
int v=dp[idx];
if(a>v) {
mn=idx;
} else {
mx=idx;
}
}
dp[mx]=a;
}
int ans=0;
rep(i, (int)A.size()) {
if(dp[i]!=MAX){
ans+=1;
} else {
break;
}
}
return ans;
}
ll uclid(ll m, ll n) {
if(n==0) {
return m;
} else {
return uclid(n,m%n);
}
}
vector<ll> yakusu(ll N) {
vector<ll> ans;
for(ll i=1;i<N+1;i++) {
if(i*i>N)break;
if(N%i==0) {
ans.push_back(i);
if(N/i!=i) {
ans.push_back(N/i);
}
}
}
return ans;
}
vector<ll> insuB(ll N) {
vector<ll> ans;
ll i=2;
while(i*i<=N) {
if(N%i==0) {
ans.push_back(i);
N=N/i;
} else {
i++;
}
}
if(N!=1) {
ans.push_back(N);
}
return ans;
}
map<ll,ll> insuBm(ll N) {
map<ll,ll> ans;
for(ll i=2;i<N;i++){
if(i*i>N)break;
while(N%i==0) {
ans[i]++;
N=N/i;
}
}
if(N!=1) {
ans[N]++;
}
return ans;
}
void rotate(vector<vector<ll>>& A) {
vector<vector<ll>> ra(A[0].size(),vector<ll>(A.size(),0));
rep(i, (int)A[0].size()) {
rep(j,(int)A.size()) {
ra[i][j]=A[A.size()-j-1][i];
}
}
A=ra;
}
vector<bool> eratostenes(int N) {
vector<bool> ans(N+1,true);
ans[0]=false;
ans[1]=false;
for(int i=2; i<=N; i++) {
if(ans[i]==false)continue;
for(int j=2*i; j<=N; j+=i) {
ans[j]=false;
}
}
return ans;
}
pair<ll,ll> invGcd(ll a,ll b) {
a%=b;
if(a==0)return make_pair(b,0);
ll s=b;
ll t=a;
ll m0=0;
ll m1=1;
while(t>0) {
ll u=s/t;
s-=t*u;
m0-=m1*u;
ll tmp=s;
s=t;
t=tmp;
tmp=m0;
m0=m1;
m1=tmp;
}
if(m0<0)m0+=b/s;
return make_pair(s,m0);
}
vector<pair<ll,pair<int,int>>> kruskal(int N, vector<pair<ll,pair<int,int>>> edges) {
sort(edges.begin(), edges.end());
dsu uf(N);
vector<pair<ll,pair<int,int>>> ans;
rep(i,(int)edges.size()) {
pair<ll,pair<int,int>> edge=edges[i];
int u=edge.second.first;
int v=edge.second.second;
if(!uf.same(u,v)) {
uf.merge(u,v);
ans.push_back(edge);
}
}
return ans;
}
vector<ll> dijkstra(vector<vector<pair<ll,int>>>& G, int s) {
ll MAX=999999999999999999LL;
vector<ll> dist(G.size(),MAX);
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<pair<ll,int>>> pq;
dist[s]=0;
pq.push(make_pair(0,s));
while((int)pq.size()>0) {
pair<ll,int> p= pq.top();
pq.pop();
ll d = p.first;
ll v = p.second;
if(dist[v]<d) {
continue;
}
vector<pair<ll,int>> el=G[v];
rep(i,(int)el.size()) {
ll nd=dist[v]+el[i].first;
if(nd<dist[el[i].second]) {
dist[el[i].second]=nd;
pq.push(make_pair(dist[el[i].second],el[i].second));
}
}
}
return dist;
}
vector<int> topologicalSort(vector<vector<int>>& G) {
vector<int> result;
vector<int> inn((int)G.size(),0);
rep(i,(int)G.size()){
vector<int> es=G[i];
rep(j,(int)es.size()) {
int e=es[j];
inn[e]++;
}
}
deque<int> deq;
rep(i,(int)G.size()){
if(inn[i]==0)deq.push_back(i);
}
while((int)deq.size()>0) {
int v=deq.front();
deq.pop_front();
result.push_back(v);
vector<int> es=G[v];
rep(j,(int)es.size()) {
int e=es[j];
inn[e]--;
if(inn[e]==0){
deq.push_back(e);
}
}
}
return result;
}
int search_with_suffix_array(str s, str t) {
vi sa =suffix_array(s);
int mn=-1;
int mx=s.length();
while(mx-mn>1) {
int idx=(mx+mn)/2;
int si=sa[idx];
str ts=s.substr(si,min(t.length(),s.length()-si));
if(ts<t) {
mn=idx;
} else{
mx=idx;
}
}
if(s.substr(sa[mx],t.length())==t)return sa[mx];
return -1;
}
int main(){
int N=gi();
vector<vi> A;
rep(i,N) {
vi a=gia(N);
A.push_back(a);
}
for(int n1=0; n1<N; n1++) {
for(int n2=0; n2<N; n2++) {
for(int n3=0; n3<N; n3++) {
int n12=A[n1][n2];
int n23=A[n2][n3];
if(A[n12][n3]!=A[n1][n23]) {
cout << "No" << endl;
return 0;
}
}
}
}
int e=-1;
rep(i,N) {
bool flg=true;
rep(j,N) {
if(A[i][j]!=j || A[j][i]!=j) {
flg=false;
break;
}
}
if(flg) {
e=i;
}
}
if(e<0) {
cout << "No" << endl;
return 0;
}
rep(i,N) {
bool hasG=false;
rep(j,N) {
if(A[i][j]==e && A[j][i]==e) {
hasG=true;
break;
}
}
if(!hasG) {
cout << "No" << endl;
return 0;
}
}
cout << "Yes" << endl;
}
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