#include<bits/stdc++.h>
#define VAR(i,n) __typeof(n) i = (n)
#define loop(i,j,s) for(int i=j;i<s;i++)
#define loopback(i,j,s) for(int i=j;i>=s;i--)
#define foreach(i,c) for(VAR(i,(c).begin());i!=(c).end();i++)
#define pln( x ) cout << x << "\n"
#define ps( x ) cout << x << " "
#define entr cout << "\n"
#define pcnt(i) __builtin_popcount(i)
#define ll long long
#define pb push_back
#define mp make_pair
#define ff first
#define ss second
#define SIZE(c) (c).size()
#define ALL(c) (c).begin(), (c).end()
using namespace std;
typedef vector<int> VI;
typedef pair<int, int> PII;
typedef vector<vector<int> > VVI;
const int INFTY=20000000;
const int MAX=100100;
const int MOD=10000000;
void coutTab(int* tab,int n){
loop(i,0,n){
cout<<tab[i]<<" ";
}
cout<<"\n";
}
template<class T> void coutVec(vector<T> tab){
for(T t : tab){
cout<<t<<" ";
}
cout<<"\n";
}
//------------------------------------------
int n,m,k;
VVI G;
VVI GC;
int a[MAX];
bool visCreateGC[MAX];
int compId[MAX]; // which GC node does original vertex belong to
int c[MAX]; //color of vertex in GC from a
int idCreateGC=0;
int N;
void coutG(VVI &G){
loop(i,0,n){
ps(i);ps(": ");
coutVec(G[i]);
}
pln("");
}
void coutGC(){
loop(i,0,N){
ps(i);ps(": ");
for(int a:GC[i]){
ps(a);
}
pln("");
}
pln("");
}
void buildGC(){
idCreateGC=0;
loop(i,0,n) visCreateGC[i]=false;
idCreateGC=0;
loop(i,0,n){
if(!visCreateGC[i]){
c[idCreateGC]=a[i];
queue<int> bfs;
bfs.push(i);
visCreateGC[i]=true;
compId[i]=idCreateGC;
while(!bfs.empty()){
int v=bfs.front(); bfs.pop();
for(int u: G[v]){
if(!visCreateGC[u] && a[u]==a[v]){
visCreateGC[u]=true;
compId[u]=idCreateGC;
bfs.push(u);
}
}
}
idCreateGC++;
}
}
loop(i,0,n){
for(int j: G[i]){
if(compId[i]!=compId[j]){
GC[compId[i]].pb(compId[j]);
GC[compId[j]].pb(compId[i]);
}
}
}
loop(i,0,idCreateGC){
sort(ALL(GC[i]));
GC[i].erase(unique(ALL(GC[i])),GC[i].end());
}
}
bool solve(){
cin>>n>>m>>k;
loop(i,0,n) cin>>a[i];
G = VVI(n);
GC = VVI(n);
int u,v;
loop(i,0,m){
cin>>u>>v;
G[u-1].pb(v-1);
G[v-1].pb(u-1);
}
buildGC();
N=idCreateGC;
// comp[col] = number of GC components of that color
VI comp(k+1,0);
loop(i,0,N) comp[c[i]]++;
VI parC(N), szC(N,1);
loop(i,0,N) parC[i]=i;
auto findC=[&](int x){ while(parC[x]!=x){ parC[x]=parC[parC[x]]; x=parC[x]; } return x; };
auto uniteC=[&](int x, int y) -> bool {
x=findC(x); y=findC(y);
if(x==y) return false;
if(szC[x]<szC[y]) swap(x,y);
parC[y]=x; szC[x]+=szC[y];
return true;
};
// Peeled DSU: only peeled GC-nodes
VI parP(N), szP(N,1);
loop(i,0,N) parP[i]=i;
// colorRep[P][d] = a d-GC-node adjacent to peeled super-node P
vector<map<int,int>> colorRep(N);
auto findP=[&](int x){ while(parP[x]!=x){ parP[x]=parP[parP[x]]; x=parP[x]; } return x; };
vector<bool> peeled(k+1,false);
queue<int> q;
auto checkAdd=[&](int col){
if(comp[col]==1 && !peeled[col]) q.push(col);
};
auto uniteP=[&](int x, int y){
x=findP(x); y=findP(y);
if(x==y) return;
if(colorRep[x].size()<colorRep[y].size()) swap(x,y);
parP[y]=x; szP[x]+=szP[y];
for(auto&[col,rep]:colorRep[y]){
if(colorRep[x].count(col)){
if(uniteC(colorRep[x][col], rep)){
comp[col]--;
checkAdd(col);
}
} else {
colorRep[x][col]=rep;
}
}
colorRep[y].clear();
};
vector<VI> colorNodes(k+1);
loop(i,0,N) colorNodes[c[i]].pb(i);
loop(col,1,k+1) if(comp[col]<=1) q.push(col);
int peeledCount=0;
while(!q.empty()){
int col=q.front(); q.pop();
if(peeled[col]) continue;
peeled[col]=true;
peeledCount++;
// Step 1: unite col-nodes with peeled-color GC-neighbors in peeled DSU
for(int node:colorNodes[col])
for(int nb:GC[node])
if(peeled[c[nb]])
uniteP(node, nb);
// Step 2: register unpeeled neighbors at their peeled super-node
for(int node:colorNodes[col]){
int P=findP(node);
for(int nb:GC[node]){
int d=c[nb];
if(!peeled[d]){
if(colorRep[P].count(d)){
if(uniteC(colorRep[P][d], nb)){
comp[d]--;
checkAdd(d);
}
} else {
colorRep[P][d]=nb;
}
}
}
}
}
return peeledCount==k;
}
int main(){
ios_base::sync_with_stdio(0);
int t;
cin>>t;
while(t--) {
if(solve()) pln("TAK");
else pln("NIE");
}
}
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 | #include<bits/stdc++.h> #define VAR(i,n) __typeof(n) i = (n) #define loop(i,j,s) for(int i=j;i<s;i++) #define loopback(i,j,s) for(int i=j;i>=s;i--) #define foreach(i,c) for(VAR(i,(c).begin());i!=(c).end();i++) #define pln( x ) cout << x << "\n" #define ps( x ) cout << x << " " #define entr cout << "\n" #define pcnt(i) __builtin_popcount(i) #define ll long long #define pb push_back #define mp make_pair #define ff first #define ss second #define SIZE(c) (c).size() #define ALL(c) (c).begin(), (c).end() using namespace std; typedef vector<int> VI; typedef pair<int, int> PII; typedef vector<vector<int> > VVI; const int INFTY=20000000; const int MAX=100100; const int MOD=10000000; void coutTab(int* tab,int n){ loop(i,0,n){ cout<<tab[i]<<" "; } cout<<"\n"; } template<class T> void coutVec(vector<T> tab){ for(T t : tab){ cout<<t<<" "; } cout<<"\n"; } //------------------------------------------ int n,m,k; VVI G; VVI GC; int a[MAX]; bool visCreateGC[MAX]; int compId[MAX]; // which GC node does original vertex belong to int c[MAX]; //color of vertex in GC from a int idCreateGC=0; int N; void coutG(VVI &G){ loop(i,0,n){ ps(i);ps(": "); coutVec(G[i]); } pln(""); } void coutGC(){ loop(i,0,N){ ps(i);ps(": "); for(int a:GC[i]){ ps(a); } pln(""); } pln(""); } void buildGC(){ idCreateGC=0; loop(i,0,n) visCreateGC[i]=false; idCreateGC=0; loop(i,0,n){ if(!visCreateGC[i]){ c[idCreateGC]=a[i]; queue<int> bfs; bfs.push(i); visCreateGC[i]=true; compId[i]=idCreateGC; while(!bfs.empty()){ int v=bfs.front(); bfs.pop(); for(int u: G[v]){ if(!visCreateGC[u] && a[u]==a[v]){ visCreateGC[u]=true; compId[u]=idCreateGC; bfs.push(u); } } } idCreateGC++; } } loop(i,0,n){ for(int j: G[i]){ if(compId[i]!=compId[j]){ GC[compId[i]].pb(compId[j]); GC[compId[j]].pb(compId[i]); } } } loop(i,0,idCreateGC){ sort(ALL(GC[i])); GC[i].erase(unique(ALL(GC[i])),GC[i].end()); } } bool solve(){ cin>>n>>m>>k; loop(i,0,n) cin>>a[i]; G = VVI(n); GC = VVI(n); int u,v; loop(i,0,m){ cin>>u>>v; G[u-1].pb(v-1); G[v-1].pb(u-1); } buildGC(); N=idCreateGC; // comp[col] = number of GC components of that color VI comp(k+1,0); loop(i,0,N) comp[c[i]]++; VI parC(N), szC(N,1); loop(i,0,N) parC[i]=i; auto findC=[&](int x){ while(parC[x]!=x){ parC[x]=parC[parC[x]]; x=parC[x]; } return x; }; auto uniteC=[&](int x, int y) -> bool { x=findC(x); y=findC(y); if(x==y) return false; if(szC[x]<szC[y]) swap(x,y); parC[y]=x; szC[x]+=szC[y]; return true; }; // Peeled DSU: only peeled GC-nodes VI parP(N), szP(N,1); loop(i,0,N) parP[i]=i; // colorRep[P][d] = a d-GC-node adjacent to peeled super-node P vector<map<int,int>> colorRep(N); auto findP=[&](int x){ while(parP[x]!=x){ parP[x]=parP[parP[x]]; x=parP[x]; } return x; }; vector<bool> peeled(k+1,false); queue<int> q; auto checkAdd=[&](int col){ if(comp[col]==1 && !peeled[col]) q.push(col); }; auto uniteP=[&](int x, int y){ x=findP(x); y=findP(y); if(x==y) return; if(colorRep[x].size()<colorRep[y].size()) swap(x,y); parP[y]=x; szP[x]+=szP[y]; for(auto&[col,rep]:colorRep[y]){ if(colorRep[x].count(col)){ if(uniteC(colorRep[x][col], rep)){ comp[col]--; checkAdd(col); } } else { colorRep[x][col]=rep; } } colorRep[y].clear(); }; vector<VI> colorNodes(k+1); loop(i,0,N) colorNodes[c[i]].pb(i); loop(col,1,k+1) if(comp[col]<=1) q.push(col); int peeledCount=0; while(!q.empty()){ int col=q.front(); q.pop(); if(peeled[col]) continue; peeled[col]=true; peeledCount++; // Step 1: unite col-nodes with peeled-color GC-neighbors in peeled DSU for(int node:colorNodes[col]) for(int nb:GC[node]) if(peeled[c[nb]]) uniteP(node, nb); // Step 2: register unpeeled neighbors at their peeled super-node for(int node:colorNodes[col]){ int P=findP(node); for(int nb:GC[node]){ int d=c[nb]; if(!peeled[d]){ if(colorRep[P].count(d)){ if(uniteC(colorRep[P][d], nb)){ comp[d]--; checkAdd(d); } } else { colorRep[P][d]=nb; } } } } } return peeledCount==k; } int main(){ ios_base::sync_with_stdio(0); int t; cin>>t; while(t--) { if(solve()) pln("TAK"); else pln("NIE"); } } |
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