#include <bits/stdc++.h>
using namespace std;
struct dfs_node {
int node;
int parent;
bool visited;
};
struct city_data {
int parent;
bool visited = false;
int dfs_in;
int dfs_out;
int depth;
};
struct edge {
int higher;
int lower;
};
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int t;
int n, m, k;
int u, v;
bool valid = true;
vector<int> colors_in_city;
cin >> t;
for(int i=0; i<t; i++) {
valid = true;
cin >> n >> m >> k;
vector<vector<int>> roads;
roads.resize(n);
colors_in_city.resize(n);
vector<city_data> c_data;
c_data.resize(n);
vector<bool> used_colors;
used_colors.assign(k, false);
for(int j=0; j<n; j++) {
cin >> colors_in_city[j];
colors_in_city[j]--;
}
for(int j=0; j<m; j++) {
cin >> u >> v;
roads[u-1].push_back(v-1);
roads[v-1].push_back(u-1);
}
int root;
vector<vector<int>> colors_used_ordered;
vector<int> highest_ancestor_for_color;
highest_ancestor_for_color.resize(k);
for(int j=0; j<n; j++) {
if(c_data[j].visited) {
continue;
}
root = j;
c_data[root].visited = true;
map<int, vector<int>> dfs_colors;
vector<edge> edges;
vector<int> nodes_in_current_tree;
//dfs from root
int dfs_order = 0;
vector<dfs_node> dfs_stack;
dfs_node dnnn;
dnnn.node = root;
dnnn.parent = root;
dnnn.visited = false;
dfs_stack.push_back(dnnn);
set<int> all_colors_in_current_subtree;
while(dfs_stack.size() > 0) {
dfs_node current = dfs_stack.back();
dfs_stack.pop_back();
if(!current.visited) {
nodes_in_current_tree.push_back(current.node);
int current_color = colors_in_city[current.node];
all_colors_in_current_subtree.insert(current_color);
if(dfs_colors.count(current_color)) {
dfs_colors[current_color].push_back(current.node);
} else {
vector<int> colors_list;
colors_list.push_back(current.node);
dfs_colors.emplace(current_color, colors_list);
}
c_data[current.node].dfs_in = dfs_order;
dfs_order++;
c_data[current.node].parent = current.parent;
c_data[current.node].visited = true;
c_data[current.node].depth = current.node == root ? 0 : c_data[current.parent].depth + 1;
dfs_node dnn;
dnn.node = current.node;
dnn.parent = current.parent;
dnn.visited = true;
dfs_stack.push_back(dnn);
for(int l=0; l<roads[current.node].size(); l++) {
int connection = roads[current.node][l];
if(connection != current.parent) {
dfs_node dn;
dn.node = connection;
dn.parent = current.node;
dn.visited = false;
dfs_stack.push_back(dn);
if(colors_in_city[current.node] != colors_in_city[connection]) {
edge ed;
ed.higher = current.node;
ed.lower = connection;
edges.push_back(ed);
}
}
}
} else {
c_data[current.node].dfs_out = dfs_order;
dfs_order++;
}
}
// check if colors in subtree were not used in other subtrees
for(auto itr : all_colors_in_current_subtree) {
if(used_colors[itr]) {
valid = false;
break;
}
used_colors[itr] = true;
}
if(!valid) {
break;
}
// find highest ancestor for each color
for(map<int,vector<int>>::iterator iter = dfs_colors.begin(); iter != dfs_colors.end(); ++iter) {
int col = iter->first;
vector<int> col_l = iter->second;
int first = col_l.front();
int last = col_l.back();
int highest_ancestor;
int depth_first = c_data[first].depth;
int depth_last = c_data[last].depth;
if(depth_first > depth_last) {
while(depth_first > depth_last) {
first = c_data[first].parent;
depth_first = c_data[first].depth;
}
} else if(depth_last > depth_first) {
while(depth_last > depth_first) {
last = c_data[last].parent;
depth_last = c_data[last].depth;
}
}
while(first != last) {
first = c_data[first].parent;
last = c_data[last].parent;
}
highest_ancestor = first;
highest_ancestor_for_color[col] = highest_ancestor;
}
// for each road in current tree add a dependency direction
vector<set<int>> dependencies;
dependencies.resize(k);
for(int l=0; l<edges.size(); l++) {
edge e = edges[l];
if(highest_ancestor_for_color[colors_in_city[e.lower]] == e.lower) {
dependencies[colors_in_city[e.higher]].insert(colors_in_city[e.lower]);
} else {
dependencies[colors_in_city[e.lower]].insert(colors_in_city[e.higher]);
}
}
// check if dependencies without cycle
vector<int> indegrees;
indegrees.assign(k, 0);
int ordered = 0;
for(auto ii: all_colors_in_current_subtree) {
for(auto itr : dependencies[ii]) {
indegrees[itr]++;
}
}
queue<int> que;
for(auto iii: all_colors_in_current_subtree) {
if(indegrees[iii] == 0) {
que.push(iii);
}
}
while(que.size() > 0) {
int ff = que.front();
que.pop();
ordered++;
for(auto itr : dependencies[ff]) {
indegrees[itr]--;
if(indegrees[itr] == 0) {
que.push(itr);
}
}
}
valid = ordered == all_colors_in_current_subtree.size();
if(!valid) {
break;
}
}
if(valid) {
cout<<"TAK\n";
} else {
cout<<"NIE\n";
}
}
return 0;
}
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 | #include <bits/stdc++.h> using namespace std; struct dfs_node { int node; int parent; bool visited; }; struct city_data { int parent; bool visited = false; int dfs_in; int dfs_out; int depth; }; struct edge { int higher; int lower; }; int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); int t; int n, m, k; int u, v; bool valid = true; vector<int> colors_in_city; cin >> t; for(int i=0; i<t; i++) { valid = true; cin >> n >> m >> k; vector<vector<int>> roads; roads.resize(n); colors_in_city.resize(n); vector<city_data> c_data; c_data.resize(n); vector<bool> used_colors; used_colors.assign(k, false); for(int j=0; j<n; j++) { cin >> colors_in_city[j]; colors_in_city[j]--; } for(int j=0; j<m; j++) { cin >> u >> v; roads[u-1].push_back(v-1); roads[v-1].push_back(u-1); } int root; vector<vector<int>> colors_used_ordered; vector<int> highest_ancestor_for_color; highest_ancestor_for_color.resize(k); for(int j=0; j<n; j++) { if(c_data[j].visited) { continue; } root = j; c_data[root].visited = true; map<int, vector<int>> dfs_colors; vector<edge> edges; vector<int> nodes_in_current_tree; //dfs from root int dfs_order = 0; vector<dfs_node> dfs_stack; dfs_node dnnn; dnnn.node = root; dnnn.parent = root; dnnn.visited = false; dfs_stack.push_back(dnnn); set<int> all_colors_in_current_subtree; while(dfs_stack.size() > 0) { dfs_node current = dfs_stack.back(); dfs_stack.pop_back(); if(!current.visited) { nodes_in_current_tree.push_back(current.node); int current_color = colors_in_city[current.node]; all_colors_in_current_subtree.insert(current_color); if(dfs_colors.count(current_color)) { dfs_colors[current_color].push_back(current.node); } else { vector<int> colors_list; colors_list.push_back(current.node); dfs_colors.emplace(current_color, colors_list); } c_data[current.node].dfs_in = dfs_order; dfs_order++; c_data[current.node].parent = current.parent; c_data[current.node].visited = true; c_data[current.node].depth = current.node == root ? 0 : c_data[current.parent].depth + 1; dfs_node dnn; dnn.node = current.node; dnn.parent = current.parent; dnn.visited = true; dfs_stack.push_back(dnn); for(int l=0; l<roads[current.node].size(); l++) { int connection = roads[current.node][l]; if(connection != current.parent) { dfs_node dn; dn.node = connection; dn.parent = current.node; dn.visited = false; dfs_stack.push_back(dn); if(colors_in_city[current.node] != colors_in_city[connection]) { edge ed; ed.higher = current.node; ed.lower = connection; edges.push_back(ed); } } } } else { c_data[current.node].dfs_out = dfs_order; dfs_order++; } } // check if colors in subtree were not used in other subtrees for(auto itr : all_colors_in_current_subtree) { if(used_colors[itr]) { valid = false; break; } used_colors[itr] = true; } if(!valid) { break; } // find highest ancestor for each color for(map<int,vector<int>>::iterator iter = dfs_colors.begin(); iter != dfs_colors.end(); ++iter) { int col = iter->first; vector<int> col_l = iter->second; int first = col_l.front(); int last = col_l.back(); int highest_ancestor; int depth_first = c_data[first].depth; int depth_last = c_data[last].depth; if(depth_first > depth_last) { while(depth_first > depth_last) { first = c_data[first].parent; depth_first = c_data[first].depth; } } else if(depth_last > depth_first) { while(depth_last > depth_first) { last = c_data[last].parent; depth_last = c_data[last].depth; } } while(first != last) { first = c_data[first].parent; last = c_data[last].parent; } highest_ancestor = first; highest_ancestor_for_color[col] = highest_ancestor; } // for each road in current tree add a dependency direction vector<set<int>> dependencies; dependencies.resize(k); for(int l=0; l<edges.size(); l++) { edge e = edges[l]; if(highest_ancestor_for_color[colors_in_city[e.lower]] == e.lower) { dependencies[colors_in_city[e.higher]].insert(colors_in_city[e.lower]); } else { dependencies[colors_in_city[e.lower]].insert(colors_in_city[e.higher]); } } // check if dependencies without cycle vector<int> indegrees; indegrees.assign(k, 0); int ordered = 0; for(auto ii: all_colors_in_current_subtree) { for(auto itr : dependencies[ii]) { indegrees[itr]++; } } queue<int> que; for(auto iii: all_colors_in_current_subtree) { if(indegrees[iii] == 0) { que.push(iii); } } while(que.size() > 0) { int ff = que.front(); que.pop(); ordered++; for(auto itr : dependencies[ff]) { indegrees[itr]--; if(indegrees[itr] == 0) { que.push(itr); } } } valid = ordered == all_colors_in_current_subtree.size(); if(!valid) { break; } } if(valid) { cout<<"TAK\n"; } else { cout<<"NIE\n"; } } return 0; } |
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