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kattis_reversingroads.cpp
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kattis_reversingroads.cpp
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/**Kattis - reversingroads
* We first define valid(adjlist) = true if adjlist has only 1 SCC and false otherwise. We check if
* valid(initial graph) then exit early if this is the case, else we complete search by testing e
* other graphs (flip each edge once). This is alright since e is small (e <= 50^2).
*
* Time: O(E^2), Space: O(E + V)
*/
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,fma")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<int> vi;
#define MAX_N 60
int t, n, e, u, v, dfsNumberCounter, numSCC;
vi dfs_num, dfs_low, visited;
stack<int> st;
vector<vector<int>> adjlist;
void tarjanSCC(int u) {
dfs_low[u] = dfs_num[u] = dfsNumberCounter;
dfsNumberCounter++;
st.push(u);
visited[u] = 1;
for (auto v : adjlist[u]) {
if (dfs_num[v] == -1) {
tarjanSCC(v);
}
if (visited[v]) dfs_low[u] = min(dfs_low[u], dfs_low[v]);
}
if (dfs_low[u] == dfs_num[u]) { // u is the root of an SCC
while (true) {
v = st.top();
st.pop();
visited[v] = 0;
if (v == u) break;
}
numSCC++;
}
}
bool only_one_scc(vector<vector<int>> &adjlist) {
dfs_num.assign(n, -1);
dfs_low.assign(n, 0);
visited.assign(n, 0);
dfsNumberCounter = numSCC = 0;
while (!st.empty()) st.pop();
for (int i = 0; i < n; i++) {
if (dfs_num[i] == -1) tarjanSCC(i);
}
return numSCC == 1;
}
int main() {
int tc = 0;
while (cin >> n >> e) {
tc++;
adjlist.assign(n, vi());
vector<pair<int, int>> edges;
for (int i = 0; i < e; i++) {
cin >> u >> v;
adjlist[u].push_back(v);
edges.push_back(make_pair(u, v));
}
if (only_one_scc(adjlist)) {
cout << "Case " << tc << ": valid" << endl;
continue;
}
bool can_be_valid = false;
for (int i = 0; i < e; i++) {
adjlist.clear();
adjlist.assign(n, vi());
for (int j = 0; j < e; j++) {
if (i == j) {
adjlist[edges[j].second].push_back(edges[j].first);
} else {
adjlist[edges[j].first].push_back(edges[j].second);
}
}
if (only_one_scc(adjlist)) {
can_be_valid = true;
cout << "Case " << tc << ": " << edges[i].first << " " << edges[i].second << endl;
break;
}
}
if (!can_be_valid) {
cout << "Case " << tc << ": invalid" << endl;
}
}
return 0;
}