// CEOI 2015 - Potemkin Cycle
// Lúcio Cardoso
// Solution:
// 1. For each edge (u, v) in the graph, create two nodes in a new graph: One node representes
// the edge u->v and the other one, v->u. Now, for each triple (u, v, w) of vertices in the original graph such that
// u is connected to v, and v is connected to w, connect vertices (u->v) with (v->w) iff u is not connected with w.
// This way, a cycle in the new graph is a cycle in the original graph and there are no 3-size cycles.
// 2. Thus, if there is a cycle in the new graph, there is an answer. To find such an answer, run a dfs in the new graph
// and print the cycle formed by the first back edge found. This way, we can assure that the conditions of the statement
// are satisfied.
// Complexity: O(nm)
#include <bits/stdc++.h>
using namespace std;
const int maxn = 2e3+10;
const int maxm = 2e5+10;
typedef pair<int, int> pii;
int n, m;
int mat[maxn][maxn];
int pai[maxn], iniCycle, fimCycle;
int mark[maxm];
pii edge[maxm];
vector<pii> grafo[maxn];
vector<int> grafo2[maxm], grafo3[maxn];
void dfs(int u, int p)
{
mark[u] = 1;
for (auto v: grafo2[u])
{
if (!mark[v])
{
pai[v] = u;
dfs(v, u);
}
}
for (auto v: grafo2[u])
{
if (!iniCycle && mark[v] == 1)
{
iniCycle = v, fimCycle = u;
break;
}
}
mark[u] = 2;
}
int main(void)
{
scanf("%d %d", &n, &m);
for (int i = 1; i <= m; i++)
{
int u, v;
scanf("%d %d", &u, &v);
mat[u][v] = mat[v][u] = 1;
edge[i] = {u, v};
grafo[u].push_back({v, i});
grafo[v].push_back({u, i+m});
}
for (int i = 1; i <= m; i++)
{
int u = edge[i].first, v = edge[i].second;
for (auto pp: grafo[v])
{
int w = pp.first, e = pp.second;
if (w != u && w != v && !mat[w][u])
grafo2[i].push_back(e);
}
for (auto pp: grafo[u])
{
int w = pp.first, e = pp.second;
if (w != u && w != v && !mat[w][v])
grafo2[i+m].push_back(e);
}
}
for (int i = 1; i <= 2*m; i++)
{
if (!mark[i])
dfs(i, 0);
if (iniCycle) break;
}
if (!iniCycle)
{
printf("no\n");
return 0;
}
int at = fimCycle;
int aux = 0;
vector<int> ciclo;
while (true)
{
if (at > m)
ciclo.push_back(edge[at-m].second);
else
ciclo.push_back(edge[at].first);
if (at == iniCycle) break;
at = pai[at];
}
for (auto c: ciclo)
printf("%d ", c);
printf("\n");
}
Compilation message
indcyc.cpp: In function 'int main()':
indcyc.cpp:114:6: warning: unused variable 'aux' [-Wunused-variable]
114 | int aux = 0;
| ^~~
indcyc.cpp:63:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
63 | scanf("%d %d", &n, &m);
| ~~~~~^~~~~~~~~~~~~~~~~
indcyc.cpp:68:8: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
68 | scanf("%d %d", &u, &v);
| ~~~~~^~~~~~~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
5120 KB |
Output is correct |
| 2 |
Correct |
4 ms |
5120 KB |
Output is correct |
| 3 |
Correct |
4 ms |
5120 KB |
Output is correct |
| 4 |
Correct |
4 ms |
5120 KB |
Output is correct |
| 5 |
Correct |
4 ms |
5120 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
4 ms |
5120 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
4 ms |
5248 KB |
Output is correct |
| 2 |
Correct |
4 ms |
5120 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
5 ms |
5760 KB |
Repeated vertex |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
6 ms |
5888 KB |
Output is correct |
| 2 |
Correct |
7 ms |
5888 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
8 ms |
7040 KB |
Output is correct |
| 2 |
Correct |
8 ms |
7040 KB |
Output is correct |
| 3 |
Correct |
14 ms |
8960 KB |
Output is correct |
| 4 |
Correct |
16 ms |
8960 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
13 ms |
8192 KB |
Output is correct |
| 2 |
Correct |
12 ms |
8320 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
139 ms |
29560 KB |
Output is correct |
| 2 |
Correct |
42 ms |
16632 KB |
Output is correct |
| 3 |
Correct |
151 ms |
29564 KB |
Output is correct |
| 4 |
Correct |
42 ms |
16632 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
156 ms |
57848 KB |
Output is correct |
| 2 |
Correct |
183 ms |
61944 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
262 ms |
10744 KB |
Output is correct |
| 2 |
Correct |
257 ms |
10976 KB |
Output is correct |
| 3 |
Correct |
325 ms |
97664 KB |
Output is correct |
| 4 |
Correct |
352 ms |
97656 KB |
Output is correct |
