Connexity on undirected graphs
Statement
Goal
Given an undirected graph with N vertices, and M lines describing the edges, output whether the defined graph is connected.Vertices are labelled from
A graph is connected if from any vertex, one can reach any other vertex by following the edges.
Input
Line 1: N the number of vertices
Line 2: M the number of edges
Following lines:a b the label of two vertices that are linked by an edge, separated by a space.
Line 2: M the number of edges
Following lines:
Output
Constraints
1 <= N <= 30
0 <= M <= 1000
For any edge,a !=b
0 <= M <= 1000
For any edge,
Example
Input
7 6 0 1 1 2 1 3 0 4 4 5 4 6
Output
True
Game modes
Fastest
Test cases
Binary tree Test
Input
7
6
0 1
1 2
1 3
0 4
4 5
4 6
Output
True
Binary tree Validator
Input
15
14
0 1
1 2
1 3
0 4
4 5
4 6
2 7
2 8
3 9
3 10
5 11
5 12
6 13
6 14
Output
True
Two loops Test
Input
17
17
0 1
1 2
2 3
3 4
4 5
5 6
6 7
7 8
8 9
9 10
10 0
11 12
12 13
13 14
14 15
15 16
16 11
Output
False
Two loops Validator
Input
10
10
0 1
1 2
2 3
3 4
4 0
5 6
6 7
7 8
8 9
9 5
Output
False
One vertex Test
Input
1
0
Output
True
One vertex Validator
Input
1
0
Output
True
Random graph Test
Input
20
77
3 0
4 0
6 0
7 0
8 0
10 0
12 0
13 0
14 0
18 0
5 1
6 1
7 1
10 1
11 1
12 1
15 1
17 1
19 1
3 2
4 2
5 2
8 2
9 2
10 2
11 2
18 2
4 3
10 3
11 3
16 3
6 4
7 4
11 4
13 4
14 4
15 4
16 4
17 4
18 4
9 5
13 5
15 5
9 6
10 6
11 6
13 6
17 6
19 6
9 7
14 7
17 7
9 8
12 8
15 8
16 8
11 9
14 9
18 9
11 10
12 10
13 10
15 10
19 10
12 11
13 11
14 12
15 12
16 12
18 12
19 12
16 13
19 13
15 14
16 14
18 14
18 17
Output
True
Random graph Validator
Input
20
23
10 0
11 0
16 0
2 1
5 1
9 3
15 3
16 3
6 4
10 4
15 4
19 4
6 5
19 5
10 8
14 10
19 10
14 11
13 12
17 12
18 12
16 14
7 18
Output
False
Big complete graph Test
Input
30
870
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
0 10
0 11
0 12
0 13
0 14
0 15
0 16
0 17
0 18
0 19
0 20
0 21
0 22
0 23
0 24
0 25
0 26
0 27
0 28
0 29
1 0
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
1 10
1 11
1 12
1 13
1 14
1 15
1 16
1 17
1 18
1 19
1 20
1 21
1 22
1 23
1 24
1 25
1 26
1 27
1 28
1 29
2 0
2 1
2 3
2 4
2 5
2 6
2 7
2 8
2 9
2 10
2 11
2 12
2 13
2 14
2 15
2 16
2 17
2 18
2 19
2 20
2 21
2 22
2 23
2 24
2 25
2 26
2 27
2 28
2 29
3 0
3 1
3 2
3 4
3 5
3 6
3 7
3 8
3 9
3 10
3 11
3 12
3 13
3 14
3 15
3 16
3 17
3 18
3 19
3 20
3 21
3 22
3 23
3 24
3 25
3 26
3 27
3 28
3 29
4 0
4 1
4 2
4 3
4 5
4 6
4 7
4 8
4 9
4 10
4 11
4 12
4 13
4 14
4 15
4 16
4 17
4 18
4 19
4 20
4 21
4 22
4 23
4 24
4 25
4 26
4 27
4 28
4 29
5 0
5 1
5 2
5 3
5 4
5 6
5 7
5 8
5 9
5 10
5 11
5 12
5 13
5 14
5 15
5 16
5 17
5 18
5 19
5 20
5 21
5 22
5 23
5 24
5 25
5 26
5 27
5 28
5 29
6 0
6 1
6 2
6 3
6 4
6 5
6 7
6 8
6 9
6 10
6 11
6 12
6 13
6 14
6 15
6 16
6 17
6 18
6 19
6 20
6 21
6 22
6 23
6 24
6 25
6 26
6 27
6 28
6 29
7 0
7 1
7 2
7 3
7 4
7 5
7 6
7 8
7 9
7 10
7 11
7 12
7 13
7 14
7 15
7 16
7 17
7 18
7 19
7 20
7 21
7 22
7 23
7 24
7 25
7 26
7 27
7 28
7 29
8 0
8 1
8 2
8 3
8 4
8 5
8 6
8 7
8 9
8 10
8 11
8 12
8 13
8 14
8 15
8 16
8 17
8 18
8 19
8 20
8 21
8 22
8 23
8 24
8 25
8 26
8 27
8 28
8 29
9 0
9 1
9 2
9 3
9 4
9 5
9 6
9 7
9 8
9 10
9 11
9 12
9 13
9 14
9 15
9 16
9 17
9 18
9 19
9 20
9 21
9 22
9 23
9 24
9 25
9 26
9 27
9 28
9 29
10 0
10 1
10 2
10 3
10 4
10 5
10 6
10 7
10 8
10 9
10 11
10 12
10 13
10 14
10 15
10 16
10 17
10 18
10 19
10 20
10 21
10 22
10 23
10 24
10 25
10 26
10 27
10 28
10 29
11 0
11 1
11 2
11 3
11 4
11 5
11 6
11 7
11 8
11 9
11 10
11 12
11 13
11 14
11 15
11 16
11 17
11 18
11 19
11 20
11 21
11 22
11 23
11 24
11 25
11 26
11 27
11 28
11 29
12 0
12 1
12 2
12 3
12 4
12 5
12 6
12 7
12 8
12 9
12 10
12 11
12 13
12 14
12 15
12 16
12 17
12 18
12 19
12 20
12 21
12 22
12 23
12 24
12 25
12 26
12 27
12 28
12 29
13 0
13 1
13 2
13 3
13 4
13 5
13 6
13 7
13 8
13 9
13 10
13 11
13 12
13 14
13 15
13 16
13 17
13 18
13 19
13 20
13 21
13 22
13 23
13 24
13 25
13 26
13 27
13 28
13 29
14 0
14 1
14 2
14 3
14 4
14 5
14 6
14 7
14 8
14 9
14 10
14 11
14 12
14 13
14 15
14 16
14 17
14 18
14 19
14 20
14 21
14 22
14 23
14 24
14 25
14 26
14 27
14 28
14 29
15 0
15 1
15 2
15 3
15 4
15 5
15 6
15 7
15 8
15 9
15 10
15 11
15 12
15 13
15 14
15 16
15 17
15 18
15 19
15 20
15 21
15 22
15 23
15 24
15 25
15 26
15 27
15 28
15 29
16 0
16 1
16 2
16 3
16 4
16 5
16 6
16 7
16 8
16 9
16 10
16 11
16 12
16 13
16 14
16 15
16 17
16 18
16 19
16 20
16 21
16 22
16 23
16 24
16 25
16 26
16 27
16 28
16 29
17 0
17 1
17 2
17 3
17 4
17 5
17 6
17 7
17 8
17 9
17 10
17 11
17 12
17 13
17 14
17 15
17 16
17 18
17 19
17 20
17 21
17 22
17 23
17 24
17 25
17 26
17 27
17 28
17 29
18 0
18 1
18 2
18 3
18 4
18 5
18 6
18 7
18 8
18 9
18 10
18 11
18 12
18 13
18 14
18 15
18 16
18 17
18 19
18 20
18 21
18 22
18 23
18 24
18 25
18 26
18 27
18 28
18 29
19 0
19 1
19 2
19 3
19 4
19 5
19 6
19 7
19 8
19 9
19 10
19 11
19 12
19 13
19 14
19 15
19 16
19 17
19 18
19 20
19 21
19 22
19 23
19 24
19 25
19 26
19 27
19 28
19 29
20 0
20 1
20 2
20 3
20 4
20 5
20 6
20 7
20 8
20 9
20 10
20 11
20 12
20 13
20 14
20 15
20 16
20 17
20 18
20 19
20 21
20 22
20 23
20 24
20 25
20 26
20 27
20 28
20 29
21 0
21 1
21 2
21 3
21 4
21 5
21 6
21 7
21 8
21 9
21 10
21 11
21 12
21 13
21 14
21 15
21 16
21 17
21 18
21 19
21 20
21 22
21 23
21 24
21 25
21 26
21 27
21 28
21 29
22 0
22 1
22 2
22 3
22 4
22 5
22 6
22 7
22 8
22 9
22 10
22 11
22 12
22 13
22 14
22 15
22 16
22 17
22 18
22 19
22 20
22 21
22 23
22 24
22 25
22 26
22 27
22 28
22 29
23 0
23 1
23 2
23 3
23 4
23 5
23 6
23 7
23 8
23 9
23 10
23 11
23 12
23 13
23 14
23 15
23 16
23 17
23 18
23 19
23 20
23 21
23 22
23 24
23 25
23 26
23 27
23 28
23 29
24 0
24 1
24 2
24 3
24 4
24 5
24 6
24 7
24 8
24 9
24 10
24 11
24 12
24 13
24 14
24 15
24 16
24 17
24 18
24 19
24 20
24 21
24 22
24 23
24 25
24 26
24 27
24 28
24 29
25 0
25 1
25 2
25 3
25 4
25 5
25 6
25 7
25 8
25 9
25 10
25 11
25 12
25 13
25 14
25 15
25 16
25 17
25 18
25 19
25 20
25 21
25 22
25 23
25 24
25 26
25 27
25 28
25 29
26 0
26 1
26 2
26 3
26 4
26 5
26 6
26 7
26 8
26 9
26 10
26 11
26 12
26 13
26 14
26 15
26 16
26 17
26 18
26 19
26 20
26 21
26 22
26 23
26 24
26 25
26 27
26 28
26 29
27 0
27 1
27 2
27 3
27 4
27 5
27 6
27 7
27 8
27 9
27 10
27 11
27 12
27 13
27 14
27 15
27 16
27 17
27 18
27 19
27 20
27 21
27 22
27 23
27 24
27 25
27 26
27 28
27 29
28 0
28 1
28 2
28 3
28 4
28 5
28 6
28 7
28 8
28 9
28 10
28 11
28 12
28 13
28 14
28 15
28 16
28 17
28 18
28 19
28 20
28 21
28 22
28 23
28 24
28 25
28 26
28 27
28 29
29 0
29 1
29 2
29 3
29 4
29 5
29 6
29 7
29 8
29 9
29 10
29 11
29 12
29 13
29 14
29 15
29 16
29 17
29 18
29 19
29 20
29 21
29 22
29 23
29 24
29 25
29 26
29 27
29 28
Output
True
Big complete graph Validator
Input
29
812
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
0 10
0 11
0 12
0 13
0 14
0 15
0 16
0 17
0 18
0 19
0 20
0 21
0 22
0 23
0 24
0 25
0 26
0 27
0 28
1 0
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
1 10
1 11
1 12
1 13
1 14
1 15
1 16
1 17
1 18
1 19
1 20
1 21
1 22
1 23
1 24
1 25
1 26
1 27
1 28
2 0
2 1
2 3
2 4
2 5
2 6
2 7
2 8
2 9
2 10
2 11
2 12
2 13
2 14
2 15
2 16
2 17
2 18
2 19
2 20
2 21
2 22
2 23
2 24
2 25
2 26
2 27
2 28
3 0
3 1
3 2
3 4
3 5
3 6
3 7
3 8
3 9
3 10
3 11
3 12
3 13
3 14
3 15
3 16
3 17
3 18
3 19
3 20
3 21
3 22
3 23
3 24
3 25
3 26
3 27
3 28
4 0
4 1
4 2
4 3
4 5
4 6
4 7
4 8
4 9
4 10
4 11
4 12
4 13
4 14
4 15
4 16
4 17
4 18
4 19
4 20
4 21
4 22
4 23
4 24
4 25
4 26
4 27
4 28
5 0
5 1
5 2
5 3
5 4
5 6
5 7
5 8
5 9
5 10
5 11
5 12
5 13
5 14
5 15
5 16
5 17
5 18
5 19
5 20
5 21
5 22
5 23
5 24
5 25
5 26
5 27
5 28
6 0
6 1
6 2
6 3
6 4
6 5
6 7
6 8
6 9
6 10
6 11
6 12
6 13
6 14
6 15
6 16
6 17
6 18
6 19
6 20
6 21
6 22
6 23
6 24
6 25
6 26
6 27
6 28
7 0
7 1
7 2
7 3
7 4
7 5
7 6
7 8
7 9
7 10
7 11
7 12
7 13
7 14
7 15
7 16
7 17
7 18
7 19
7 20
7 21
7 22
7 23
7 24
7 25
7 26
7 27
7 28
8 0
8 1
8 2
8 3
8 4
8 5
8 6
8 7
8 9
8 10
8 11
8 12
8 13
8 14
8 15
8 16
8 17
8 18
8 19
8 20
8 21
8 22
8 23
8 24
8 25
8 26
8 27
8 28
9 0
9 1
9 2
9 3
9 4
9 5
9 6
9 7
9 8
9 10
9 11
9 12
9 13
9 14
9 15
9 16
9 17
9 18
9 19
9 20
9 21
9 22
9 23
9 24
9 25
9 26
9 27
9 28
10 0
10 1
10 2
10 3
10 4
10 5
10 6
10 7
10 8
10 9
10 11
10 12
10 13
10 14
10 15
10 16
10 17
10 18
10 19
10 20
10 21
10 22
10 23
10 24
10 25
10 26
10 27
10 28
11 0
11 1
11 2
11 3
11 4
11 5
11 6
11 7
11 8
11 9
11 10
11 12
11 13
11 14
11 15
11 16
11 17
11 18
11 19
11 20
11 21
11 22
11 23
11 24
11 25
11 26
11 27
11 28
12 0
12 1
12 2
12 3
12 4
12 5
12 6
12 7
12 8
12 9
12 10
12 11
12 13
12 14
12 15
12 16
12 17
12 18
12 19
12 20
12 21
12 22
12 23
12 24
12 25
12 26
12 27
12 28
13 0
13 1
13 2
13 3
13 4
13 5
13 6
13 7
13 8
13 9
13 10
13 11
13 12
13 14
13 15
13 16
13 17
13 18
13 19
13 20
13 21
13 22
13 23
13 24
13 25
13 26
13 27
13 28
14 0
14 1
14 2
14 3
14 4
14 5
14 6
14 7
14 8
14 9
14 10
14 11
14 12
14 13
14 15
14 16
14 17
14 18
14 19
14 20
14 21
14 22
14 23
14 24
14 25
14 26
14 27
14 28
15 0
15 1
15 2
15 3
15 4
15 5
15 6
15 7
15 8
15 9
15 10
15 11
15 12
15 13
15 14
15 16
15 17
15 18
15 19
15 20
15 21
15 22
15 23
15 24
15 25
15 26
15 27
15 28
16 0
16 1
16 2
16 3
16 4
16 5
16 6
16 7
16 8
16 9
16 10
16 11
16 12
16 13
16 14
16 15
16 17
16 18
16 19
16 20
16 21
16 22
16 23
16 24
16 25
16 26
16 27
16 28
17 0
17 1
17 2
17 3
17 4
17 5
17 6
17 7
17 8
17 9
17 10
17 11
17 12
17 13
17 14
17 15
17 16
17 18
17 19
17 20
17 21
17 22
17 23
17 24
17 25
17 26
17 27
17 28
18 0
18 1
18 2
18 3
18 4
18 5
18 6
18 7
18 8
18 9
18 10
18 11
18 12
18 13
18 14
18 15
18 16
18 17
18 19
18 20
18 21
18 22
18 23
18 24
18 25
18 26
18 27
18 28
19 0
19 1
19 2
19 3
19 4
19 5
19 6
19 7
19 8
19 9
19 10
19 11
19 12
19 13
19 14
19 15
19 16
19 17
19 18
19 20
19 21
19 22
19 23
19 24
19 25
19 26
19 27
19 28
20 0
20 1
20 2
20 3
20 4
20 5
20 6
20 7
20 8
20 9
20 10
20 11
20 12
20 13
20 14
20 15
20 16
20 17
20 18
20 19
20 21
20 22
20 23
20 24
20 25
20 26
20 27
20 28
21 0
21 1
21 2
21 3
21 4
21 5
21 6
21 7
21 8
21 9
21 10
21 11
21 12
21 13
21 14
21 15
21 16
21 17
21 18
21 19
21 20
21 22
21 23
21 24
21 25
21 26
21 27
21 28
22 0
22 1
22 2
22 3
22 4
22 5
22 6
22 7
22 8
22 9
22 10
22 11
22 12
22 13
22 14
22 15
22 16
22 17
22 18
22 19
22 20
22 21
22 23
22 24
22 25
22 26
22 27
22 28
23 0
23 1
23 2
23 3
23 4
23 5
23 6
23 7
23 8
23 9
23 10
23 11
23 12
23 13
23 14
23 15
23 16
23 17
23 18
23 19
23 20
23 21
23 22
23 24
23 25
23 26
23 27
23 28
24 0
24 1
24 2
24 3
24 4
24 5
24 6
24 7
24 8
24 9
24 10
24 11
24 12
24 13
24 14
24 15
24 16
24 17
24 18
24 19
24 20
24 21
24 22
24 23
24 25
24 26
24 27
24 28
25 0
25 1
25 2
25 3
25 4
25 5
25 6
25 7
25 8
25 9
25 10
25 11
25 12
25 13
25 14
25 15
25 16
25 17
25 18
25 19
25 20
25 21
25 22
25 23
25 24
25 26
25 27
25 28
26 0
26 1
26 2
26 3
26 4
26 5
26 6
26 7
26 8
26 9
26 10
26 11
26 12
26 13
26 14
26 15
26 16
26 17
26 18
26 19
26 20
26 21
26 22
26 23
26 24
26 25
26 27
26 28
27 0
27 1
27 2
27 3
27 4
27 5
27 6
27 7
27 8
27 9
27 10
27 11
27 12
27 13
27 14
27 15
27 16
27 17
27 18
27 19
27 20
27 21
27 22
27 23
27 24
27 25
27 26
27 28
28 0
28 1
28 2
28 3
28 4
28 5
28 6
28 7
28 8
28 9
28 10
28 11
28 12
28 13
28 14
28 15
28 16
28 17
28 18
28 19
28 20
28 21
28 22
28 23
28 24
28 25
28 26
28 27
Output
True
One vertex missing Test
Input
11
11
0 1
1 5
5 6
4 3
3 1
8 7
5 9
9 7
9 3
9 1
2 7
Output
False
One vertex missing Validator
Input
12
11
1 7
7 4
4 8
4 1
0 9
10 2
2 5
10 5
10 3
6 7
6 3
Output
False
Solution language
Solution
Stub generator input