Problem:


Bridges

Find bridges of an undirected graph G(V, E).

A bridge (also known as a cut-edge) is an edge whose deletion increase the number of connected components.

Input

|V| |E|
s0 t0
s1 t1
:
s|E|-1 t|E|-1

, where |V| is the number of nodes and |E| is the number of edges in the graph. The graph nodes are named with the numbers 0, 1,..., |V|-1 respectively.

si and ti represent source and target nodes of i-th edge (undirected).

Output

A list of bridges of the graph ordered by name. For each bridge, names of its end-ponints, source and target (source < target), should be printed separated by a space. The sources should be printed ascending order, then the target should also be printed ascending order for the same source.

Constraints

1 ≤ |V| ≤ 100,000

0 ≤ |E| ≤ 100,000

The graph is connected

There are no parallel edges

There are no self-loops

Sample Input 1

4 4
0 1
0 2
1 2
2 3

Sample Output 1

2 3

Sample Input 2

5 4
0 1
1 2
2 3
3 4

Sample Output 2

0 1
1 2
2 3
3 4



Sample input:
4 4
0 1
0 2
1 2
2 3


Sample output:
2 3

Submission status: Runtime Error

Solution code:
#!/usr/bin/env python
# -*- coding: utf-8 -*-

"""
input:
5 4
0 1
1 2
2 3
3 4

output:
0 1
1 2
2 3
3 4
"""

import sys
# sys.setrecursionlimit(int(3e6))


def generate_adj_table(_v_info):
    for v_detail in _v_info:
        v_from, v_to = map(int, v_detail)
        init_adj_table[v_from].append(v_to)
        # undirected graph
        init_adj_table[v_to].append(v_from)
    return init_adj_table


def graph_dfs(u, visited, parent, low, disc):
    global Time
    # Count of children in current node
    children = 0

    # Mark the current node as visited and print it
    visited[u] = True

    # Initialize discovery time and low value
    disc[u] = Time
    low[u] = Time
    Time += 1

    # Recur for all the vertices adjacent to this vertex
    for v in adj_table[u]:
        # If v is not visited yet, then make it a child of u
        # in DFS tree and recur for it
        if not visited[v]:
            parent[v] = u
            children += 1
            graph_dfs(v, visited, parent, low, disc)

            # Check if the subtree rooted with v has a connection to
            # one of the ancestors of u
            low[u] = min(low[u], low[v])

            ''' If the lowest vertex reachable from subtree
            under v is below u in DFS tree, then u-v is
            a bridge'''
            if low[v] > disc[u]:
                ans.append(sorted([u, v]))
        elif v != parent[u]:  # Update low value of u for parent function calls.
            low[u] = min(low[u], disc[v])

    return None


def bridge():
    visited = [False] * vertices
    disc = [float("Inf")] * vertices
    low = [float("Inf")] * vertices
    parent = [-1] * vertices

    for v in range(vertices):
        if not visited[v]:
            graph_dfs(v, visited, parent, low, disc)

    return ans


if __name__ == '__main__':
    _input = sys.stdin.readlines()
    vertices, edges = map(int, _input[0].split())
    v_info = map(lambda x: x.split(), _input[1:])
    Time = 0
    ans = []

    init_adj_table = tuple([] for _ in range(vertices))
    adj_table = generate_adj_table(v_info)
    res = bridge()
    res.sort()
    for ele in res:
        print(*ele)

Submission status: Runtime Error

Solution code:
#!/usr/bin/env python
# -*- coding: utf-8 -*-

"""
input:
5 4
0 1
1 2
2 3
3 4

output:
0 1
1 2
2 3
3 4
"""

import sys
sys.setrecursionlimit(int(1e10))


def generate_adj_table(_v_info):
    for v_detail in _v_info:
        v_from, v_to = map(int, v_detail)
        init_adj_table[v_from].append(v_to)
        # undirected graph
        init_adj_table[v_to].append(v_from)
    return init_adj_table


def graph_dfs(u, visited, parent, low, disc):
    global Time
    # Count of children in current node
    children = 0

    # Mark the current node as visited and print it
    visited[u] = True

    # Initialize discovery time and low value
    disc[u] = Time
    low[u] = Time
    Time += 1

    # Recur for all the vertices adjacent to this vertex
    for v in adj_table[u]:
        # If v is not visited yet, then make it a child of u
        # in DFS tree and recur for it
        if not visited[v]:
            parent[v] = u
            children += 1
            graph_dfs(v, visited, parent, low, disc)

            # Check if the subtree rooted with v has a connection to
            # one of the ancestors of u
            low[u] = min(low[u], low[v])

            ''' If the lowest vertex reachable from subtree
            under v is below u in DFS tree, then u-v is
            a bridge'''
            if low[v] > disc[u]:
                ans.append(sorted([u, v]))
        elif v != parent[u]:  # Update low value of u for parent function calls.
            low[u] = min(low[u], disc[v])

    return None


def bridge():
    visited = [False] * vertices
    disc = [float("Inf")] * vertices
    low = [float("Inf")] * vertices
    parent = [-1] * vertices

    for v in range(vertices):
        if not visited[v]:
            graph_dfs(v, visited, parent, low, disc)

    return ans


if __name__ == '__main__':
    _input = sys.stdin.readlines()
    vertices, edges = map(int, _input[0].split())
    v_info = map(lambda x: x.split(), _input[1:])
    Time = 0
    ans = []

    init_adj_table = tuple([] for _ in range(vertices))
    adj_table = generate_adj_table(v_info)
    res = bridge()
    res.sort()
    for ele in res:
        print(*ele)

Submission status: Runtime Error

Solution code:
from collections import defaultdict
import sys
sys.setrecursionlimit(100000)

def seq():
    a = 1
    while True:
        yield a
        a += 1

def dfs(here, went, connect, discovery, low, answer, seq):
    went |= {here}
    discovery[here] = low[here] = next(seq)
    child = 0
    for con in connect[here]:
        if con not in went:
            parent[con] = here
            child += 1
            dfs(con, went, connect, discovery, low, answer, seq)
            low[here] = min(low[here], low[con])
            if discovery[here] < low[con]:
                answer[min(here,con)].append(max(here,con))
        elif parent[here] != con:
            low[here] = min(low[here], discovery[con])

vertices, edges = (int(n) for n in input().split(" "))
connect = defaultdict(list)
for _ in range(edges):
    v1, v2 = (int(n) for n in input().split(" "))
    connect[v1].append(v2)
    connect[v2].append(v1)
answer = defaultdict(list)
new_seq = seq()
went = set()
discovery = [0 for n in range(vertices)]
low = [float("inf") for n in range(vertices)]
parent = [None for n in range(vertices)]
dfs(0, went, connect, discovery, low, answer, new_seq)

for k in range(answer.keys()):
    for n in range(answer[k]):
        print(k,n)