basic_graphs.py

from __future__ import print_function

try:
    raw_input  # Python 2
except NameError:
    raw_input = input  # Python 3

try:
    xrange  # Python 2
except NameError:
    xrange = range  # Python 3

# Accept No. of Nodes and edges
n, m = map(int, raw_input().split(" "))

# Initialising Dictionary of edges
g = {}
for i in xrange(n):
    g[i + 1] = []

"""
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    Accepting edges of Unweighted Directed Graphs
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"""
for _ in xrange(m):
    x, y = map(int, raw_input().split(" "))
    g[x].append(y)

"""
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    Accepting edges of Unweighted Undirected Graphs
--------------------------------------------------------------------------------
"""
for _ in xrange(m):
    x, y = map(int, raw_input().split(" "))
    g[x].append(y)
    g[y].append(x)

"""
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    Accepting edges of Weighted Undirected Graphs
--------------------------------------------------------------------------------
"""
for _ in xrange(m):
    x, y, r = map(int, raw_input().split(" "))
    g[x].append([y, r])
    g[y].append([x, r])

"""
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    Depth First Search.
        Args :  G - Dictionary of edges
                s - Starting Node
        Vars :  vis - Set of visited nodes
                S - Traversal Stack
--------------------------------------------------------------------------------
"""


def dfs(G, s):
    vis, S = set([s]), [s]
    print(s)
    while S:
        flag = 0
        for i in G[S[-1]]:
            if i not in vis:
                S.append(i)
                vis.add(i)
                flag = 1
                print(i)
                break
        if not flag:
            S.pop()


"""
--------------------------------------------------------------------------------
    Breadth First Search.
        Args :  G - Dictionary of edges
                s - Starting Node
        Vars :  vis - Set of visited nodes
                Q - Traveral Stack
--------------------------------------------------------------------------------
"""
from collections import deque


def bfs(G, s):
    vis, Q = set([s]), deque([s])
    print(s)
    while Q:
        u = Q.popleft()
        for v in G[u]:
            if v not in vis:
                vis.add(v)
                Q.append(v)
                print(v)


"""
--------------------------------------------------------------------------------
    Dijkstra's shortest path Algorithm
        Args :  G - Dictionary of edges
                s - Starting Node
        Vars :  dist - Dictionary storing shortest distance from s to every other node
                known - Set of knows nodes
                path - Preceding node in path
--------------------------------------------------------------------------------
"""


def dijk(G, s):
    dist, known, path = {s: 0}, set(), {s: 0}
    while True:
        if len(known) == len(G) - 1:
            break
        mini = 100000
        for i in dist:
            if i not in known and dist[i] < mini:
                mini = dist[i]
                u = i
        known.add(u)
        for v in G[u]:
            if v[0] not in known:
                if dist[u] + v[1] < dist.get(v[0], 100000):
                    dist[v[0]] = dist[u] + v[1]
                    path[v[0]] = u
    for i in dist:
        if i != s:
            print(dist[i])


"""
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    Topological Sort
--------------------------------------------------------------------------------
"""
from collections import deque


def topo(G, ind=None, Q=[1]):
    if ind is None:
        ind = [0] * (len(G) + 1)  # SInce oth Index is ignored
        for u in G:
            for v in G[u]:
                ind[v] += 1
        Q = deque()
        for i in G:
            if ind[i] == 0:
                Q.append(i)
    if len(Q) == 0:
        return
    v = Q.popleft()
    print(v)
    for w in G[v]:
        ind[w] -= 1
        if ind[w] == 0:
            Q.append(w)
    topo(G, ind, Q)


"""
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    Reading an Adjacency matrix
--------------------------------------------------------------------------------
"""


def adjm():
    n, a = raw_input(), []
    for i in xrange(n):
        a.append(map(int, raw_input().split()))
    return a, n


"""
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    Floyd Warshall's algorithm
        Args :  G - Dictionary of edges
                s - Starting Node
        Vars :  dist - Dictionary storing shortest distance from s to every other node
                known - Set of knows nodes
                path - Preceding node in path

--------------------------------------------------------------------------------
"""


def floy(A_and_n):
    (A, n) = A_and_n
    dist = list(A)
    path = [[0] * n for i in xrange(n)]
    for k in xrange(n):
        for i in xrange(n):
            for j in xrange(n):
                if dist[i][j] > dist[i][k] + dist[k][j]:
                    dist[i][j] = dist[i][k] + dist[k][j]
                    path[i][k] = k
    print(dist)


"""
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    Prim's MST Algorithm
        Args :  G - Dictionary of edges
                s - Starting Node
        Vars :  dist - Dictionary storing shortest distance from s to nearest node
                known - Set of knows nodes
                path - Preceding node in path
--------------------------------------------------------------------------------
"""


def prim(G, s):
    dist, known, path = {s: 0}, set(), {s: 0}
    while True:
        if len(known) == len(G) - 1:
            break
        mini = 100000
        for i in dist:
            if i not in known and dist[i] < mini:
                mini = dist[i]
                u = i
        known.add(u)
        for v in G[u]:
            if v[0] not in known:
                if v[1] < dist.get(v[0], 100000):
                    dist[v[0]] = v[1]
                    path[v[0]] = u


"""
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    Accepting Edge list
        Vars :  n - Number of nodes
                m - Number of edges
        Returns : l - Edge list
                n - Number of Nodes
--------------------------------------------------------------------------------
"""


def edglist():
    n, m = map(int, raw_input().split(" "))
    l = []
    for i in xrange(m):
        l.append(map(int, raw_input().split(' ')))
    return l, n


"""
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    Kruskal's MST Algorithm
        Args :  E - Edge list
                n - Number of Nodes
        Vars :  s - Set of all nodes as unique disjoint sets (initially)
--------------------------------------------------------------------------------
"""


def krusk(E_and_n):
    # Sort edges on the basis of distance
    (E, n) = E_and_n
    E.sort(reverse=True, key=lambda x: x[2])
    s = [set([i]) for i in range(1, n + 1)]
    while True:
        if len(s) == 1:
            break
        print(s)
        x = E.pop()
        for i in xrange(len(s)):
            if x[0] in s[i]:
                break
        for j in xrange(len(s)):
            if x[1] in s[j]:
                if i == j:
                    break
                s[j].update(s[i])
                s.pop(i)
                break


# find the isolated node in the graph
def find_isolated_nodes(graph):
    isolated = []
    for node in graph:
        if not graph[node]:
            isolated.append(node)
    return isolated