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Basic Graphs

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from collections import deque


def _input(message):
    return input(message).strip().split(" ")


def initialize_unweighted_directed_graph(
    node_count: int, edge_count: int
) -> dict[int, list[int]]:
    graph: dict[int, list[int]] = {}
    for i in range(node_count):
        graph[i + 1] = []

    for e in range(edge_count):
        x, y = (int(i) for i in _input(f"Edge {e + 1}: <node1> <node2> "))
        graph[x].append(y)
    return graph


def initialize_unweighted_undirected_graph(
    node_count: int, edge_count: int
) -> dict[int, list[int]]:
    graph: dict[int, list[int]] = {}
    for i in range(node_count):
        graph[i + 1] = []

    for e in range(edge_count):
        x, y = (int(i) for i in _input(f"Edge {e + 1}: <node1> <node2> "))
        graph[x].append(y)
        graph[y].append(x)
    return graph


def initialize_weighted_undirected_graph(
    node_count: int, edge_count: int
) -> dict[int, list[tuple[int, int]]]:
    graph: dict[int, list[tuple[int, int]]] = {}
    for i in range(node_count):
        graph[i + 1] = []

    for e in range(edge_count):
        x, y, w = (int(i) for i in _input(f"Edge {e + 1}: <node1> <node2> <weight> "))
        graph[x].append((y, w))
        graph[y].append((x, w))
    return graph


if __name__ == "__main__":
    n, m = (int(i) for i in _input("Number of nodes and edges: "))

    graph_choice = int(
        _input(
            "Press 1 or 2 or 3 \n"
            "1. Unweighted directed \n"
            "2. Unweighted undirected \n"
            "3. Weighted undirected \n"
        )[0]
    )

    g = {
        1: initialize_unweighted_directed_graph,
        2: initialize_unweighted_undirected_graph,
        3: initialize_weighted_undirected_graph,
    }[graph_choice](n, m)


"""
--------------------------------------------------------------------------------
    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 = {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 - Traversal Stack
--------------------------------------------------------------------------------
"""


def bfs(g, s):
    vis, q = {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])


"""
--------------------------------------------------------------------------------
    Topological Sort
--------------------------------------------------------------------------------
"""


def topo(g, ind=None, q=None):
    if q is 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)


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


def adjm():
    n = input().strip()
    a = []
    for _ in range(n):
        a.append(map(int, input().strip().split()))
    return a, n


"""
--------------------------------------------------------------------------------
    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 range(n)]
    for k in range(n):
        for i in range(n):
            for j in range(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)


"""
--------------------------------------------------------------------------------
    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
    return dist


"""
--------------------------------------------------------------------------------
    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, input().split(" "))
    edges = []
    for _ in range(m):
        edges.append(map(int, input().split(" ")))
    return edges, n


"""
--------------------------------------------------------------------------------
    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 = [{i} for i in range(1, n + 1)]
    while True:
        if len(s) == 1:
            break
        print(s)
        x = e.pop()
        for i in range(len(s)):
            if x[0] in s[i]:
                break
        for j in range(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