

from __future__ import annotations

import random

# Adjacency list representation of this graph:
# https://en.wikipedia.org/wiki/File:Single_run_of_Karger%E2%80%99s_Mincut_algorithm.svg
UpperCamelCase__	:   str								=     {
    "1": ["2", "3", "4", "5"],
    "2": ["1", "3", "4", "5"],
    "3": ["1", "2", "4", "5", "10"],
    "4": ["1", "2", "3", "5", "6"],
    "5": ["1", "2", "3", "4", "7"],
    "6": ["7", "8", "9", "10", "4"],
    "7": ["6", "8", "9", "10", "5"],
    "8": ["6", "7", "9", "10"],
    "9": ["6", "7", "8", "10"],
    "10": ["6", "7", "8", "9", "3"],
}


def        _UpperCAmelCase							(	_SCREAMING_SNAKE_CASE       :		dict[str, list[str]]							):





    """simple docstring"""


    SCREAMING_SNAKE_CASE_						=    {node: {node} for node in graph}

    SCREAMING_SNAKE_CASE_						=    {node: graph[node][:] for node in graph}

    while len(_SCREAMING_SNAKE_CASE							) > 2:
        # Choose a random edge.
        SCREAMING_SNAKE_CASE_						=    random.choice(list(graph_copy.keys()							)							)
        SCREAMING_SNAKE_CASE_						=    random.choice(graph_copy[u]							)

        # Contract edge (u, v) to new node uv
        SCREAMING_SNAKE_CASE_						=    u + v
        SCREAMING_SNAKE_CASE_						=    list(set(graph_copy[u] + graph_copy[v]							)							)
        uv_neighbors.remove(_SCREAMING_SNAKE_CASE							)
        uv_neighbors.remove(_SCREAMING_SNAKE_CASE							)
        SCREAMING_SNAKE_CASE_						=    uv_neighbors
        for neighbor in uv_neighbors:
            graph_copy[neighbor].append(_SCREAMING_SNAKE_CASE							)

        SCREAMING_SNAKE_CASE_						=    set(contracted_nodes[u].union(contracted_nodes[v]							)							)

        # Remove nodes u and v.
        del graph_copy[u]
        del graph_copy[v]
        for neighbor in uv_neighbors:
            if u in graph_copy[neighbor]:
                graph_copy[neighbor].remove(_SCREAMING_SNAKE_CASE							)
            if v in graph_copy[neighbor]:
                graph_copy[neighbor].remove(_SCREAMING_SNAKE_CASE							)

    # Find cutset.
    SCREAMING_SNAKE_CASE_						=    [contracted_nodes[node] for node in graph_copy]
    return {
        (node, neighbor)
        for node in groups[0]
        for neighbor in graph[node]
        if neighbor in groups[1]
    }


if __name__ == "__main__":
       print(partition_graph(TEST_GRAPH))





from __future__ import annotations


def        _UpperCAmelCase							(	_SCREAMING_SNAKE_CASE       :		list[int]							):





    """simple docstring"""


    SCREAMING_SNAKE_CASE_						=    [0] * len(_SCREAMING_SNAKE_CASE							)
    for i in range(1			, len(_SCREAMING_SNAKE_CASE							)							):
        SCREAMING_SNAKE_CASE_						=    duration_times[i - 1] + waiting_times[i - 1]
    return waiting_times


def        _UpperCAmelCase							(	_SCREAMING_SNAKE_CASE       :		list[int]			, _SCREAMING_SNAKE_CASE       :		list[int]							):





    """simple docstring"""


    return [
        duration_time + waiting_times[i]
        for i, duration_time in enumerate(_SCREAMING_SNAKE_CASE							)
    ]


def        _UpperCAmelCase							(	_SCREAMING_SNAKE_CASE       :		list[int]							):





    """simple docstring"""


    return sum(_SCREAMING_SNAKE_CASE							) / len(_SCREAMING_SNAKE_CASE							)


def        _UpperCAmelCase							(	_SCREAMING_SNAKE_CASE       :		list[int]							):





    """simple docstring"""


    return sum(_SCREAMING_SNAKE_CASE							) / len(_SCREAMING_SNAKE_CASE							)


if __name__ == "__main__":
       # process id's
       UpperCamelCase__	:   List[str]								=     [1, 2, 3]

       # ensure that we actually have processes
       if len(processes) == 0:
              print("Zero amount of processes")
              raise SystemExit(0)

       # duration time of all processes
       UpperCamelCase__	:   Any								=     [19, 8, 9]

       # ensure we can match each id to a duration time
       if len(duration_times) != len(processes):
              print("Unable to match all id's with their duration time")
              raise SystemExit(0)

       # get the waiting times and the turnaround times
       UpperCamelCase__	:   List[str]								=     calculate_waiting_times(duration_times)
       UpperCamelCase__	:   Union[str, Any]								=     calculate_turnaround_times(duration_times, waiting_times)

       # get the average times
       UpperCamelCase__	:   str								=     calculate_average_waiting_time(waiting_times)
       UpperCamelCase__	:   List[Any]								=     calculate_average_turnaround_time(turnaround_times)

       # print all the results
       print("Process ID\tDuration Time\tWaiting Time\tTurnaround Time")
       for i, process in enumerate(processes):
              print(
                  F'{process}\t\t{duration_times[i]}\t\t{waiting_times[i]}\t\t'
                  F'{turnaround_times[i]}'
              )
       print(F'Average waiting time = {average_waiting_time}')
       print(F'Average turn around time = {average_turnaround_time}')


