main.py

import random

from graph import Graph
import unittest as ut
import matplotlib.pyplot as plt
import sys
from collections import defaultdict
import time
import numpy as np
import math
from scipy.special import comb


class BB:

    def __init__(self, g, m, s, e):
        self.graph = g
        self.min_items = m
        self.start_node = s
        self.end_node = e

    # calculate cost
    def calc_cost(self, path_from_start):
        if path_from_start is not None:
            return self.lower_bound(path_from_start[-1], path_from_start)
        else:
            return 0

    # select from F the (v,path_from_start) where the cost between s and v is the lowest
    def select_v_with_lowest_cost(self, f):
        min_node = None
        min_cost = sys.maxsize
        for node in f.keys():
            if min_cost > f[node][1]:
                min_node = node
                min_cost = f[node][1]
        return min_node

    # expand configuration
    def expand(self, node, f):
        if f[node][0] is None:
            path_from_start = []
        else:
            path_from_start = f[node][0]

        configuration = []
        for neighbour in self.graph[node].keys():
            temp = list.copy(path_from_start)
            if node not in temp:
                temp.insert(0, node)
            if neighbour not in path_from_start:
                temp.append(neighbour)
                configuration.append(temp)
        return configuration

    # return distance of edges in path
    def calculate_distance(self, path):
        distances = []
        for i in range(len(path) - 1):
            distances.append(self.graph[path[i]][path[i + 1]])
        return distances

    def shortest_path(self):
        if self.start_node not in self.graph.keys():
            print("start node not in graph")
            return
        if self.start_node not in self.graph.keys():
            print("end nod not in graph")
            return
        f = defaultdict(lambda: [])  # contains {v:path_from_start, cost}
        f[self.start_node] = [[], 1.0]
        b = ["", [], sys.maxsize]  # [lastNode, path_from_start,cost]}
        visited = defaultdict(lambda: [])  # contains {v:[path_from_start, cost]}
        while f is not None:
            # select from f the (v,path_from_start) where the cost between s and v is the lowest
            min_v = self.select_v_with_lowest_cost(f)
            # Expand
            configurations = self.expand(min_v, f)
            # if we arrived to dead end
            if not configurations:
                del f[min_v]

            for path_from_start in configurations:
                last_node_in_path_from_start = path_from_start[-1]
                # calculate cost for v
                c = self.calc_cost(path_from_start)
                # check if this node visited before or not
                if min_v not in visited.keys():
                    visited[min_v] = []
                    visited[min_v].append(path_from_start)  # add path_from_start
                    visited[min_v].append(c)  # add cost

                # update best if it contains path from start that already discarded
                flag = False
                for i in f.values():
                    if b[1] is i[0]:
                        flag =True
                if flag is False:
                    b = ["", [], sys.maxsize]
                # delete the node because we dont want it to expand again
                if min_v in f.keys():
                    del f[min_v]

                if visited[last_node_in_path_from_start] != [] and visited[last_node_in_path_from_start][1] < c:
                    check = "dead end"
                elif last_node_in_path_from_start is self.end_node and len(path_from_start) >= self.min_items:
                    check = "solution found"
                else:
                    check = "continue"

                if check == "solution found":
                    return path_from_start
                elif check == "dead end":
                    # discard configuration
                    configurations.remove(path_from_start)
                else:

                    if self.lower_bound(last_node_in_path_from_start, path_from_start) < b[2]:
                        cost = self.lower_bound(last_node_in_path_from_start, path_from_start)
                        f[last_node_in_path_from_start] = [path_from_start, cost]
                        b = [last_node_in_path_from_start, path_from_start, cost]

        return b

    def lower_bound(self, v, path_from_start):
        all_edge_weights = self.calculate_distance(path_from_start)
        total_distance = sum(all_edge_weights)
        items = len(path_from_start)
        cost = total_distance / items
        return cost


class Experiments:
    def __init__(self):
        self.totalTime = []

    def test_tiny_graph(self):
        """
       :param None

       :return: an bb object
       """
        g2 = Graph()
        # create a graph
        g2.add_edge_undirected("a", "b", 3)
        g2.add_edge_undirected("a", "c", 5)
        g2.add_edge_undirected("b", "d", 1)
        g2.add_edge_undirected("b", "e", 3)
        g2.add_edge_undirected("c", "a", 5)
        g2.add_edge_undirected("c", "e", 3)
        g2.add_edge_undirected("d", "f", 2)
        g2.add_edge_undirected("d", "e", 1)
        g2.add_edge_undirected("d", "b", 1)
        g2.add_edge_undirected("e", "c", 3)
        g2.add_edge_undirected("e", "b", 2)
        g2.add_edge_undirected("e", "d", 1)
        g2.add_edge_undirected("e", "f", 4)
        g2.add_edge_undirected("f", "g", 1)
        g2.add_edge_undirected("g", "f", 1)
        g2.create_adjacency_list()
        print("graph = ", g2.adjacency_list)
        min = 2
        start = "a"
        end = "g"
        b = BB(g2.adjacency_list, min, start, end)
        print("shortest path = ", b.shortest_path())
        return b


    def trials(self, n):
        """ Takes number of trials and expierment"""
        for i in range(1, n):
            self.test_tiny_graph(2)

    def timer(self, bb):
        """
        Time analysis

        Takes in a bb object, and calculates the time to run
        the shortest path on it once

        :type bb: BB
        :param bb:
        :return: float
        """
        timer_on = time.time()
        bb.shortest_path()
        timer_off = time.time()
        self.totalTime.append(timer_off - timer_on)
        timer_off = time.time()

        return timer_off - timer_on

    def plot_by_min(self, mins, t):
        """
        :param mins: List
            list of mins
        :param t: int
            num of trials
        :return: None, but prints plots
        """

        all_data = []
        for min_ in mins:
            runtimes = []
            for i in range(0, t):
                b = self.min_graphs(min_)
                runtimes.append(self.timer(b))
            all_data.append(runtimes)
        means = []
        sd = []
        for x in all_data:
            means.append(sum(x) / t)
            sd.append(np.std(x))  # get standard deviations

        plt.errorbar(mins, means, sd, linestyle='-', marker='^')
        plt.xlabel('Min')
        plt.ylabel('Runtime')
        plt.title('BB')

        # plt.legend()
        plt.show()

    def plot_by_size(self, t):
        """
        :param t: int
            num of trials
        :return: None, but prints plots
        """
        sizes = [10, 50, 90, 140, 190]
        all_data = []
        for size in sizes:
            runtimes = []
            for i in range(0, t):
                b = self.size_graph(size)
                runtimes.append(self.timer(b))
            all_data.append(runtimes)
        means = []
        sd = []
        for x in all_data:
            means.append(sum(x) / t)
            sd.append(np.std(x))  # get standard deviations

        plt.errorbar(sizes, means, sd, linestyle='-', marker='^')
        plt.xlabel('Size')
        plt.ylabel('Runtime')
        plt.title('BB')

        plt.show()

    def plot_by_density(self, t):
        """
        :param t: int
            num of trials
        :return: None, but prints plots
        """
        sizes = [10, 50, 90, 140,190]
        densities = []
        all_data = []

        for size in sizes:
            runtimes = []
            densities.append(self.get_density(self.size_graph(size,"graph")))
            for i in range(0, t):
                b = self.size_graph(size)
                runtimes.append(self.timer(b))
            all_data.append(runtimes)

        means = []
        sd = []
        for x in all_data:
            means.append(sum(x) / t)
            sd.append(np.std(x))  # get standard deviations

        plt.errorbar(densities, means, sd, linestyle='-', marker='^')
        plt.xlabel('Density')
        plt.ylabel('Runtime')
        plt.title('BB')

        plt.show()


    def plot_by_random_density(self, t):
        """
        :param t: int
            num of trials
        :return: None, but prints plots
        """
        size = 100
        edges = [100, 500, 1000, 1500, 2000, 2500, 3000, 3500, 4000, 4500]
        density = []
        for e in edges:
                d = e/4950
                density.append(d)

        all_data = []
        for edge in edges:
            runtimes = []
            for i in range(0, t):
                g = Graph()
                g.generate_connected_graph(size, edge, 50)
                g.create_adjacency_list()
                # self.graph = g
                # self.min_items = m
                # self.start_node = s
                # self.end_node = e
                start = 1
                end = 100
                try:
                    b = BB(g.adjacency_list, 3, start, end)
                    runtimes.append(self.timer(b))
                except:
                    # print("Something went wrong")
                    pass
                finally:
                    pass
                    # print("The 'try except' is finished")

            all_data.append(runtimes)
        means = []
        sd = []
        for x in all_data:
            means.append(sum(x) / t)
            sd.append(np.std(x))  # get standard deviations

        plt.errorbar(density, means, sd, linestyle='-', marker='^')
        plt.xlabel('Density')
        plt.ylabel('Runtime')
        plt.title('BB')

        plt.show()

    def min_graphs(self,min):
        """
        :param min: minimum desired nodes

        :return: an bb object
        """
        # for size 100 start =1 end = 38
        minsize100 = {1: {2: 35, 3: 43, 5: 26, 6: 21, 12: 45, 82: 50, 7: 14, 11: 34, 19: 11, 30: 49}, 2: {1: 35, 4: 41, 9: 24, 21: 21, 22: 23, 28: 7, 49: 19, 84: 8, 82: 11, 98: 5, 8: 13, 100: 48, 71: 4, 45: 37}, 3: {1: 43, 7: 4, 83: 31, 80: 26, 70: 45, 43: 23, 31: 9, 74: 42}, 4: {2: 41, 13: 49, 16: 28, 17: 44, 58: 19, 11: 18, 67: 43, 73: 25, 98: 33, 85: 36}, 5: {1: 26, 10: 30, 15: 6, 99: 44, 11: 37, 34: 34, 80: 12}, 6: {1: 21, 31: 48, 41: 48, 73: 19, 24: 6, 90: 47, 88: 41, 72: 37, 15: 44}, 7: {3: 4, 8: 30, 11: 22, 24: 1, 43: 28, 50: 25, 85: 13, 1: 14, 82: 28, 100: 36, 22: 14, 33: 27}, 8: {7: 30, 60: 14, 93: 18, 2: 13, 28: 40, 69: 27}, 9: {2: 24, 19: 13, 27: 22, 89: 16, 57: 14, 100: 29, 22: 8, 92: 21, 86: 2, 55: 49}, 10: {5: 30, 78: 10, 92: 14}, 11: {7: 22, 29: 31, 52: 12, 5: 37, 1: 34, 30: 41, 4: 18, 43: 32, 54: 10, 36: 35, 23: 36, 46: 45, 89: 38, 71: 50, 88: 30}, 12: {1: 45, 14: 49, 44: 10, 74: 17, 29: 49, 94: 44, 47: 12}, 13: {4: 49, 32: 11}, 14: {12: 49, 18: 20, 61: 24, 24: 18, 47: 22, 78: 30, 84: 39}, 15: {5: 6, 26: 32, 95: 37, 56: 12, 6: 44, 50: 1}, 16: {4: 28, 30: 32, 33: 5, 45: 36, 58: 22, 81: 3, 52: 18, 68: 10}, 17: {4: 44, 36: 21, 37: 19, 69: 22, 68: 47, 44: 5, 81: 10, 43: 3, 41: 39}, 18: {14: 20, 20: 25, 80: 43}, 19: {9: 13, 25: 11, 21: 31, 75: 3, 1: 11, 82: 19, 57: 8}, 20: {18: 25, 26: 23, 35: 25, 60: 20, 74: 44, 41: 18, 45: 7}, 21: {2: 21, 23: 14, 63: 34, 86: 39, 99: 18, 97: 20, 19: 31, 79: 12, 30: 30, 93: 32, 80: 19, 50: 9, 91: 5}, 22: {2: 23, 39: 38, 42: 2, 59: 24, 9: 8, 7: 14, 34: 27, 71: 31}, 23: {21: 14, 40: 20, 66: 11, 64: 10, 98: 50, 65: 20, 83: 7, 93: 42, 11: 36, 54: 35}, 24: {7: 1, 65: 18, 91: 5, 6: 6, 71: 41, 14: 18, 60: 21, 28: 1, 97: 50}, 25: {19: 11, 78: 27, 84: 23}, 26: {20: 23, 15: 32, 53: 50, 78: 22, 85: 1, 66: 16, 27: 37, 87: 42}, 27: {9: 22, 68: 15, 81: 31, 76: 25, 26: 37}, 28: {2: 7, 68: 50, 37: 33, 8: 40, 24: 1}, 29: {11: 31, 39: 1, 12: 49, 48: 14}, 30: {16: 32, 45: 15, 11: 41, 42: 3, 50: 40, 21: 30, 93: 40, 1: 49}, 31: {6: 48, 47: 28, 64: 15, 74: 46, 51: 9, 89: 28, 32: 35, 3: 9, 84: 18}, 32: {13: 11, 34: 5, 71: 8, 96: 8, 68: 35, 43: 38, 31: 35}, 33: {16: 5, 45: 15, 63: 21, 47: 40, 40: 24, 7: 27}, 34: {32: 5, 5: 34, 95: 9, 79: 2, 22: 27}, 35: {20: 25, 92: 11, 88: 4, 63: 7, 72: 24, 54: 16}, 36: {17: 21, 38: 28, 57: 12, 80: 22, 96: 39, 11: 35, 66: 42, 67: 31}, 37: {17: 19, 42: 24, 100: 24, 63: 40, 28: 33, 96: 2}, 38: {36: 28, 49: 23, 87: 31, 68: 2, 98: 41}, 39: {22: 38, 29: 1, 82: 17}, 40: {23: 20, 95: 17, 78: 18, 99: 34, 69: 15, 42: 32, 33: 24}, 41: {6: 48, 49: 31, 57: 14, 90: 35, 82: 31, 17: 39, 20: 18}, 42: {22: 2, 46: 21, 55: 1, 61: 40, 78: 2, 81: 50, 37: 24, 99: 38, 30: 3, 98: 22, 40: 32}, 43: {7: 28, 54: 14, 74: 32, 11: 32, 58: 18, 32: 38, 17: 3, 45: 24, 3: 23, 82: 5}, 44: {12: 10, 48: 40, 53: 17, 98: 23, 57: 10, 17: 5, 59: 42, 73: 2, 86: 25}, 45: {16: 36, 30: 15, 33: 15, 43: 24, 59: 3, 20: 7, 95: 32, 2: 37}, 46: {42: 21, 58: 30, 99: 36, 71: 10, 11: 45, 63: 20}, 47: {31: 28, 62: 1, 75: 10, 82: 33, 14: 22, 33: 40, 12: 12}, 48: {44: 40, 100: 26, 29: 14, 60: 22}, 49: {2: 19, 38: 23, 41: 31, 76: 18, 81: 17}, 50: {7: 25, 51: 27, 70: 19, 30: 40, 21: 9, 15: 1, 61: 10}, 51: {50: 27, 67: 40, 31: 9, 98: 37, 91: 23, 77: 24, 90: 30}, 52: {11: 12, 56: 38, 16: 18, 97: 47}, 53: {44: 17, 74: 45, 77: 28, 26: 50, 71: 42, 57: 37, 97: 34}, 54: {43: 14, 93: 43, 11: 10, 99: 39, 94: 39, 23: 35, 35: 16}, 55: {42: 1, 97: 17, 56: 30, 75: 9, 9: 49}, 56: {52: 38, 55: 30, 15: 12}, 57: {36: 12, 9: 14, 44: 10, 41: 14, 53: 37, 70: 6, 19: 8}, 58: {16: 22, 72: 8, 4: 19, 46: 30, 43: 18, 93: 45, 83: 30}, 59: {22: 24, 44: 42, 95: 20, 45: 3, 61: 1}, 60: {8: 14, 79: 2, 20: 20, 95: 12, 24: 21, 78: 44, 69: 50, 71: 25, 62: 49, 48: 22, 75: 7}, 61: {42: 40, 14: 24, 76: 25, 80: 23, 50: 10, 59: 1}, 62: {47: 1, 70: 30, 60: 49}, 63: {21: 34, 88: 21, 33: 21, 84: 36, 37: 40, 35: 7, 46: 20}, 64: {31: 15, 23: 10, 86: 21}, 65: {24: 18, 23: 20}, 66: {23: 11, 76: 25, 99: 36, 91: 21, 36: 42, 26: 16}, 67: {51: 40, 4: 43, 86: 24, 96: 48, 97: 26, 36: 31}, 68: {27: 15, 17: 47, 72: 27, 32: 35, 93: 16, 16: 10, 28: 50, 69: 1, 38: 2, 100: 18}, 69: {17: 22, 79: 5, 99: 15, 60: 50, 68: 1, 40: 15, 83: 1, 8: 27}, 70: {50: 19, 75: 6, 3: 45, 91: 44, 74: 28, 62: 30, 57: 6, 99: 1}, 71: {32: 8, 84: 18, 24: 41, 53: 42, 60: 25, 46: 10, 2: 4, 22: 31, 11: 50}, 72: {58: 8, 90: 11, 68: 27, 6: 37, 89: 27, 35: 24, 78: 18, 74: 40}, 73: {6: 19, 87: 49, 97: 11, 4: 25, 98: 26, 44: 2}, 74: {53: 45, 92: 32, 43: 32, 31: 46, 70: 28, 12: 17, 20: 44, 72: 40, 3: 42}, 75: {47: 10, 70: 6, 19: 3, 55: 9, 76: 21, 60: 7}, 76: {66: 25, 84: 10, 27: 25, 49: 18, 75: 21, 85: 27, 61: 25}, 77: {53: 28, 82: 35, 51: 24}, 78: {10: 10, 42: 2, 40: 18, 98: 45, 26: 22, 87: 9, 83: 22, 60: 44, 14: 30, 72: 18, 25: 27}, 79: {69: 5, 60: 2, 21: 12, 34: 2, 84: 46}, 80: {36: 22, 3: 26, 21: 19, 18: 43, 61: 23, 5: 12}, 81: {27: 31, 16: 3, 42: 50, 92: 11, 17: 10, 49: 17, 88: 25, 82: 10, 87: 6}, 82: {1: 50, 94: 11, 7: 28, 47: 33, 2: 11, 39: 17, 41: 31, 77: 35, 19: 19, 81: 10, 43: 5}, 83: {3: 31, 23: 7, 78: 22, 58: 30, 69: 1}, 84: {76: 10, 2: 8, 71: 18, 63: 36, 79: 46, 31: 18, 25: 23, 14: 39}, 85: {7: 13, 26: 1, 4: 36, 86: 34, 76: 27}, 86: {21: 39, 67: 24, 9: 2, 64: 21, 85: 34, 44: 25, 92: 35}, 87: {73: 49, 98: 48, 78: 9, 38: 31, 81: 6, 26: 42}, 88: {63: 21, 90: 15, 6: 41, 81: 25, 35: 4, 11: 30}, 89: {9: 16, 94: 24, 72: 27, 31: 28, 90: 42, 11: 38}, 90: {72: 11, 88: 15, 41: 35, 6: 47, 93: 39, 89: 42, 51: 30}, 91: {24: 5, 70: 44, 66: 21, 51: 23, 21: 5}, 92: {74: 32, 81: 11, 9: 21, 35: 11, 95: 29, 10: 14, 86: 35}, 93: {8: 18, 54: 43, 58: 45, 68: 16, 90: 39, 21: 32, 23: 42, 30: 40}, 94: {82: 11, 100: 29, 89: 24, 12: 44, 54: 39}, 95: {40: 17, 60: 12, 15: 37, 34: 9, 92: 29, 59: 20, 45: 32}, 96: {32: 8, 36: 39, 67: 48, 37: 2}, 97: {55: 17, 73: 11, 21: 20, 52: 47, 53: 34, 67: 26, 24: 50}, 98: {87: 48, 23: 50, 44: 23, 78: 45, 2: 5, 4: 33, 73: 26, 42: 22, 51: 37, 38: 41}, 99: {5: 44, 21: 18, 66: 36, 46: 36, 40: 34, 42: 38, 69: 15, 54: 39, 70: 1}, 100: {48: 26, 9: 29, 7: 36, 94: 29, 37: 24, 2: 48, 68: 18}}
        start = 1
        end = 100
        test = BB(minsize100, min, start, end)
        return test

    def size_graph(self,size,select=None):
        """
        :param size: size of graph

        :return: an bb object or graph
        """
        # all for min 3
        if size == 10:
            size10 = {1: {2: 32, 3: 22, 4: 19, 7: 41, 10: 43, 5: 37, 8: 34, 9: 3, 6: 40}, 2: {1: 32, 9: 14, 3: 28, 10: 15, 7: 32, 5: 2, 8: 30, 6: 15, 4: 44}, 3: {1: 22, 5: 18, 6: 14, 2: 28, 9: 47, 4: 28, 8: 35, 10: 44, 7: 8}, 4: {1: 19, 7: 43, 3: 28, 6: 18, 10: 35, 8: 42, 5: 48, 9: 30, 2: 44}, 5: {3: 18, 8: 28, 6: 28, 7: 6, 9: 45, 1: 37, 4: 48, 2: 2, 10: 36}, 6: {3: 14, 5: 28, 9: 3, 10: 39, 4: 18, 1: 40, 8: 42, 2: 15, 7: 5}, 7: {4: 43, 1: 41, 5: 6, 8: 12, 9: 19, 10: 30, 2: 32, 3: 8, 6: 5}, 8: {5: 28, 10: 20, 7: 12, 3: 35, 4: 42, 1: 34, 9: 38, 6: 42, 2: 30}, 9: {2: 14, 3: 47, 10: 18, 6: 3, 5: 45, 7: 19, 1: 3, 8: 38, 4: 30}, 10: {8: 20, 9: 18, 6: 39, 4: 35, 2: 15, 1: 43, 7: 30, 5: 36, 3: 44}}
            g = size10
        if size == 50:
            size50 = {1: {2: 48, 3: 27, 4: 38, 9: 32, 13: 40, 46: 14, 34: 8, 33: 47, 50: 41, 44: 3, 24: 29, 27: 36, 32: 49, 19: 50, 49: 44, 36: 2, 39: 10, 41: 46, 29: 42, 26: 22, 8: 4, 14: 19, 18: 36, 15: 17, 22: 47, 30: 49, 31: 3, 5: 2, 25: 17, 10: 13, 23: 9, 40: 17, 45: 43, 37: 27, 12: 45, 11: 8, 42: 43, 21: 10, 6: 31, 38: 46, 7: 15, 35: 27, 28: 46, 48: 20, 43: 20, 20: 46, 16: 21, 17: 30, 47: 50}, 2: {1: 48, 12: 49, 17: 16, 42: 1, 7: 3, 31: 23, 4: 30, 15: 18, 33: 41, 6: 40, 50: 3, 16: 9, 35: 29, 46: 19, 30: 16, 23: 16, 44: 44, 3: 13, 27: 34, 32: 28, 47: 15, 34: 12, 43: 22, 24: 10, 28: 13, 10: 19, 18: 7, 9: 2, 26: 39, 25: 50, 38: 45, 40: 37, 39: 15, 36: 1, 19: 10, 14: 36, 20: 45, 41: 19, 48: 34, 8: 34, 11: 11, 13: 43, 49: 17, 45: 34, 37: 25, 5: 36, 22: 27, 21: 10, 29: 29}, 3: {1: 27, 5: 46, 6: 44, 35: 46, 48: 19, 33: 2, 17: 14, 46: 14, 49: 31, 19: 27, 11: 25, 12: 13, 40: 10, 9: 36, 22: 20, 2: 13, 34: 16, 38: 9, 23: 39, 45: 47, 43: 14, 42: 8, 30: 24, 24: 49, 36: 16, 14: 46, 13: 14, 25: 7, 27: 36, 37: 36, 32: 9, 29: 33, 44: 49, 16: 34, 28: 1, 7: 7, 20: 1, 47: 40, 41: 27, 26: 6, 8: 26, 10: 16, 31: 43, 50: 14, 4: 9, 15: 35, 39: 42, 18: 23, 21: 42}, 4: {1: 38, 7: 18, 8: 9, 28: 4, 27: 41, 2: 30, 20: 44, 6: 36, 43: 8, 37: 39, 13: 40, 26: 3, 45: 31, 44: 28, 24: 5, 29: 29, 32: 35, 36: 45, 17: 36, 16: 22, 18: 39, 31: 9, 50: 48, 38: 2, 5: 20, 25: 40, 11: 9, 15: 22, 40: 28, 22: 46, 46: 18, 34: 33, 33: 46, 35: 46, 48: 46, 12: 41, 14: 2, 23: 43, 41: 50, 47: 2, 21: 42, 49: 35, 19: 30, 10: 27, 3: 9, 30: 2, 42: 25, 39: 1, 9: 8}, 5: {3: 46, 19: 21, 50: 5, 36: 24, 23: 38, 20: 43, 45: 14, 49: 43, 12: 43, 33: 4, 13: 4, 31: 36, 11: 4, 9: 46, 25: 17, 37: 17, 15: 31, 48: 36, 4: 20, 34: 30, 46: 15, 47: 48, 7: 39, 32: 27, 16: 35, 8: 44, 40: 40, 1: 2, 27: 3, 26: 8, 28: 39, 14: 18, 38: 12, 24: 5, 41: 27, 29: 15, 30: 32, 22: 38, 10: 15, 6: 3, 42: 17, 18: 1, 43: 17, 35: 49, 39: 16, 44: 2, 2: 36, 21: 50, 17: 35}, 6: {3: 44, 15: 45, 22: 27, 24: 45, 26: 18, 23: 12, 2: 40, 4: 36, 34: 50, 18: 48, 29: 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            g = size50
        if size == 90:
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            g = size90
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            g = size140
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            g = size190

        min = 3
        start = size/2
        end = len(g.keys())
        test = BB(g, min, start, end)
        if select == "graph":
            return g
        else:
            return test


    def get_density(self,graph):
        """ Calculate the density of a graph
        :param graph: the graph that we calculate its density
        density = (actual number of edges)/(possible number of edges)
        possible number of edges = number of nodes choose 2

        returns: float
            density
        """
        possible_edges = comb(len(graph), 2, exact=True, repetition=False)
        # get actual number of edges
        edges = (sum([len(graph[x]) for x in graph])) / 2
        density = edges / possible_edges
        return density



def main():

    # start experiments
    test = Experiments()
    # test by different sizes
    print("plotting..........")
    test.plot_by_size(10)
    # test by different mins
    test.plot_by_min([5,10,15,20,25],10)
    # test by density
    test.plot_by_density(10)
    # test tiny graph
    test.test_tiny_graph()


    # test.plot_by_random_density(10)


if __name__ == "__main__":
    main()