Consider the following preferences:

$6>13>17>11>12>14>18>15$

$5>26>27>21>23>22>28>24$

$7>35>34>33>32>31>38>36$

$3>48>47>45>44>41>42>46$

$7>51>53>56>52>58>54>55$

$3>62>61>64>67>68>66>65$

$6>75>74>73>72>71>78>77$

$2>83>84>85>86>87>88>81$

$($a$)$ Assume the i$-$th individual is taking the i$-$th house. Conduct the top trading cycle algorithm.

$($b$)$ Assume the order of priority is $1,2,3,4,5,6,7,8.$ Conduct the serial dictatorship algorithm.

$($c$)$ Assume the order of priority is $8,7,6,5,4,3,2,1.$ Conduct the serial dictatorship algorithm.

$($d$)$ Assume player $1$ and player $4$ choose to stay at their own house. Conduct the serial

dictatorship algorithm with squatting right with the order of priority is $1,2,3,4,5,6,7,8$