## 6 Graphical Representation of Implemented Pathfinding Algorithms  
Figure 15 shows a graph that compares the performances of the four implemented Algorithms without taking the obstacles into consideration. The execution time is taken as a parameter for comparing the performances of the Algorithms. The x-axis represents the Algorithm names and the y-axis depicts the execution time in milliseconds. The Algorithms compared are [PERSON]'s, A-star, BFS, and Greedy Best First Search. The 4 \(\times\) 4 grid system without obstacles shows that the execution time for [PERSON]'s is 39.7 ms, for A-star is 27.95 ms, for BFS is 33.76 ms, and Greedy BFS is 14.38 ms. From this, we can see that in the case of the 4 \(\times\) 4 system, the Greedy BFS Algorithm performed the best among all Algorithms. The worst performing was [PERSON]'s. A-star was the second best and BFS was third best in performance. For the 8 \(\times\) 8 grid system without obstacles, it is shown that the execution time for [PERSON]'s is 177.08 ms, for A-star is 140.5 ms, for BFS is 164.49 ms, and Greedy BFS is 36.01 ms. From this, we can see that in case of the 8 \(\times\) 8 system, the Greedy BFS Algorithm again performed the best among all Algorithms. Once again, [PERSON]'s Algorithm performed the worst. A-star was the second best and BFS was third best in performance. In addition, the performance of BFS and [PERSON]'s was almost similar for the 8 \(\times\) 8 system as there was very little difference in execution times. The 16 \(\times\) 16 grid system without obstacles shows that the execution time for [PERSON]'s is 899.27 ms, for A-star is 787.43 ms, for BFS is 868.56 ms, and Greedy BFS is 97.9 ms. From this, we can see that in the case of the 16 \(\times\) 16 system, the Greedy BFS Algorithm again performed the best among all Algorithms. Once again, [PERSON]'s Algorithm performed the worst. A-star was the second best and BFS was third best in performance. Moreover, the performance of BFS and [PERSON]'s was again almost similar for the 16 \(\times\) 16 system as there was very less difference in execution times. In this system, the A-star Algorithm's performance was also close to [PERSON]'s and BFS. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Grid Size** & **Grid Model** & **Algorithm** & **Total Iterations** (Blocks)** & **Total Computed** **Blocks without SPL** & **Execution** **Time (ms)** & **Shortest Path Length (Blocks)** \\ \hline \hline \multirow{4}{*}{\(32\times 32\)} & \multirow{4}{*}{Dijkstra’s} & \multirow{4}{*}{754} & \multirow{4}{*}{679} & \multirow{4}{*}{5678.25} & \multirow{4}{*}{75} \\  & & & & & \\ \cline{1-1}  & & [PERSON]’s & & & \\ \cline{1-1}  & & A-star & 587 & 512 & 3975.34 & 75 \\ \cline{1-1}  & & & & & \\ \cline{1-1}  & & & & & \\ \cline{1-1}  & & & & & \\ \cline{1-1}  & & & & & \\ \cline{1-1}  & & & & & \\ \cline{1-1}  & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._The 32 \(\times\) 32 grid system without obstacles concludes that the execution time for [PERSON]'s is 7500.14 ms, for A-star is 6757.75 ms, for BFS is 7449.17 ms, and Greedy BFS is 346.6 ms. From this, we can see that in the case of the 32 \(\times\) 32 system, the Greedy BFS Algorithm again performed the best among all Algorithms. Once again, [PERSON]'s Algorithm performed the worst. A-star was the second best and BFS was third best in performance again. Moreover, the performance of BFS and [PERSON]'s was again almost similar for 32 \(\times\) 32 system as there was very little difference in execution times. In this system, the A-star Algorithm's performance was also close to [PERSON]'s and BFS again. From the above graph, we can conclude that the best pathfinding Algorithm for without obstacles, which required the least memory and least execution time, was Greedy Best First Search. However, this Algorithm is not optimal. The worst Algorithm for without obstacles requiring most memory usage was [PERSON]'s Algorithm. The second-best Algorithm was found to be A-star, followed by Breadth First Search.