Num States Expanded L UCS A*1 A*2 ID IDA*1 IDA*2 2 6.13 2.0 2.0 9.96 4.0 4.0 4 23.13 4.13 4.0 44.77 8.07 8.0 6 75.73 7.81 6.72 178.31 14.27 12.49 8 215.95 16.33 10.68 538.54 27.69 18.02 10 591.97 38.63 17.89 1667.05 68.23 28.67 12 1548.93 89.05 31.72 5178.22 175.59 50.17 Num States Generated L UCS A*1 A*2 ID IDA*1 IDA*2 2 18.36 7.1 7.1 30.3 13.3 13.3 4 64.4 13.03 12.64 125.05 21.81 21.6 6 208.64 23.59 20.23 488.89 40.27 35.2 8 591.46 47.43 31.37 1474.05 76.23 48.73 10 1604.36 107.99 50.92 4550.47 188.3 78.41 12 4212.48 245.71 88.16 14129.42 479.64 134.47 Max States in Memory L UCS A*1 A*2 ID IDA*1 IDA*2 2 13.23 6.1 6.1 3.0 3.0 3.0 4 42.27 9.9 9.64 5.0 5.0 5.0 6 130.98 16.78 14.49 7.0 7.0 7.0 8 359.47 31.98 21.59 9.0 9.0 9.0 10 955.46 69.69 33.85 11.0 11.0 11.0 12 2496.36 154.07 56.77 13.0 13.0 13.0

Above is the results of my program

1) Describe in words the relative pattern of number of expanded states for Uniform Cost Search (UCS) and A* with the two different heuristics.

Why do we find that pattern? Thank you