2. Use Prim's algorithm to find the minimum spanning tree for the graph below starting from node a: S 18 59 17 32 10. 45 b 25 12 28 10 3. Given n d-digit numbers in which each digit can take up to k possible values, prove that Radix Sort correctly sorts these numbers in (d(n+k)) time if the stable sort it uses takes e(n+k) time. 4. Show the comparisons that the Nave String Matcher algorithm makes for the pattern P = 0001 in the text T=000010001010001.