Encoding word using given Huffman code tree, and other tree related problems.

[1] Encode "LEADEN" using the Huffman code tree given in the attachment. [2] What can you say about a vertex in a rooted tree that has no descendants? Please see the attachment for more tree related problems.

Find a minimal spanning tree (MST) for the given graph using Prim's algorithm.

Find a minimal spanning tree for the connected weighted graph, following Prim's algorithm. Please see attached 4.doc for the details on graph and Prim's algorithm for finding a minimal spanning tree.

Encode and decode strings using given Huffman code tree.

Using the Huffman code given in the attached image, (a) encode the string "NEEDLE". (b) decode the bit string "01111001001110".

Find the bad coin out of given 8 coins using only a pan balance.

Eight coins are identical in appearance, but one coin is either heavier or lighter than the others, which all weigh the same. Describe an algorithm that identifies the bad coin in at most three weighings and also determines whether it is heavier or lighter than the others, using only a pan balance.

Solve for coefficient.

When (x-2)^17 is expanded, what is the coefficient of x^12? Be careful, don’t forget about the –2.