For the following set of points, describe how the CLOSET-PAIR algorithm finds a closest pair of points:
(1,2),(2,−1),(3,−3),(3,2),(−3,4),(−1,2),(2,3),(1,1),(−5,−2).
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Using bipartite checking algorithm find out whether the graph given below is bipartite or not.
Write an algorithm to find the first two largest numbers in an in array of integers. For example, given the input ,2 ,3 ,7 − ,4 ,1,5 the algorithm should output ,7 .5 State precisely a loop invariant for you algorithm. Prove that your loop invariant holds and hence conclude that your algorithm works.
Analyse the algorithm to find the upper bound for run time of the above algorith.
Construct a MAXHEAP tree on the following list of numbers
15, 22, 7, 10, 43, 52 13, 16,
Apply DFS algorithm to find a spanning tree of the following graph. Also find all the fundamental cycles of the spanning tree.
Construct the Huffman code tree for the set of frequencies in the table below:
| Character | Frequency |
| A | 5 |
| B | 1 |
| C | 6 |
| D | 3 |
| E | 4 |
With the help of an example, explain the following:
i) Algorithm,
ii) Input and output for an algorithm
iii) Running time of an algorithm (5)
b) Illustrate the operations of partition in quick sort on the array
.