Using bipartite checking algorithm find out whether the graph given below is bipartite or not.
Answer: The graph is *not bipartite*. ### Reasoning using the bipartite checking (2-coloring) algorithm A graph is bipartite iff it contains no odd-length cycle. _____ __________ __________ ______ ___.
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Show the minimum heap after each of the following operations
i) Create with values 13, 46, 68, 15, 87, 4, 33, 21, 1, 79.
ii) Insertion of value 9.
iii) Update of value 1 by 71.
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.
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 |
Taking v1 as the root, find a spanning tree of the following graph using the breadth first search (BFS) algorithm.
Use Dijkstra's algorithm to find the shortest paths in the graph given below with a as the source vertex.
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).
Apply DFS algorithm to find a spanning tree of the following graph. Also find all the fundamental cycles of the spanning tree.