Construct a binary search tree with the following keys, inserting them in the given order:
110, 8, 19, 6, 9, 12, 32.
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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
.
Using bipartite checking algorithm find out whether the graph given below is bipartite or not.
Apply DFS algorithm to find a spanning tree of the following graph. Also find all the fundamental cycles of the spanning tree.
Analyse the algorithm to find the upper bound for run time of the above algorith.
Use Kruskal's algorithm to find a minimal spanning tree in the graph given below
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.
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.