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 |
The frequencies are A=5, B=1, C=6, D=3, and E=4. First arrange them in increasing order: B(1), D(3), E(4), A(5), C(6). The two smallest are B(1) and D(3), so they are combined to form a node BD with weight 1+3=4. Now the set becomes BD(4), E(4), A(5), C(6). The two smallest are BD(4) ________ _____ ____ _____ ________ __________ ___.
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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
.
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).
Taking v1 as the root, find a spanning tree of the following graph using the breadth first search (BFS) algorithm.
Determine an LCS of (1, 1, 1, 1, 0, 1, 1, 0, 1, 0) and (1, 1, 1, 0, 0, 1, 1, 0, 1, 0).
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.
Construct a binary search tree with the following keys, inserting them in the given order:
110, 8, 19, 6, 9, 12, 32.
Using bipartite checking algorithm find out whether the graph given below is bipartite or not.
