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The characters a to h have the set of frequencies based on the first 8 Fibonacci numbers as follows
a : 1, b : 1, c : 2, d : 3, e : 5, f : 8, g : 13, h : 21
A Huffman code is used to represent the characters. What is the sequence of characters corresponding to the following code? 110111100111010
  • a)
    fdheg
  • b)
    ecgdf
  • c)
    dchfg
  • d)
    fehdg
Correct answer is option 'A'. Can you explain this answer?
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The characters a to h have the set of frequencies based on the first 8...
Background Required -  Generating Prefix codes using Huffman Coding. First we apply greedy algorithm on the frequencies of the characters to generate the binary tree as shown in the Figure given below. Assigning 0 to the left edge and 1 to the right edge, prefix codes for the characters are as below.
a - 1111110
b - 1111111
c - 111110
d - 11110
e - 1110
f - 110
g - 10
h - 0
Given String can be decomposed as 110 11110 0 1110 10 fdheg
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Most Upvoted Answer
The characters a to h have the set of frequencies based on the first 8...
Explanation:

  • The given set of frequencies can be arranged in ascending order as follows:


    • a : 1, b : 1, c : 2, d : 3, e : 5, f : 8, g : 13, h : 21


  • Now we need to construct a Huffman code based on these frequencies.

  • To do that, we first need to construct a Huffman tree.

  • The steps to construct a Huffman tree are as follows:


    • Arrange the characters in ascending order of their frequencies.

    • Take the two characters with the lowest frequencies and merge them to form a new node with a frequency equal to the sum of their frequencies.

    • Add this new node to the list of characters in ascending order of their frequencies.

    • Repeat steps 2 and 3 until there is only one node left in the list. This node is the root of the Huffman tree.


  • The Huffman tree for the given set of frequencies is shown below:


    • https://i.imgur.com/7ncknFJ.png


  • Now we can assign codes to each character based on their position in the Huffman tree.

  • The codes for each character are as follows:


    • a: 110

    • b: 1111

    • c: 00

    • d: 10

    • e: 01

    • f: 1110

    • g: 1101

    • h: 101


  • Using these codes, we can decode the given sequence as follows:


    • 110 1110 10 01 1101 1111 00 10

    • fdhegb


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The procedure given below is required to find and replace certain characters inside an input character string supplied in array A. The characters to be replaced are supplied in array oldc, while their respective replacement characters are supplied in array newc. Array A has a fixed length of five characters, while arrays oldc and newc contain three characters each.However, the procedure is flawed.void find_and_replace (char *A, char *oldc, char *new c) {for (int i=0; i5; i++)for (int j=0; j3; j++)if (A[i] == oldc[j])A[i] = newc[j];}The procedure is tested with the following four test cases.(1) oldc = abc, newc = dab (2) oldc = cde, newc = bcd(3) oldc = bca, newc = cda (4) oldc = abc, newc = bacThe tester now tests the program on all input strings of length five consisting of characters a, b, c, d and e with duplicates allowed. If the tester carries out this testing with the four test cases given above, how many test cases will be able to capture the flaw?

The procedure given below is required to find and replace certain characters inside an input character string supplied in array A. The characters to be replaced are supplied in array oldc, while their respective replacement characters are supplied in array newc. Array A has a fixed length of five characters, while arrays oldc and newc contain three characters each.However, the procedure is flawed.void find_and_replace (char *A, char *oldc, char *new c) { for (int i=0; i5; i++) for (int j=0; j3; j++) if (A[i] == oldc[j]) A[i] = newc[j];}The procedure is tested with the following four test cases.(1) oldc = abc, newc = dab (2) oldc = cde, newc = bcd(3) oldc = bca, newc = cda (4) oldc = abc, newc = bacIf array A is made to hold the string abcde, which of the above four test cases will be successful in exposing the flaw in this procedure?

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The characters a to h have the set of frequencies based on the first 8 Fibonacci numbers as followsa : 1, b : 1, c : 2, d : 3, e : 5, f : 8, g : 13, h : 21A Huffman code is used to represent the characters. What is the sequence of characters corresponding to the following code? 110111100111010a)fdhegb)ecgdfc)dchfgd)fehdgCorrect answer is option 'A'. Can you explain this answer?
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