A company manufacturing telemetry equipment has been asked to quote for a Remote Site Monitor. A telemetry monitor system is required to check periodically, the building main power supply, the site perimeter security, the building security system, the fire alarm system, the power supply to the transmitter equipment rack, the power supply to the receiver equipment rack, the cooling water pressure and a flood alarm system. Some of these checks are required more frequently than others and are in the ratio {0.01, 0.001, 0.08, 0.09, 0.18, 0.2, 0.23, 0.209} respectively.Design a Huffman code for a suitable command set.
Question
A company manufacturing telemetry equipment has been asked to quote for a Remote Site Monitor. A telemetry monitor system is required to check periodically, the building main power supply, the site perimeter security, the building security system, the fire alarm system, the power supply to the transmitter equipment rack, the power supply to the receiver equipment rack, the cooling water pressure and a flood alarm system. Some of these checks are required more frequently than others and are in the ratio {0.01, 0.001, 0.08, 0.09, 0.18, 0.2, 0.23, 0.209} respectively.Design a Huffman code for a suitable command set.
Solution
To design a Huffman code for a suitable command set, we first need to understand what a Huffman code is. A Huffman code is a particular type of optimal prefix code that is commonly used for lossless data compression. The process of creating a Huffman Tree or Huffman Code involves a priority queue (usually implemented as a min-heap), and has a time complexity of O(n log n).
Here are the steps to design a Huffman code:
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First, we need to create a node for each command with their frequency and add it to the priority queue. In this case, the frequencies are given as ratios, which are {0.01, 0.001, 0.08, 0.09, 0.18, 0.2, 0.23, 0.209}.
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Then, we create a new internal node, with the frequency equal to the sum of the two nodes with the smallest frequencies. This new node becomes the parent of the two nodes.
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We remove the two nodes from the priority queue and add the new node into the priority queue.
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We repeat steps 2 and 3 until only one node is left in the priority queue. This node is the root of the Huffman tree.
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Finally, we assign codes to each command according to their position in the Huffman tree. We assign '0' for left branch and '1' for right branch.
Please note that the Huffman code is not unique. Different ways of creating the Huffman tree can lead to different Huffman codes. However, all of them will have the same length and the same optimality.
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