Questions and Answers
What is the initial state of the trees in the Huffman coding algorithm?
There are C single-node trees—one for each character.
What is the purpose of the Divide step in the Divide and Conquer algorithm?
To solve smaller problems recursively.
What is the condition to select two trees in the Huffman coding algorithm?
The two trees with the smallest weight, breaking ties arbitrarily.
What is the result of the Huffman coding algorithm?
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What is the weight of a tree in the Huffman coding algorithm?
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How are the solutions to the subproblems combined in the Divide and Conquer algorithm?
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What is the purpose of the Conquer step in the Divide and Conquer algorithm?
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What is the role of the base case in the Divide and Conquer algorithm?
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How many times does the Huffman coding algorithm select the two trees with the smallest weight?
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What is the main difference between the Huffman coding algorithm and the Divide and Conquer algorithm?
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Study Notes
Hash Table and Hash Function
- A hash table is a data structure that maps keys to indices of a backing array using a hash function.
- Linear probing is a collision resolution technique that searches for the next available slot in the array.
- If the end of the array is reached, the search wraps around to the beginning of the array.
- Quadratic probing is another collision resolution technique that uses a quadratic formula to find the next available slot.
Hash Table Examples
- Example 1: Inserting keys (11, 85, 77, 10, 35) into a hash table with a table size of 10.
- The hash function is key modulo table size.
- Collisions are resolved using quadratic probing.
- Example 2: Inserting keys (99, 28, 88) into a hash table with a table size of 10.
- The same hash function and collision resolution technique are used.
Double Hashing
- Double hashing is a technique that uses two hash functions to probe for an available slot.
- The first hash function determines the initial index, and the second hash function determines the increment for the probe sequence.
- The increment should never be zero, and all cells in the table should be probed.
Quicksort
- Quicksort is a sorting algorithm that uses a partitioning strategy to divide the array into smaller subarrays.
- The partitioning strategy involves swapping the pivot element with the last element, and then moving a "wall" of elements smaller than the pivot to the left and a "wall" of elements larger than the pivot to the right.
- The algorithm repeats the partitioning process until the entire array is sorted.
External Sorting
- External sorting is a technique used when the input data does not fit into main memory.
- Previous algorithms, such as Shellsort and Quicksort, require that the input fit into main memory.
Dijkstra's Algorithm
- Dijkstra's algorithm is a graph search algorithm used to find the shortest path between nodes in a graph.
Huffman's Algorithm
- Huffman's algorithm is a greedy algorithm used to construct an optimal prefix code.
- The algorithm maintains a forest of trees, where each tree represents a character in the input data.
- The algorithm repeatedly selects the two trees of smallest weight, combines them into a new tree, and updates the weights of the remaining trees.
Divide and Conquer
- Divide and Conquer is a algorithm design paradigm that breaks down a complex problem into smaller sub-problems.
- The algorithm solves each sub-problem recursively, and then combines the solutions to the sub-problems to form the solution to the original problem.
