Comparing map performance with different underlying data structures
In this assignment, you will implement the map ADT using the following underlying data structures:
1) BST (binary search tree)
2) Hash table (separate chaining)
3) Hash table (linear probing)
4) Skip list
You may use the hash table implementations from the notes (lecture 16 and 17). Base your BST code on the pseudocode in lecture 14 notes. Base your skip list code on the pseudocode from lecture 18 notes.
The operations supported by map ADT are below:
Your goal is to implement these operations using the 4 data structures listed above (BST, hash tables, and skip list). you can omit the iter operation because we did not cover this in class. Also, this is not an ordered map ADT, so the hash tables should perform better (skip list and BST can be used for unordered and ordered map implementations, while hash table is used exclusively for unordered map).
The hash table should provide (1) performance for all map operations. Skip list and BST should provide ( ) performance for [ ], [ ] = , and [ ]. Your job is to verify these time complexities by 1) implementing the map using the 4 data structures listed above and 2) performing timing experiments like you did in assignment 4 and plotting the resulting curves.
In addition to your code in .py format, you should provide a pdf showing the results of your timing experiments.
Timing experiments: Generate 10,000 random key-value pairs (keys can be anything that is comparable (float, string, int, etc.), value can be anything) and insert them into your map, getting the time for each insertion (before the first insertion, your map will have 0 elements, before the last insertion, your map will have 9,999 elements). Provide three plots in your pdf:
1) Number of elements on x-axis, time in ms on y-axis for M[k] = v operation (insertion). The plot should have 4 curves (red = BST, blue = separate chaining hash table, green = linear probing hash table, magenta = skip list).
2) Same as (1) but for M[k] operation (return value). Perform each M[k] operation after inserting the element (get the time it takes to access an element directly after inserting it), so you can have number of elements on the x-axis like in figure 1.
3) del M[k]. after inserting all your elements so your map has 10,000 elements, delete them one by one by using del M[k]. the x-axis of this plot is the number of elements and the y-axis is time, similar to figure 1 and 2 (use same color scheme also).
Comment on your plots. Do they show the expected O(log n) and O(1) for the BST/skip list and hash tables, respectively? Which hash table implementation (separate chaining or linear probing) is faster?
