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Median Finding and Quick Sort. Suvarna Angal. Project Requirements. Implement the median-finding algorithms – Random and Linear Median Finding Algorithms. The user is able to select the “k”, i.e., the rank of the number desired as output (k = n/2 is the median).

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project requirements
Project Requirements
  • Implement the median-finding algorithms – Random and Linear Median Finding Algorithms.
  • The user is able to select the “k”, i.e., the rank of the number desired as output (k = n/2 is the median).
  • The user is also able to select groups of 3 or 5 in the linear-time median finding algorithm.
project requirements3
Project Requirements
  • The user can compare the performance of Random and Linear Median Finding Algorithms.
  • Implement quick sort using both algorithms and compare the performances of these different versions.
randomized median finding
Randomized Median Finding
  • QSel(S,k)
  • m = a random element of S is the pivot.
  • S1 = all numbers in S < m
  • S2 = all numbers in S > m
  • if |S1| >= k return Qsel(S1,k);

else if |S| - |S2| >= k return m;

else return Qsel(S2,k-|S|+|S2|);

median finding
Median Finding
  • The difference with this approach is about the pivot selection.
  • To find the pivot element, we divide S into n/5 groups of 5 elements each.
  • Each group is then sorted and its median is selected.
  • Then invoke a recursive call to the same function to find median of medians.
median finding6
Median Finding
  • Then this median of medians becomes the pivot element for the QSel function.
  • This will find the k-th smallest element in a sequence S of n elements in worst-case time O(n).
implementation
Implementation
  • The project is implemented in java.
  • The User Interface is done using Java Swing- MedianClient.java
  • This takes a list of numbers, k and number of elements in a group as input.
  • 4 classes – MedianQuickSort.java, MedianRandomQuickSort.java, Median.java, and MedianRandom.java are written.
analysis
Analysis
  • Used simple counter to measure performance.
  • Checked performance for varying input sizes like 100, 1000 and 10000 for all 4 algortihms.
  • Also changed the group size 3 or 5 for the Linear Median Finding Algorithm.