Question

1. Write a Java program to implement Counting Sort and write a driver to test it. Note: use
random number generator to generate your input with n = 10, 50, and 100. Verify that
the running time is O(n).

2. Write a Java program to implement Bucket Sort and write a driver to test it. Note: use
random number generator to generate your input with n = 10, 50, and 100. Verify that
the running time is O(n).

3. In this assignment you will investigate three different variants of algorithms that we have
discussed in the class to solve the selection problem.

Version 1. “Simultaneous minimum and maximum” selection algorithm.
Version 2. Randomized selection algorithm.
Version 3. “Median of Medians” selection algorithm.

Each version should be:
1. Run once on a small size array (say n = 16) with voluminous output at each stage, as a
correctness check.
2. Run 10 times each on arrays of size 50, 100, 200, and 400 on random input. You should
include a counter in each version to count a) comparisons and b) swaps for each version
and each size, find the mean and maximum of your statistics.
3. Repeat part 2 on “almost sorted” arrays. To produce an almost sorted array of size n:

a. Initialize a[ i ] as i;
b. Do n/50 times: randomly choose indices i, j and swap the ith and jth array elements.
Tabulate your results, and draw whatever conclusions you think are appropriate

can some one please give me the answer to third part ?

Answer 1

1)

import java.util.Random;

class CountingSort

{

void sort(char arr[])

{

int n = arr.length;

char output[] = new char[n];

int count[] = new int[256];

for (int i=0; i<256; ++i)

count[i] = 0;

for (int i=0; i<n; ++i)

++count[arr[i]];

for (int i=1; i<=255; ++i)

count[i] += count[i-1];

for (int i = n-1; i>=0; i--)

{

output[count[arr[i]]-1] = arr[i];

--count[arr[i]];

}

for (int i = 0; i<n; ++i)

arr[i] = output[i];

}

}

public class Main {

public static char[] getRandomArray(int n) {

char arr[] = new char[n];

Random rand = new Random();

for (int i=0; i<n; i++) {

arr[i] = (char) (rand.nextInt(26) + 'a');

}

return arr;

}

public static void main(String args[])

{

CountingSort ob = new CountingSort();

char arr[] = getRandomArray(10);

long start = System.currentTimeMillis();

ob.sort(arr);

long end = System.currentTimeMillis();

System.out.println("Time taken for arr of size 10 is: " + (end - start) + "ms");

arr = getRandomArray(50);

start = System.currentTimeMillis();

ob.sort(arr);

end = System.currentTimeMillis();

System.out.println("Time taken for arr of size 50 is: " + (end - start) + "ms");

arr = getRandomArray(100);

start = System.currentTimeMillis();

ob.sort(arr);

end = System.currentTimeMillis();

System.out.println("Time taken for arr of size 100 is: " + (end - start) + "ms");

}

}

NOTE: As per Chegg policy I am allowed to answer specific number of questions (including sub-parts) on a single post. Kindly post the remaining questions separately and I will try to answer them. Sorry for the inconvenience caused.