12. Arrays Exercises 3

Compactor

Given an array of integers nums, return an array containing only the indices k for which nums[k] is one.

Example: compactor({1,0,1,1}) => {0,2,3}.

Example:

{//               0 1 2 3 4 5 6 7
    int[] nums = {0,0,1,0,1,0,0,1};
    int[] cpct = compactor(nums);
    int[] expected = {2,4,7};
}

Prime Number Sieve

Write a function public static int[] primeSieve (int n) that returns an array of length n with a 1 in index k when k is a prime number, and 0 otherwise.

Use some tester code to show the results of your function.

Recommended process:

1. Mark every number that is at least two as prime. Run your function and make sure that at this stage primeSieve(10) gives {0,0,1,1,1,1,1,1,1,1}.

2. Change every multiple of 2 to a zero. At this stage, primeSieve(10) should give {0,0,1,1,0,1,0,1,0,1}.

3. Automate the process of giving multiples a value of zero for every other number.

Prime Factorization

Use the tools you have to write a program to find the prime factorization of a number. It is OK to limit your program to working with numbers with less than 20 factors.

Signature: public static int[] pf (int n).

Examples:

• pf(8) => {2,2,2}
• pf(18) => {2,3,3}