Part 1
Note: Answer to each question should be accompanied with the correctness argument and analysis for time complexity
1. Given an array a[0, , n-1] of n nonzero integers ordered in the ascending order, develop an algorithm to remove all duplicates by replacing a duplicate with 0 value; the algorithm should also return the effective size of the output array. An instance of an ordered array before duplicate removal is: |2|2|4|8|8|23|37|37|42|. After the duplicate removal we have the following array: |2|4|8|23|37|42|0|0|0 with an effective size of this output array to be 6.
2. Given a randomly ordered array of n elements partition the elements into two subsets such that elements less than x are in one subset and elements greater than x are in separate subset. For instance, |28|26|25|11|16|12|24|29|6|10| and x = 17 lead to the array |10|6|12|11|16|25|24|29|26|28|. We provide here a high level algorithmic description of the problem.
• Establish the array a[0, ..., n − 1] and the partitioning value x.
• Move the partitions towards each other until the wrongly placed elements are encountered.
Allow for special cases such as x being outside the range of array values.
• While the two partitions have not crossed over
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