Remarks: In all the algorithms, always explain (more precisely try to prove) the correct- ness of your algorithm You Always Must analyze the running time of any algorithm. The time complexity should be as small as possible. A correct algorithm with large complexity, may not get full credit. Do EVEN THINK OF WRITING PROGRAMS. The Rollo Thomasi legacy: work alone. Question 4: If in Quicksort every partition of an array of size m has at least m/20 elements in every side, what is the running time of the algorithm? Question 5: 1. What needs to happen for the maximum and minimum to be compared in Quick- sort. 2. Is the following true or false and try to prove it. Let A be the i'th smallest number in an array, and let A.+1 be the (i+1) - th smaller number in an array. Then in every algorithm based on comparisons A, and Au must be compared. 3. Answer yes or no and explain: If there are i