Problem 1 (20 points). For each of the following questions indicate whether the statement is true or false. No explanations are required. 1. 2 (2+2) 2. log(n!) (n1gn) 4. The average-case running time of Quick-sort is (n). 5. In the worst-case Merge-sort is an asymptotically faster algorithm than Quick-sort. 6. If the input array A consists of distinct numbers and A is stored as a heap (Max- Heap). then the 2nd largest element in A will be stored either in A[2) or Al3) 7. Heapsort is stable. 8. Quicksort is an in-place sorting algorithm. 9. The worst case running time of any sorting algorithm is (n lg n). 10. The running time of best case of heapsort algorithm is e(nlgn) when the inputs are al distinct. ane and arrange them nd arrange them in ascending order