The amortized time efficiency for performing deletion of a minimum element is? a) O(N) b) O(log N) c) O(N2) d) O(M log N)
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The amortized time efficiency for performing deletion of a minimum element is?
a) O(N)
b) O(log N)
c) O(N2)
d) O(M log N)
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- Merge sort is an efficient sorting algorithm with a time complexity of O(n log n). This means that as the number of elements (chocolates or students) increases significantly, the efficiency of merge sort remains relatively stable compared to other sorting algorithms. Merge sort achieves this efficiency by recursively dividing the input array into smaller sub-arrays, sorting them individually, and then merging them back together. The efficiency of merge sort is primarily determined by its time complexity, which is , where n is the number of elements in the array. This time complexity indicates that the time taken by merge sort grows logarithmically with the size of the input array. Therefore, even as the number of chocolates or students increases significantly, merge sort maintains its relatively efficient performance. Regarding the distribution of a given set of x to y using iterative and recursive functions, the complexity analysis depends on the specific implementation of each…Solve the following recurrences assuming that T(n) = Θ(1) for n ≤ 1. a) T (n) = 3T (n/π) + n/π b) T(n) = T(log n) + log nFor each question, an algorithm will be described that operates on N elements, and your answer should include: (a) a big-O expression that describes the total number of operations in the worst case (for ex- ample, O(N³)) (b) a description of how to achieve the same effect as the algorithm described, but achieved with a better big-O time bound (for example, "use mergesort instead of insertion sort") (c) the big-O time bound for your improved approach. Your improved algorithm does not need to be provably the best possible, but it should have a different and better big-O bound. (It may not be as simple as substituting one named algorithm for another; consider what is redundant about the work done by the existing algorithm.) You don't need to use pseudocode to describe your algorithms - the style used in the problem descriptions is also sufficient for your solutions. You can use pseudocode if you like. Do not write real code. If you wish to use an algorithm described in class, you can name…
- Sort the following functions in terms of asymptotic growth from smallest to largest. In particular, the resulting order should be such that f₁ =0(f₂), f₂=0 (f 3), and so on. 1 2 I I I - ✓ 3" ✓ log (23) 14 1 1010 n 11/10 ✓ nln(12n) ✓ 52! ✓ log_²(n) ✓20200.1Consider the following recurrence: T(1)=1; T(n) = 2.T()+n, for n> 1, n a power of 3. =..... Find T(27) by substitution, starting with n = 1, n = 65 2 169 29 15 611. Show that lower order terms don't matter in the O() notation by showing that if g(n) = O(f(n)) then g(n) + f(n) = O(f(n)).
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