Explain why the statement, "The running time of algorithm A is at least O (n2)," is meaningless.
Answer to relevant QuestionsIs 2n+1 = O (2n’’)? Is 22n = O (2n’’)?Suppose that you want to output 0 with probability 1/2 and 1 with probability 1/2. At your disposal is a procedure BIASED-RANDOM, that outputs either 0 or 1. It outputs 1 with some probability p and 0 with probability 1 - p, ...Suppose that instead of swapping element A[i] with a random element from the subarray A[i ..n], we swapped it with a random element from anywhere in the array: PERMUTE-WITH-ALL (A) 1 n ← length [A] 2 for i ...Illustrate the operation of MAX-HEAP-INSERT (A, 10) on the heap A = 15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1. Use the heap of Figure 6.5 as a model for the HEAP-INCREASE-KEY call.Use induction to prove that radix sort works. Where does your proof need the assumption that the intermediate sort is stable?
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