# Question: Use mathematical induction to show that when n is an

Use mathematical induction to show that when n is an exact power of 2, the solution of the recurrence

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Insertion sort can be expressed as a recursive procedure as follows. In order to sort A [1 ¬ n], we recursively sort A [1 ¬n -1] and then insert A[n] into the sorted array A [1 ¬ ¬n – 1]. Write a ...Let f (n) and g (n) be asymptotically nonnegative functions. Using the basic definition of Θ- notation, prove that max (f (n), g (n)) = Θ (f (n) + g (n)).Use a recursion tree to give an asymptotically tight solution to the recurrence T(n) = T(αn) + T((1 - α)n) + cn, where α is a constant in the range 0 0 is also a constant.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 ...Show that the running time of QUICKSORT is Θ (n2) when the array A contains distinct elements and is sorted in decreasing order.Post your question