In this question, you will construct the max heap that results from using BUILD-MAX-HEAP to create a heap from the following array:  . Step 1 is constructing the initial heap.  Fill in tree which results after constructing the initial heap below. [A5] / \ [A8] [A12] / \ / \ [A7] [A3] [A11] [A9] / \ / \ [A6] [A2] [A4] [A10]    

Use the Master Theorem to give tight asymptotic bounds for the following recurrence: T(n) = 3T(n/2) + n2log(n)

In this question, you will find the maximum subarray of the array A = [1, -2, 8, -25, 3, 4, -1, 3] using the θ(nlog(n)) divide and conquer algorithm discussed in class. Step 6: Use Master Theorem to demonstrate how the asymptotic bound θ(nlog(n)) is achieved for T(n) given in Step 5.  (Note: T(n) must be correct in order to receive credit in this step.)

Use the Master Theorem to give tight asymptotic bounds for the following recurrence: T(n) = 3T(n/2) + n2log(n)

Which of the following disorders is characterized by freckle-like pigmentations around the mouth and inside the oral cavity, including labial mucosa and gingiva?

Solve the problem. For the equation y = – 3cos(2x – 2π), identify (i) the amplitude, (ii) the phase shift, and (iii) the period. Graph one cycle of the function on your paper. Be sure to label each value of x on the x axis and each value of y on the y-axis.

Decide whether each of the following pairs of structures more likely represents analogy or homology, and explain your reasoning: a. a echidna’s quills and rose thorns; b. a bat’s wing and a human hand; c. a chicken’s wing and a butterfly’s wing.

Which of these is potential energy?

Which name is correct for AlF3?

Which of these is not an SI unit?