More reductions given an array a = [a1, a2, . . , an] of nonnegative integers, consider the following problems: 1 p partition: determine whether there is a subset p ⊆ [n] ([n] : = {1, 2, · · · , n}) such that i∈p ai = p j∈[n]\p aj 2 subset sum: given some integer k, determine whether there is a subset p ⊆ [n] such that p i∈p ai = k 3 knapsack: given some set of items each with weight wi and value vi , and fixed numbers w and v , determine whether there is some subset p ⊆ [n] such that p p i∈p wi ≤ w and i∈p vi ≥ v for each of the following clearly describe your reduction, justify runtime and correctness.
(a) find a linear time reduction from subset sum to partition.
(b) find a linear time reduction from subset sum to knapsack

4.11 painting a wall (1) prompt the user to input integers for a wall's height and width. calculate and output the wall's area (integer). note that in this case there is a new line after each prompt. (submit for 1 point). enter wall height (feet): 11 enter wall width (feet): 15 wall area: 165 square feet (2) extend to also calculate and output the amount of paint in gallons needed to paint the wall (floating point). assume a gallon of paint covers 350 square feet. store this value in a variable. output the amount of paint needed using the %f conversion specifier. (submit for 2 points, so 3 points total). enter wall height (feet): 11 enter wall width (feet): 15 wall area: 165 square feet paint needed: 0.471429 gallons (3) extend to also calculate and output the number of 1 gallon cans needed to paint the wall. hint: use a math function to round up to the nearest gallon. (submit for 2 points, so 5 points total). enter wall height (feet): 11 enter wall width (feet): 15 wall area: 165 square feet paint needed: 0.471429 gallons

Awide variety of “ apps “ are available to customize devices. which category of app does the word processing software fall into?

Which tab is used to change the theme of a photo album slide show? a. design b. view c. transitions d. home