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

This program reads a file called 'test.txt'. you are required to write two functions that build a wordlist out of all of the words found in the file and print all of the unique words found in the file. remove punctuations using 'string.punctuation' and 'strip()' before adding words to the wordlist. write a function build_wordlist() that takes a 'file pointer' as an argument and reads the contents, builds the wordlist after removing punctuations, and then returns the wordlist. another function find_unique() will take this wordlist as a parameter and return another wordlist comprising of all unique words found in the wordlist. example: contents of 'test.txt': test file another line in the test file output: ['another', 'file', 'in', 'line', 'test', 'the']

What key should you press and hold to select and open multiple files at one time? enter alt control esc

In excel - calculate the actual increase/decrease from first quarter to the second quarter then subtract subtract first quarter value from second quarter total then divide result by first quarter value