Write an algorithm called ArrayColumnSum(A[0..n-1, 0..n-1], B[0..n-1 ]) which takes as input, one n x n matrix A and a list B of size n and outputs B such that B[k] as the sum of the elements of column k of A.

What is the return value if B = {1, 3, 5}? Algorithm Ex5(A): Input: Arrays A and B each storing n ≥ 1 integers. Output: The number of elements in B equal to the sum of the prefix sums in A. c ← 0 for i ← 0 to n - 1 do       s ← 0      for j ← 0 to i do            s ← s + A[0]            for k ← 1 to j do                  s ← s + A[k]      if B[i] = s then           c ← c + 1 return c

Algorthim of how to find the largest element missing in an unsorted array of n positive  integers and the running time of the algorthim is in O(n).  Example of this is that the n=6 array C= [5,90,8,6,26,9] The largest element missing in the array is 7

Consider this alogrithm:// pre: array A of length n, each A[i] is picked randomly uniformly// from the set {0,1,2,3,4,5,6,7,8,9}.// post: return the index of the first occurrence of "check digit" of A// (already computed in the code)// return -1 if check digit is not foundint FindCheckDigit(A) {check_digit = 0for (i=0; i < n; i++)     check_digit = check_digit + A[i]check_digit = check_digit % 10 # % means remainder of divisionfor (i = 0; i < n; i++) {     if (A[i] == check_digit) {          return i     }}return -1;}Compute the average runtime for this algorithm. Show all details of your computation for both loops.

Given A[1...n] which is an increasingly sorted array of distinct positive integers, and t which is an integer; provide an O(n) algorithm deciding whether A contains two distinct elements x and y such that x + y = t.

Let A[1, ., n] be a sorted array of distinct integers. Write an efficient algorithm with proper pseudocode for finding whether an element exists such that: A[i] i, for 1 <= i <= n. (i.e., an element whose index and value are both equal to 'i'). ==

Now let's examine a Dynamic Program algorithm to solve this problem. 3.3 Let's say we have an array of length X+1. How would we define array[x]? or What is array[x] defined for?

Consider the following problem:L is a sorted list containing n signed integers (n being big enough), for example [-5, -2, -1, 0, 1, 2, 4] (here, nhas a value of 7). If L is known to contain the integer 0, how can you find the index of 0 ?

Consider the following algorithm that uses a sorted list of n elements (alist). What is the worst case runtime of this algorithm? for each element in alist    1. ask the user for an input, call it value    2. search value in alist using binary search    3. if value exists in alist, print "successful"       otherwise print "unsuccessful"      Question options: a. O(log n) b. O(n) c. O(n log n) d. O(2^n) e. O(n^2) f. O(1)

Given an unsorted array of integers, write a function in Python to find the length of the longest increasing subsequence (LIS) in the array. For example, given the array [10, 9, 2, 5, 3, 7, 101, 18], the LIS is [2, 3, 7, 101], which has a length of 4. Your solution should have a time complexity of O(n log n), where n is the length of the input array. Here's some code to get you started: def longest increasing_subsequence(arr): # TODO: implement function pass # example usage arr = [10, 9, 2, 5, 3, 7, 101, 18] print(longest_increasing_subsequence(arr)) # should print 4