What is the expected speedup of a recursive algorithm with runtime (2") to a dynamic programming solution with a one-dimensional array as a memoization structure? ○ 0((log n)²) ○ O(n²) O(n) ○ O(n log n)

If |V| = n and |E| = m, the running time complexity for Dijkstra's algorithm if implemented by an array is    Question 28 options:   O(n+m)   O(nm)   O(nlogm)   O(n^2)

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

Explain the complete work !

Given the following recursive function T(n) in master-form recurrence, apply Master Theorem to compute the complexity class Big-Oh and select the correct option: T(n) = 2T(n/4) + n+1 O O(log n) O O(n log n) O (n) O O(n^2) O none of these options

Consider the following recursive algorithm, where // denotes integer division: 3//2 = 1, 5//2 = 2, etc. F(n):if n <= 1:    returnF(n//2)for i from 0 to n    for j from 0 to n//2        print(i+j)    Let function T(n) denote the running time of this algorithm. Derive T(n) and prove its worst case timecomplexity

What is the running time of the following piece of code for a given integer n: x=2; while(x