You are givenn items sorted based on hi ratio and the knapsack capacity is W. Now, what is the time complexity of fractional knapsack problem? O(n log n) O(n) O(n*n) O(nW) You are given 4 items as {value, weight} pairs in this format {{20, 5}, {60, 20},{25, 10}, {X,25}}. You can assume that the array is sorted ratio. The capacity of knapsack is 39. The item no. 4 (whose weight is 25 ) is taken fractionally to fill upto the knapsack value weight based on the capacity. That fraction is represented in format. What is the lowest possible value of a?
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- Note: Your solution should have O(n) time complexity, where n is the number of elements in l, and O(1) additional space complexity, since this is what you would be asked to accomplish in an interview. Given a linked list l, reverse its nodes k at a time and return the modified list. k is a positive integer that is less than or equal to the length of l. If the number of nodes in the linked list is not a multiple of k, then the nodes that are left out at the end should remain as-is. You may not alter the values in the nodes - only the nodes themselves can be changed.Let X(1..n) and Y(1..n) contain two lists of n integers, each sorted in nondecreasingorder. Give the best (worst-case complexity) algorithm that you can think for finding(a) the largest integer of all 2n combined elements.(b) the second largest integer of all 2n combined elements.(c) the median (or the nth smallest integer) of all 2n combined elements.For instance, X = (4, 7, 8, 9, 12) and Y = (1, 2, 5, 9, 10), then median = 7, the nthsmallest, in the combined list (1, 2, 4, 5, 7, 8, 9, 9, 10, 12). [Hint: use the conceptsimilar to binary search]The time complexity equation of merger-sort is T(n) = 2* T(n/2) + n, where T(1) = C and C is a constant. Solve this equation by giving detailed steps. If you have an equation like the following T(n) = 3* T(n/3) + n, where T(1)=T(2)=C, what would be T(n)?
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- In the sequence alignment problem, suppose you knew that the input strings were relatively similar, in the sense that there is an optimal alignment that uses at most k gaps, where k is much smaller than the lengths m and n of the strings. Show how to compute the NW score in O((m+n)k) time.we consider a problem where we are given a set of coins andour task is to form a sum of money n using the coins. The values of the coins arecoins = {c1, c2,..., ck}, and each coin can be used as many times we want. Whatis the minimum number of coins needed?For example, if the coins are the euro coins (in cents){1,2,5,10,20,50,100,200}and n = 520, we need at least four coins. The optimal solution is to select coins200+200+100+20 whose sum is 520.Consider the LCS problem discussed in class. Suppose we only want to compute the length of the LCS of x[1..m] and y[1..n] (i.e. we do not care about the actual subsequence itself). This means we do not need to “traceback” to find the LCS. In this setting, show how the algorithm can be altered so that it only needs min(m,n) + O(1) space rather than m · n space (note that it must be min(m,n) and not O(min(m, n))).
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