Problem Introduction This problem is about implementing an algorithm for the knapsack without repetitions problem. Problem Description Task.In this problem, you are given a set of bars of gold and your goal is to take as much gold as possible into yo…

Problem Introduction In this problem, your goal is to compute the length of a longest common subsequence of three sequences. Problem Description Task.Given three sequences \(A=(a_1,a_2,\cdots,a_n)\); \(B = (b_1, b_2,\cdots,b_m)\), and \(C=(c_1,c_2,\c…

Problem Introduction In the problem, your goal is to add parentheses to a given arithmetic expression to maximize its value. Problem Description Task.Find the maximum value of an arithmetic expression by specifying the order of applying its arithmeti…

Problem Introduction The edit distinct between two strings is the minimum number of insertions, deletions and mismatches in an alignment of two strings. Problem Description Task.The goal of this problem is to implement the algorithm for computing the…

Problem Introduction You are given a primitive calculator that can perform the following three operations with the current number \(x\): multiply \(x\) by 2, multiply \(x\) by 3, or add 1 to \(x\). Your goal is given a positive integer \(n\), find th…

Problem Introduction The goal in this problem is given a set of segments on a line and a set of points on a line, to count, for each point, the number of segments which contain it. Problem Description Task.In this problem you are given a set of point…

Problem Introduction An inversion of a sequence \(a_0,a_1,\cdots,a_{n-1}\) is a pair of indices \(0 \leq i < j < n\) such that \(a_i>a_j\). The number of inversions of a sequence in some sense measures how close the sequence is to being sorted. F…

Problem Introduction The goal in this problem is to redesign a given implementation of the randomized quick sort algorithm so that it works fast even on sequences containing many equal elements. Problem Description Task.To force the given implementat…

Problem Introduction An element of a sequence of length \(n\) is called a majority element if it appears in the sequence strictly more than \(n/2\) times. Problem Description Task.The goal in this code problem is to check whether an input sequence co…

Problem Introduction In this problem, you will implemented the binary search algorithm that allows searching very efficiently(even huge) lists provided that the list is sorted. Problem Description Task.The goal in this code problem is to implement th…