Problem Introduction The dot product of two sequences \(a_1,a_2,\cdots,a_n\) and \(b_1,b_2,\cdots,b_n\) of the same length is equal to \(\sum\limits_{i=1}^na_ib_i=a_1b_1+a_2b_2+\cdots+a_nb_n\) Problem Description Task.The goal is,given two sequences…

Problem Description Task.Given a sequence of non-negative integers \(a_0, ..., a_{n-1}\),find the maximum pairwise product,that is,the largest integer that can be obtained by multiplying two different elements from the sequence(or,more formally,\(\ma…

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 You are given a set of segments on a line and your goal is to mark as few points on a line as possible so that each segment contains at least one marked point. Problem Description Task.Given a set of n segments \(\{ [a_0, b_0], […

Problem Introduction In this problem,you will design an algorithm for changing money optimally. Problem Description Task.The goal in this problem is to find the minimum number of coins needed to change the input value(an integer) into coins with deno…

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 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 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…