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 Fibonacci numbers are defined as follows: \(F_0=0\), \(F_1=1\),and \(F_i=F_{i-1}+F_{i-2}\) for $ i \geq 2$. Problem Description Task.Given an integer \(n\),find the last digit of the \(n\)th Fibonacci number \(F_n\)(that is ,…

Problem Introduction The Fibonacci numbers are defined as follows: \(F_0=0\), \(F_1=1\),and \(F_i=F_{i-1}+F_{i-2}\) for $ i \geq 2$. Problem Description Task.Given an integer \(n\),find the \(n\)th Fibonacci number \(F_n\). Input Format.The input con…

Problem Introduction The Fibonacci numbers are defined as follows: \(F_0=0\), \(F_1=1\),and \(F_i=F_{i-1}+F_{i-2}\) for $ i \geq 2$. Problem Description Task.Given two integers \(n\) and \(m\), output \(F_n \ mod \ m\)(that is, the remainder of \(F_n…

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 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 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 This is an example of a problem where a subproblem of the corresponding greedy algorithm is slightly distinct from the initial problem. Problem Description Task.The goal of this problem is to represent a given positive integer \(…

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], […