CS-6515 Algorithms latest already passed

DFS outputs - ANSWER-pre array, post array, ccnum array, prev array BFS outputs - ANSWER-dist array, prev array Explore outputs - ANSWER-visited array. When to use Dijkstra's? - ANSWER-Works for both directed and undirected graphs. Must have only non-negative edge weights. Dijkstra's outputs ...

CS6515 Exam 3 questions and answers

CS6515 Exam 3 Study Guide questions and answers

Weak Duality Theorem Feasible x <= Feasible y where c^(zT) x <= b^(T) y. Here c^(T) means transpose and same for b^(T). Weak Duality Theorem Corollary 1 If Feasible x = Feasible y, they are optimums c^(T) x^(asterisk) = b^(T) y^(asterisk) . Weak Duality Theorem Corollary 2 If Primal/Dual...

Basic Properties of Trees - ANSWER-Tree's are undirected, connected and acyclic that connect all nodes. 1. Tree on n vertices has (n-1) edges -> would have a cycle otherwise (more than n-1 edges means cycle) 2. In tree exactly one path between every pair of vertices (otherwise it's not con...

CS6515 Exam 2 Questions and answers If graph G has more than |V | − 1 edges, and there is a unique heaviest edge, then this edge cannot be part of a minimum spanning tree - ANSWER-False, because the unique heaviest edge may not be part of a cycle If G has a cycle with a unique heaviest edge e,...

Knapsack without repetition - ANSWER-k(0) = 0 for w = 1 to W: if w_j >w: k(w,j) = k(w, j - 1) else: K(w,j) = max{K(w, j -1),K(w - w_j, j -1) + v_i} knapsack with repetition - ANSWER-knapsack repeat(w_i....w_n, w_i... w_n, B) k(0) = 0 for i = 1 to n if w_i <= b & k(b) <v_i + K(b-w_i) ...

In a DAG, what makes a pair of vertices strongly connected? - answer-There is a path `V→W` and `W→V` Conservation of flow - answer-The flow into a vertex V must me equal to the flow out of the vertex V What problems are in the class NP-Hard? - answer-Any problem to which any problem in NP c...

Traversing, reversing, copying, or otherwise working on the full graph running time - ANSWER-O(n+m) Checking, reading, or removing one vertex running time - ANSWER-O(1) Iterating, checking, reading, removing, or otherwise working on all vertices running time - ANSWER-O(n) Checking, reading, or ...

Equivalence - ANSWER-"x ≡ y (mod N) means that x/N and y/N have the same remainder a ≡ b (mod N) and c ≡ d (mod N) then: a + c ≡ a + d ≡ b + c ≡ b + d (mod N) a - c ≡ a - d ≡ b - c ≡ b - d (mod N) a ** c ≡ a ** d ≡ b ** c ≡ b ** d (mod N) ka ≡ kb (mod N) for any inte...

What is the running time for Longest Increasing Subsequence (LIS) - ANSWER-O(n^2) What is the recurrence for Longest Increasing Subsequence (LIS)? - ANSWER-L(i) = 1 + max{ L(j) | xj < xi} This reads as the answer to index I is 1 + the maximum over all j's between 1 and i where xj is less th...

How do you tell if a graph has negative edges? - ANSWER-when fitting graph on a table, if the number of moves decreases the w() from edge to edge, then there is a negative edge; check from 1 to n Why are all pairs Dist(y,z) n^2? - ANSWER-Because it builds a two dim table! What is the run time o...

Search Problem - ANSWER-A search problem is specified by an algorithm C that takes two inputs, an instance I and a proposed solution S, and runs in time polynomial in |I|. We say S is a solution to I if and only if C(I, S) = true Steps for an NP Proof - ANSWER-1. Demonstrate that problem B is in ...

Dynamic Programming Purpose - ANSWER-Used for optimization problems A set of choices must be made to get an optimal solution Find a solution with the optimal value (minimum or maximum) Dynamic Programming Applicability - ANSWER-Subproblems are not independent A divide-and-conquer approach would ...