Cs 6515 - Study guides, Class notes & Summaries

CS 6515 FINAL EXAM ACTUAL COMPLETE 90 QUESTIONS AND CORRECT DETAILED ANSWERS (VERIFIED ANSWERS) WITH RATIONALES |ALREADY GRADED A+||BRAND NEW VERSION!!.

CS 6515 Algos Test 3 with complete solution

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 the class of NP problems 2. Demonstrate that problem B is at least as hard as a problem believed to be NP-Complete*. This is done via reduction from a known problem A (A→B) 2a. Show how an inst...

Kite Reduction Prove Kite is in np by verifying that - check for the clique - O(n^2) - check for the tail of degree <= 2 nodes O(n) - check for that the tail is connected to the clique with Explore (O(n) Reduce Clique to kite by adding a tail of length g to each vertex in graph G O(n^2) Transform back to Clique by removing all vertexs of degree <= 2 (prune the tails) If there is no solution to kite then there is no clique in G If there is a solution to kite, removin...

How can you find how many numbers between 1 and x are relatively prime with x. - Answer-For a number to be relatively prime it must share no common factors aside from 1 (gcd(a,b)=1). Thus, first we factor x to find if it has any factors. Then we know if a factor is shared it would have to be these ones, so we can check the factors and multiples of the factors, counting up the number of matches as we go. Then subtract the number of matches from (x-1) and you have the answer. Other numbers ca...

Quick Sort Runtime O(n^2) O(nlogn) with median of medians Merge Sort Runtime O(nlogn) Quick Select Runtime O(n^2) O(n) with median of medians (Fast select) Dijkstra's algorithm An algorithm for finding the shortest paths between nodes in a weighted graph. For a given source node in the graph, the algorithm finds the shortest path between that node and every other. It can also be used for finding the shortest paths from a single node to a single destination node by stoppin...

D&C Steps 1. Figure out your Black Box if needed. ○ Sorted = Binary Search (usually) ○ Unsorted = Merge sort (usually) ○ Polynomials, convolution, multiplication = FFT(usually) 2. State the Modification if needed. You may use the blackbox as is. ○ Which part of the black box you are changing. ○ What are your inputs and outputs to the black box. 3. State the steps of your algorithm. ○ NO PSEUDOCODE - use words ○ Must include base case(s) if needed. ○ Always r...

CS-6515 Algorithms with complete solution