
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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Transcribed Image Text:Dijkstra's single Shortest Path algorithm is an example of following type of algorithm
Divide and Conquer
Dynamic Programming
Greedy
Other
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- The algorithm of Euclid computes the greatest common divisor (GCD) of two integer numbers a and b. The following pseudo-code is the original version of this algorithm. Algorithm 1 Euclid1(a,b)Require: a, b > 0Ensure: a = GCD(a, b) while a ̸= b do if a > b then a ← a − b else b ← b − a end if end whilereturn a We want to prove the correctness of this algorithm using the loop invariant technique. a. In a first attempt to prove the correctness of this algorithm, we propose the following loop invariant property: “GCD(a, b) is a factor of a and b”. Explain why this property willnot help you as is. b. Use your previous observation to propose another loop invariant property that willhelp you to prove the correctness of the version of Euclid’s algorithm presented above. c. Show that your loop invariant property is true before executing the While loop forthe first time (i.e., initialization property)arrow_forwardUsing Pythonarrow_forwardQuestion 15 What is the complexity of Dijkstra's Algorithm for shortest path? O(IEI) O 0(티 log |V) O O(I\V) O O(IVI log JEI)arrow_forward
- Kruskal's MSP algorithm is an example of following type of algorithm Divide and Conquer Dynamic Programming Greedy Otherarrow_forwardA two dimensional array of red and green entries represents a maze. Green entries are passable and red entries are blocked (like a wall). Two special green entries en and ex denote the entrance and exit of the maze. (1) Abstract the problem as a graph; (2) Design an efficient algorithm (pseudo code) to find a shortest path from en to ex if it exists and then print out the path; (3) Analyze the complexity of the algorithm.arrow_forwardNeed output for: Distance S=0 & Previousarrow_forward
- There are many applications of Shortest Path Algorithm. Consider the problem of solving a jumbled Rubik's Cube in the fewest number of moves. I claim that this problem can be solved using a Shortest Path Algorithm. Determine whether this statement is TRUE or FALSE. NOTE: if you want to check if this statement is TRUE, think about how the Rubik's Cube Problem can be represented as a graph. What are the vertices? Which pairs of vertices are connected with edges? What is your source vertex and what is your destination vertex? How would Dijkstra's Algorithm enable you to find the optimal sequence of moves to solve a jumbled cube in the fewest number of moves?arrow_forwardusing java to solve this algorithm problemarrow_forward
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