3. In a forest, there lies a fortune teller that will give a yes or no response
ID: 3831518 • Letter: 3
Question
3. In a forest, there lies a fortune teller that will give a yes or no response as to whether a particular graph contains a Hamiltonian cycle. Given an arbitrary graph G, describe an algorithm that will allow you to solve this problem by asking the fortune teller a series of questions, each involving a modified version of the original graph G. The solution must not be slower than a number that grows polynomially as a function of the number of vertices in G. (Hence, prove that if the Hamiltonian cycle decision problem can be solved in polynomial time, so can the search problem.)
Explanation / Answer
The main purpose of the Hamiltonian cycle is a undirected graph that visits each vertex exactly once in the total route path.
I have written the algorithm for hamiltonian cycle which gives the reponses for each and every fortune teller along with the comments for each line in the program
Algorithm for Hamiltonian Cycle
// Hamiltonian Cycle staring point
function HamiltonianCycle(G)
// Create a variable Z
Z = []
//create an edge with v and u pairs
e = (v, u)
next
// check the hamilton conditions using if-else statement
if HamiltonianCycle(G) then
for all edges on v do
e (v, u)
G0 G e
if HamiltonianCycle(G0
) then
G = G0
else . Sorry. There is No HamiltonianCycle available, so keep e
add v to Z
next u
v next
return Z
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