PLEASE SOLVE IT USING PYTHON AND ACTUALLY WRITE THE FULL CODE! THANKS! Write a program that uses Ore's theorem to determine if a graph has a Hamilton

circuit. You do not have to find the circuit.

a$)$ Debug your program with the Example $5$ graphs $G_1,G_2,$ and $G_3$ from the

"Euler, Hamilton, & Shortest Path Problems" lecture slides.

b$)$ Test your program with this graph:

Write a program that creates a min$-$max strategy for the game of Nim. Display the

strategy in a manner that will be clear to the grader and includes all of the

elements shown in the "Minmax Strategy for Nim $(11\mathrm{.}2\mathrm{.}5)"$ slide in the

"Application of Trees" lecture.

a$)$ Debug your program with a version of Nim with the starting position

where there are $3$ piles of stones containing $2,2,$ and $1$ stone each,

respectively $($same as one in the "Minmax Strategy for Nim $(11\mathrm{.}2\mathrm{.}5)"$

slide.

b$)$ Test your program with a version of Nim with the starting position

consists of three piles with one, two, and three stones, respectively. When

drawing the tree, represent by the same vertex symmetric positions that

result from the same move.

c$)$ Write a simulation of two players playing the game of Nim. Player A uses

the min$-$max code you wrote for $4a.$ Player B makes the next move

randomly. Alternate between which player goes first. Play the game $100$

times and keep track of who wins and display it$.$ The simulation should

show the progression of each game. For example:

Start: $221$

Player A: $21$

Player B: $11$

Player A: $1($Player A wins$)$

Write a program for finding an Euler circuit, if one exists, using the algorithm

from the lecture on Euler circuits and paths. If an Euler circuit does not exist,

print out the vertices with odd degrees $($see Theorem $1).$ If an Euler circuit does

exist, print it out with the vertices of the circuit in order, separated by dashes, e$.$g$.,$

a$-$b$-$c$.$

a$)$ Debug your program with the Example $1$ graphs $G_1,G_2,G_3,$ and the graph

of the Bridges of K$$nigsberg from the "Euler, Hamilton, & Shortest Path

Problems" lecture slides.

b$)$ Test your program with this graph:

Write a program that uses Dirac's theorem to determine if a graph has a Hamilton

circuit. You do not have to find the circuit.

a$)$ Debug your program with the Example $5$ graphs $G_1,G_2,$ and $G_3$ from the

"Euler, Hamilton, & Shortest Path Problems" lecture slides.

b$)$ Test your program with this graph: