Problem 92 Implement CutRod(p,n) (page 363) and BottomUpCutRod(p,n) (page 366) in R or Python. Compare running times for a few different values of nn and report your results. (In R, use the system.time() function.) Use the following values for the price table.

p <- c(1,5,8,9,10,17,17,20,24,30) 

Cut_Rod(p,n)

if n ==0

return 0

q = -infinity

for i = 1 to n

q = max(q,p[i] + Cut-Rod(p,n-i))

return q

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Bottom-Up-Cut-Rod(p,n)

let r[0..n] be a new array

r[0] = 0

for j = 1 to n

q = - infinity

for i = 1 to j

q = max(q,p[i] + r[ j - i])

r[j] = q

return r[n]