Rod Cutting Exercise

15.1-3

# when c=2 

def BOTTOM_UP_CUT_ROD(p, n, c):
    r = [0] * (n+1)
    for i in range(1, n+1):
        q = p[i]
        for j in range(1, i):
            q = max(q, p[j] + r[i-j] - c)
        r[i] = q
    return r[n]

def main():
    p = [0, 1, 5, 8, 9, 10, 17, 17, 20, 24, 30]
    c = 2
    print('when cost c = 2: \n')
    for i in range(1, len(p)):
        print('the max profit of n = %i is: ' %i, BOTTOM_UP_CUT_ROD(p, i, c))

main()

Output-1

15.1-4

def MEMOIZED_CUT_ROD_AUX(p, n, r, s):
    if r[n] >= 0:
        return r[n], s

    if n == 0:
        q = 0
    else:
        q = -1
        for i in range(1, n+1):
            temp_q, temp_s = MEMOIZED_CUT_ROD_AUX(p, n-i, r, s) 
            if q < temp_q + p[i]:
                q = temp_q + p[i]
                s = temp_s
                s[n] = i
    r[n] = q
    return q, s

def MEMOIZED_CUT_ROD(p, n):
    r = [-1] * (n+1)
    s = [0] * (n+1)
    return MEMOIZED_CUT_ROD_AUX(p, n, r, s)

def PRINT_CUT_ROD_SOLUTION(p, n):
    r_nth, s = MEMOIZED_CUT_ROD(p, n)
    print('the max profit of n = %i is: %i' %(n,r_nth))
    print('the sulution of max profit is: ', end = '')
    while n > 0:
        print(s[n], end = '\t')
        n = n - s[n]

def main():
    p = [0, 1, 5, 8, 9, 10, 17, 17, 20, 24, 30]
    for i in range(1, len(p)):
        PRINT_CUT_ROD_SOLUTION(p, i)
        print('\n')

main()

Output-2

15.1-5

def fibonacci(n):
    f = [0] * (n+1)
    f[0] = 0
    f[1] = 1
    for i in range(2, n+1):
        f[i] = f[i-1] + f[i-2]
    return f[n]

def main():
    n = 6
    print('the %ith of fibonacci sequence is: ' %n, fibonacci(n))

main()

Output-3