cutting a rod

I studied cuttingrod dp alogorithm.

first cuttingrod is recursive function
and
cuttingRodDP is dynamic problem.

If we want to use by using recursive function
to speed up. we have to use memoized array

def cuttingRod(s, arr):

    m = arr[s-1]
    for i in range(1,int(s/2)+1):
        left=  i
        right =s-i
        val = cuttingRod(left, arr) + cuttingRod(right,arr)
        print(left, right, val)
        m= max(m, val )

    return m

def cuttingRodDP(s, arr):

    m = [0 for i in range(len(arr)+1)]
    for i in range(1, len(arr)+1):
        m[i]= arr[i-1]


    maxValue =0
    for i in range(1, len(arr)+1):
        for j in range(1,i+1):
           maxValue =  max(maxValue, m[j] + m[i-j])
        m[i] = maxValue
        print(m)

    return maxValue


arr= [ 1 ,  5,   8 ,  9 , 10,  17,  17,  20]
print(cuttingRod(len(arr), arr))

print(cuttingRodDP(len(arr), arr))