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import unittest
def cutRod(p, n):
if n == 0:
return 0
q = -1
for i in range(1, n+1):
q = max(q, p[i] + cutRod(p, n-i))
return q
def topDownCutRodAux(p, n, r):
if n == 0:
return 0
if r[n] >= 0:
return r[n]
q = -1
for i in range(1, n+1):
q = max(q, p[i] + topDownCutRodAux(p, n-i, r))
r[n] = q
return q
def topDownCutRod(p, n):
r = []
for i in range(n+1):
r.append(-1)
return topDownCutRodAux(p, n, r)
def bottomUpCutRod(p, n):
if n == 0:
return 0
r = [0]
for i in range(1, n+1):
r.append(-1)
for j in range(1, n+1):
q = -1
for i in range(1, j+1):
q = max(q, p[i] + r[j-i])
r[j] = q
return r[n]
class TestRodCutting(unittest.TestCase):
def setUp(self):
self.p = [0, 1, 5, 8, 9, 10, 17, 17, 20, 24, 30]
self.r = [0, 1, 5, 8, 10, 13, 17, 18, 22, 25, 30]
def test_recursive(self):
for n in range(10):
self.assertEqual(self.r[n], cutRod(self.p, n))
def test_top_down(self):
for n in range(10):
self.assertEqual(self.r[n], topDownCutRod(self.p, n))
def test_bottom_up(self):
for n in range(10):
self.assertEqual(self.r[n], bottomUpCutRod(self.p, n))
if __name__ == '__main__':
unittest.main()
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