Python:实现动态规划之棒材切割算法
def naive_cut_rod_recursive(n: int, prices: list):
_enforce_args(n, prices)
if n == 0:
return 0
max_revue = float("-inf")
for i in range(1, n + 1):
max_revue = max(
max_revue, prices[i - 1] + naive_cut_rod_recursive(n - i, prices)
)
return max_revue
def top_down_cut_rod(n: int, prices: list):
_enforce_args(n, prices)
max_rev = [float("-inf") for _ in range(n + 1)]
return _top_down_cut_rod_recursive(n, prices, max_rev)
def _top_down_cut_rod_recursive(n: int, prices: list, max_rev: list):
if max_rev[n] >= 0:
return max_rev[n]
elif n == 0:
return 0
else:
max_revenue = float("-inf")
for i in range(1, n + 1):
max_revenue = max(
max_revenue,
prices[i - 1] + _top_down_cut_rod_recursive(n - i, prices, max_rev),
)
max_rev[n] = max_revenue
return max_rev[n]
def bottom_up_cut_rod(n: int, prices: list):
_enforce_args(n, prices)
# length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
# length 0.
max_rev = [float("-inf") for _ in range(n + 1)]
max_rev[0] = 0
for i in range(1, n + 1):
max_revenue_i = max_rev[i]
for j in range(1, i + 1):
max_revenue_i = max(max_revenue_i, prices[j - 1] + max_rev[i - j])
max_rev[i] = max_revenue_i
return max_rev[n]
def _enforce_args(n: int, prices: list):
if n < 0:
raise ValueError(f"n must be greater than or equal to 0. Got n = {n}")
if n > len(prices):
raise ValueError(
"Each integral piece of rod must have a corresponding "
f"price. Got n = {n} but length of prices = {len(prices)}"
)
def main():
prices = [6, 10, 12, 15, 20, 23]
n = len(prices)
# the best revenue comes from cutting the rod into 6 pieces, each
# of length 1 resulting in a revenue of 6 * 6 = 36.
expected_max_revenue = 36
max_rev_top_down = top_down_cut_rod(n, prices)
max_rev_bottom_up = bottom_up_cut_rod(n, prices)
max_rev_naive = naive_cut_rod_recursive(n, prices)
assert expected_max_revenue == max_rev_top_down
assert max_rev_top_down == max_rev_bottom_up
assert max_rev_bottom_up == max_rev_naive
if __name__ == "__main__":
main()
