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Optimized recursive_bubble_sort (#2410)

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* optimized recursive_bubble_sort

* Fixed doctest error due whitespace

* reduce loop times for optimization

* fixup! Format Python code with psf/black push

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
This commit is contained in:
Du Yuanchao
2020-09-10 16:31:26 +08:00
committed by GitHub
parent 25946e4570
commit 4d0a8f2355
60 changed files with 900 additions and 859 deletions
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168
dynamic_programming/rod_cutting.py
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@ -13,30 +13,30 @@ pieces separately or not cutting it at all if the price of it is the maximum obt
def naive_cut_rod_recursive(n: int, prices: list):
"""
Solves the rod-cutting problem via naively without using the benefit of dynamic
programming. The results is the same sub-problems are solved several times
leading to an exponential runtime
Solves the rod-cutting problem via naively without using the benefit of dynamic
programming. The results is the same sub-problems are solved several times
leading to an exponential runtime
Runtime: O(2^n)
Runtime: O(2^n)
Arguments
-------
n: int, the length of the rod
prices: list, the prices for each piece of rod. ``p[i-i]`` is the
price for a rod of length ``i``
Arguments
-------
n: int, the length of the rod
prices: list, the prices for each piece of rod. ``p[i-i]`` is the
price for a rod of length ``i``
Returns
-------
The maximum revenue obtainable for a rod of length n given the list of prices
for each piece.
Returns
-------
The maximum revenue obtainable for a rod of length n given the list of prices
for each piece.
Examples
--------
>>> naive_cut_rod_recursive(4, [1, 5, 8, 9])
10
>>> naive_cut_rod_recursive(10, [1, 5, 8, 9, 10, 17, 17, 20, 24, 30])
30
"""
Examples
--------
>>> naive_cut_rod_recursive(4, [1, 5, 8, 9])
10
>>> naive_cut_rod_recursive(10, [1, 5, 8, 9, 10, 17, 17, 20, 24, 30])
30
"""
_enforce_args(n, prices)
if n == 0:
@ -52,35 +52,35 @@ def naive_cut_rod_recursive(n: int, prices: list):
def top_down_cut_rod(n: int, prices: list):
"""
Constructs a top-down dynamic programming solution for the rod-cutting
problem via memoization. This function serves as a wrapper for
_top_down_cut_rod_recursive
Constructs a top-down dynamic programming solution for the rod-cutting
problem via memoization. This function serves as a wrapper for
_top_down_cut_rod_recursive
Runtime: O(n^2)
Runtime: O(n^2)
Arguments
--------
n: int, the length of the rod
prices: list, the prices for each piece of rod. ``p[i-i]`` is the
price for a rod of length ``i``
Arguments
--------
n: int, the length of the rod
prices: list, the prices for each piece of rod. ``p[i-i]`` is the
price for a rod of length ``i``
Note
----
For convenience and because Python's lists using 0-indexing, length(max_rev) =
n + 1, to accommodate for the revenue obtainable from a rod of length 0.
Note
----
For convenience and because Python's lists using 0-indexing, length(max_rev) =
n + 1, to accommodate for the revenue obtainable from a rod of length 0.
Returns
-------
The maximum revenue obtainable for a rod of length n given the list of prices
for each piece.
Returns
-------
The maximum revenue obtainable for a rod of length n given the list of prices
for each piece.
Examples
-------
>>> top_down_cut_rod(4, [1, 5, 8, 9])
10
>>> top_down_cut_rod(10, [1, 5, 8, 9, 10, 17, 17, 20, 24, 30])
30
"""
Examples
-------
>>> top_down_cut_rod(4, [1, 5, 8, 9])
10
>>> top_down_cut_rod(10, [1, 5, 8, 9, 10, 17, 17, 20, 24, 30])
30
"""
_enforce_args(n, prices)
max_rev = [float("-inf") for _ in range(n + 1)]
return _top_down_cut_rod_recursive(n, prices, max_rev)
@ -88,24 +88,24 @@ def top_down_cut_rod(n: int, prices: list):
def _top_down_cut_rod_recursive(n: int, prices: list, max_rev: list):
"""
Constructs a top-down dynamic programming solution for the rod-cutting problem
via memoization.
Constructs a top-down dynamic programming solution for the rod-cutting problem
via memoization.
Runtime: O(n^2)
Runtime: O(n^2)
Arguments
--------
n: int, the length of the rod
prices: list, the prices for each piece of rod. ``p[i-i]`` is the
price for a rod of length ``i``
max_rev: list, the computed maximum revenue for a piece of rod.
``max_rev[i]`` is the maximum revenue obtainable for a rod of length ``i``
Arguments
--------
n: int, the length of the rod
prices: list, the prices for each piece of rod. ``p[i-i]`` is the
price for a rod of length ``i``
max_rev: list, the computed maximum revenue for a piece of rod.
``max_rev[i]`` is the maximum revenue obtainable for a rod of length ``i``
Returns
-------
The maximum revenue obtainable for a rod of length n given the list of prices
for each piece.
"""
Returns
-------
The maximum revenue obtainable for a rod of length n given the list of prices
for each piece.
"""
if max_rev[n] >= 0:
return max_rev[n]
elif n == 0:
@ -125,28 +125,28 @@ def _top_down_cut_rod_recursive(n: int, prices: list, max_rev: list):
def bottom_up_cut_rod(n: int, prices: list):
"""
Constructs a bottom-up dynamic programming solution for the rod-cutting problem
Constructs a bottom-up dynamic programming solution for the rod-cutting problem
Runtime: O(n^2)
Runtime: O(n^2)
Arguments
----------
n: int, the maximum length of the rod.
prices: list, the prices for each piece of rod. ``p[i-i]`` is the
price for a rod of length ``i``
Arguments
----------
n: int, the maximum length of the rod.
prices: list, the prices for each piece of rod. ``p[i-i]`` is the
price for a rod of length ``i``
Returns
-------
The maximum revenue obtainable from cutting a rod of length n given
the prices for each piece of rod p.
Returns
-------
The maximum revenue obtainable from cutting a rod of length n given
the prices for each piece of rod p.
Examples
-------
>>> bottom_up_cut_rod(4, [1, 5, 8, 9])
10
>>> bottom_up_cut_rod(10, [1, 5, 8, 9, 10, 17, 17, 20, 24, 30])
30
"""
Examples
-------
>>> bottom_up_cut_rod(4, [1, 5, 8, 9])
10
>>> bottom_up_cut_rod(10, [1, 5, 8, 9, 10, 17, 17, 20, 24, 30])
30
"""
_enforce_args(n, prices)
# length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
@ -166,16 +166,16 @@ def bottom_up_cut_rod(n: int, prices: list):
def _enforce_args(n: int, prices: list):
"""
Basic checks on the arguments to the rod-cutting algorithms
Basic checks on the arguments to the rod-cutting algorithms
n: int, the length of the rod
prices: list, the price list for each piece of rod.
n: int, the length of the rod
prices: list, the price list for each piece of rod.
Throws ValueError:
Throws ValueError:
if n is negative or there are fewer items in the price list than the length of
the rod
"""
if n is negative or there are fewer items in the price list than the length of
the rod
"""
if n < 0:
raise ValueError(f"n must be greater than or equal to 0. Got n = {n}")