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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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126
linear_algebra/src/lib.py
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@ -26,29 +26,29 @@ import random
class Vector:
"""
This class represents a vector of arbitrary size.
You need to give the vector components.
This class represents a vector of arbitrary size.
You need to give the vector components.
Overview about the methods:
Overview about the methods:
constructor(components : list) : init the vector
set(components : list) : changes the vector components.
__str__() : toString method
component(i : int): gets the i-th component (start by 0)
__len__() : gets the size of the vector (number of components)
euclidLength() : returns the euclidean length of the vector.
operator + : vector addition
operator - : vector subtraction
operator * : scalar multiplication and dot product
copy() : copies this vector and returns it.
changeComponent(pos,value) : changes the specified component.
TODO: compare-operator
constructor(components : list) : init the vector
set(components : list) : changes the vector components.
__str__() : toString method
component(i : int): gets the i-th component (start by 0)
__len__() : gets the size of the vector (number of components)
euclidLength() : returns the euclidean length of the vector.
operator + : vector addition
operator - : vector subtraction
operator * : scalar multiplication and dot product
copy() : copies this vector and returns it.
changeComponent(pos,value) : changes the specified component.
TODO: compare-operator
"""
def __init__(self, components=None):
"""
input: components or nothing
simple constructor for init the vector
input: components or nothing
simple constructor for init the vector
"""
if components is None:
components = []
@ -56,9 +56,9 @@ class Vector:
def set(self, components):
"""
input: new components
changes the components of the vector.
replace the components with newer one.
input: new components
changes the components of the vector.
replace the components with newer one.
"""
if len(components) > 0:
self.__components = list(components)
@ -67,14 +67,14 @@ class Vector:
def __str__(self):
"""
returns a string representation of the vector
returns a string representation of the vector
"""
return "(" + ",".join(map(str, self.__components)) + ")"
def component(self, i):
"""
input: index (start at 0)
output: the i-th component of the vector.
input: index (start at 0)
output: the i-th component of the vector.
"""
if type(i) is int and -len(self.__components) <= i < len(self.__components):
return self.__components[i]
@ -83,13 +83,13 @@ class Vector:
def __len__(self):
"""
returns the size of the vector
returns the size of the vector
"""
return len(self.__components)
def euclidLength(self):
"""
returns the euclidean length of the vector
returns the euclidean length of the vector
"""
summe = 0
for c in self.__components:
@ -98,9 +98,9 @@ class Vector:
def __add__(self, other):
"""
input: other vector
assumes: other vector has the same size
returns a new vector that represents the sum.
input: other vector
assumes: other vector has the same size
returns a new vector that represents the sum.
"""
size = len(self)
if size == len(other):
@ -111,9 +111,9 @@ class Vector:
def __sub__(self, other):
"""
input: other vector
assumes: other vector has the same size
returns a new vector that represents the difference.
input: other vector
assumes: other vector has the same size
returns a new vector that represents the difference.
"""
size = len(self)
if size == len(other):
@ -124,8 +124,8 @@ class Vector:
def __mul__(self, other):
"""
mul implements the scalar multiplication
and the dot-product
mul implements the scalar multiplication
and the dot-product
"""
if isinstance(other, float) or isinstance(other, int):
ans = [c * other for c in self.__components]
@ -141,15 +141,15 @@ class Vector:
def copy(self):
"""
copies this vector and returns it.
copies this vector and returns it.
"""
return Vector(self.__components)
def changeComponent(self, pos, value):
"""
input: an index (pos) and a value
changes the specified component (pos) with the
'value'
input: an index (pos) and a value
changes the specified component (pos) with the
'value'
"""
# precondition
assert -len(self.__components) <= pos < len(self.__components)
@ -158,7 +158,7 @@ class Vector:
def zeroVector(dimension):
"""
returns a zero-vector of size 'dimension'
returns a zero-vector of size 'dimension'
"""
# precondition
assert isinstance(dimension, int)
@ -167,8 +167,8 @@ def zeroVector(dimension):
def unitBasisVector(dimension, pos):
"""
returns a unit basis vector with a One
at index 'pos' (indexing at 0)
returns a unit basis vector with a One
at index 'pos' (indexing at 0)
"""
# precondition
assert isinstance(dimension, int) and (isinstance(pos, int))
@ -179,9 +179,9 @@ def unitBasisVector(dimension, pos):
def axpy(scalar, x, y):
"""
input: a 'scalar' and two vectors 'x' and 'y'
output: a vector
computes the axpy operation
input: a 'scalar' and two vectors 'x' and 'y'
output: a vector
computes the axpy operation
"""
# precondition
assert (
@ -194,10 +194,10 @@ def axpy(scalar, x, y):
def randomVector(N, a, b):
"""
input: size (N) of the vector.
random range (a,b)
output: returns a random vector of size N, with
random integer components between 'a' and 'b'.
input: size (N) of the vector.
random range (a,b)
output: returns a random vector of size N, with
random integer components between 'a' and 'b'.
"""
random.seed(None)
ans = [random.randint(a, b) for i in range(N)]
@ -224,8 +224,8 @@ class Matrix:
def __init__(self, matrix, w, h):
"""
simple constructor for initializing
the matrix with components.
simple constructor for initializing
the matrix with components.
"""
self.__matrix = matrix
self.__width = w
@ -233,8 +233,8 @@ class Matrix:
def __str__(self):
"""
returns a string representation of this
matrix.
returns a string representation of this
matrix.
"""
ans = ""
for i in range(self.__height):
@ -248,7 +248,7 @@ class Matrix:
def changeComponent(self, x, y, value):
"""
changes the x-y component of this matrix
changes the x-y component of this matrix
"""
if 0 <= x < self.__height and 0 <= y < self.__width:
self.__matrix[x][y] = value
@ -257,7 +257,7 @@ class Matrix:
def component(self, x, y):
"""
returns the specified (x,y) component
returns the specified (x,y) component
"""
if 0 <= x < self.__height and 0 <= y < self.__width:
return self.__matrix[x][y]
@ -266,19 +266,19 @@ class Matrix:
def width(self):
"""
getter for the width
getter for the width
"""
return self.__width
def height(self):
"""
getter for the height
getter for the height
"""
return self.__height
def determinate(self) -> float:
"""
returns the determinate of an nxn matrix using Laplace expansion
returns the determinate of an nxn matrix using Laplace expansion
"""
if self.__height == self.__width and self.__width >= 2:
total = 0
@ -305,8 +305,8 @@ class Matrix:
def __mul__(self, other):
"""
implements the matrix-vector multiplication.
implements the matrix-scalar multiplication
implements the matrix-vector multiplication.
implements the matrix-scalar multiplication
"""
if isinstance(other, Vector): # vector-matrix
if len(other) == self.__width:
@ -332,7 +332,7 @@ class Matrix:
def __add__(self, other):
"""
implements the matrix-addition.
implements the matrix-addition.
"""
if self.__width == other.width() and self.__height == other.height():
matrix = []
@ -347,7 +347,7 @@ class Matrix:
def __sub__(self, other):
"""
implements the matrix-subtraction.
implements the matrix-subtraction.
"""
if self.__width == other.width() and self.__height == other.height():
matrix = []
@ -363,7 +363,7 @@ class Matrix:
def squareZeroMatrix(N):
"""
returns a square zero-matrix of dimension NxN
returns a square zero-matrix of dimension NxN
"""
ans = [[0] * N for i in range(N)]
return Matrix(ans, N, N)
@ -371,8 +371,8 @@ def squareZeroMatrix(N):
def randomMatrix(W, H, a, b):
"""
returns a random matrix WxH with integer components
between 'a' and 'b'
returns a random matrix WxH with integer components
between 'a' and 'b'
"""
random.seed(None)
matrix = [[random.randint(a, b) for j in range(W)] for i in range(H)]