CS计算机代考程序代写 python Java Agenda

Agenda
1. Installation

2. Basics

3. Iterables

4. Numpy (for math and matrix operations)

5. Matplotlib (for plotting)

6. Q&A

In [162]:
# Note: This tutorial is based on Python 3.8
# but it should apply to all Python 3.X versions
# Please note that this tutorial is NOT exhaustive
# We try to cover everything you need for class assignments
# but you should also navigate external resources
#
# More tutorials:
# NUMPY:
# https://cs231n.github.io/python-numpy-tutorial/#numpy
# https://numpy.org/doc/stable/user/quickstart.html
# MATPLOTLIB:
# https://matplotlib.org/gallery/index.html
# BASICS:
# https://www.w3schools.com/python/
# CONSULT THESE WISELY:
# The official documentation, Google, and Stack-overflow are your friends!

1. Installation
Anaconda for environment management
https://www.anaconda.com/
common commands
conda env list <-- list all environments conda create -n newenv python=3.8 <-- create new environment conda enc create -f env.yml <-- create environment from config file conda activate envname <-- activate a environment conda deactivate <-- exit environment pip install packagename <-- install package for current environment jupyter notebook <-- open jupyter in current environment Package installation using conda/pip Live demo Recommended IDEs Spyder (in-built in Anaconda) 
Pycharm (the most popular choice, compatible with Anaconda) In [163]: # common anaconda commands #conda env list #conda create -n name python=3.8 #conda env create -f env.yml #conda activate python2.7 #conda deactivate #install packages #pip install

2. Basics
https://www.w3schools.com/python/
In [164]:
# input and output
name = input()
print(“hello, ” + name)

cs229
hello, cs229
In [165]:
print(“print with new line”)
print(“print without new line”, end=””)
print()
print(“print multiple variables separated by a space:”, name, 1, 3.0, True)

print with new line
print without new line
print multiple variables separated by a space: cs229 1 3.0 True
In [166]:
# line comment
“””
block
comments
“””
Out[166]:
‘\nblock \ncomments\n’
In [167]:
# variables don’t need explicit declaration
var = “hello” # string
var = 10.0 # float
var = 10 # int
var = True # boolean
var = [1,2,3] # pointer to list
var = None # empty pointer
In [168]:
# type conversions
var = 10
print(int(var))
print(str(var))
print(float(var))

10
10
10.0
In [169]:
# basic math operations
var = 10
print(“var + 4 =”, 10 + 4)
print(“var – 4 =”, 10 – 4)
print(“var * 4 =”, 10 * 4)
print(“var ^ 4=”, 10 ** 4)
print(“int(var) / 4 =”, 10//4) # // for int division
print(“float(var) / 4 =”, 10/4) # / for float division
# All compound assignment operators available
# including += -= *= **= /= //=
# pre/post in/decrementers not available (++ –)

var + 4 = 14
var – 4 = 6
var * 4 = 40
var ^ 4= 10000
int(var) / 4 = 2
float(var) / 4 = 2.5
In [170]:
# basic boolean operations include “and”, “or”, “not”
print(“not True is”, not True)
print(“True and False is”, True and False)
print(“True or False is”, True or False)

not True is False
True and False is False
True or False is True
In [171]:
# String operations
# ” and “” are equivalent
s = “String”
#s = ‘Mary said “Hello” to John’
#s = “Mary said \”Hello\” to John”

# basic
print(len(s)) # get length of string and any iterable type
print(s[0]) # get char by index
print(s[1:3]) # [1,3)
print(“This is a ” + s + “!”)

# handy tools
print(s.lower())
print(s*4)
print(“ring” in s)
print(s.index(“ring”))

# slice by delimiter
print(“I am a sentence”.split(” “))
# concatenate a list of string using a delimiter
print(“…”.join([‘a’,’b’,’c’]))

# formatting variables
print(“Formatting a string like %.2f”%(0.12345))
print(f”Or like {s}!”)

6
S
tr
This is a String!
string
StringStringStringString
True
2
[‘I’, ‘am’, ‘a’, ‘sentence’]
a…b…c
Formatting a string like 0.12
Or like String!
In [172]:
# control flows
# NOTE: No parentheses or curly braces
# Indentation is used to identify code blocks
# So never ever mix spaces with tabs
for i in range(0,5):
for j in range(i, 5):
print(“inner loop”)
print(“outer loop”)

inner loop
inner loop
inner loop
inner loop
inner loop
outer loop
inner loop
inner loop
inner loop
inner loop
outer loop
inner loop
inner loop
inner loop
outer loop
inner loop
inner loop
outer loop
inner loop
outer loop
In [173]:
# if-else
var = 10
if var > 10:
print(“>”)
elif var == 10:
print(“=”)
else:
print(“<") = In [174]: # use "if" to check null pointer or empty arrays var = None if var: print(var) var = [] if var: print(var) var = "object" if var: print(var) object In [175]: # while-loop var = 5 while var > 0:
print(var)
var -=1

5
4
3
2
1
In [176]:
# for-loop
for i in range(3): # prints 0 1 2
print(i)

“””
equivalent to
for (int i = 0; i < 3; i++) """ print("-------") # range (start-inclusive, stop-exclusive, step) for i in range(2, -3, -2): print(i) """ equivalent to for (int i = 2; i > -3; i-=2)
“””

0
1
2
——-
2
0
-2
Out[176]:
‘\nequivalent to\nfor (int i = 2; i > -3; i-=2)\n’
In [177]:
# define function
def func(a, b):
return a + b
func(1,3)
Out[177]:
4
In [178]:
# use default parameters and pass values by parameter name
def rangeCheck(a, min_val = 0, max_val=10):
return min_val < a < max_val # syntactic sugar rangeCheck(5, max_val=4) Out[178]: False In [179]: # define class class Foo: # optinal constructor def __init__(self, x): # first parameter "self" for instance reference, like "this" in JAVA self.x = x # instance method def printX(self): # instance reference is required for all function parameters print(self.x) # class methods, most likely you will never need this @classmethod def printHello(self): print("hello") obj = Foo(6) obj.printX() 6 In [180]: # class inheritance - inherits variables and methods # You might need this when you learn more PyTorch class Bar(Foo): pass obj = Bar(3) obj.printX() 3 3. Iterables In [181]: alist = list() # linear, size not fixed, not hashable atuple = tuple() # linear, fixed size, hashable adict = dict() # hash table, not hashable, stores (key,value) pairs aset = set() # hash table, like dict but only stores keys acopy = alist.copy() # shallow copy print(len(alist)) # gets size of any iterable type 0 In [182]: # examplar tuple usage # creating a dictionary to store ngram counts d = dict() d[("a","cat")] = 10 d[["a","cat"]] = 11 --------------------------------------------------------------------------- TypeError Traceback (most recent call last) in
3 d = dict()
4 d[(“a”,”cat”)] = 10
—-> 5 d[[“a”,”cat”]] = 11

TypeError: unhashable type: ‘list’
In [183]:
“””
List: not hashable (i.e. can’t use as dictionary key)
dynamic size
allows duplicates and inconsistent element types
dynamic array implementation
“””
# list creation
alist = [] # empty list, equivalent to list()
alist = [1,2,3,4,5] # initialized list

print(alist[0])
alist[0] = 5
print(alist)

print(“-“*10)
# list indexing
print(alist[0]) # get first element (at index 0)
print(alist[-2]) # get last element (at index len-1)
print(alist[3:]) # get elements starting from index 3 (inclusive)
print(alist[:3]) # get elements stopping at index 3 (exclusive)
print(alist[2:4]) # get elements within index range [2,4)
print(alist[6:]) # prints nothing because index is out of range
print(alist[::-1]) # returns a reversed list

print(“-“*10)
# list modification
alist.append(“new item”) # insert at end
alist.insert(0, “new item”) # insert at index 0
alist.extend([2,3,4]) # concatenate lists
# above line is equivalent to alist += [2,3,4]
alist.index(“new item”) # search by content
alist.remove(“new item”) # remove by content
alist.pop(0) # remove by index
print(alist)

print(“-“*10)
if “new item” in alist:
print(“found”)
else:
print(“not found”)

print(“-“*10)
# list traversal
for ele in alist:
print(ele)

print(“-“*10)
# or traverse with index
for i, ele in enumerate(alist):
print(i, ele)

1
[5, 2, 3, 4, 5]
———-
5
4
[4, 5]
[5, 2, 3]
[3, 4]
[]
[5, 4, 3, 2, 5]
———-
[2, 3, 4, 5, ‘new item’, 2, 3, 4]
———-
found
———-
2
3
4
5
new item
2
3
4
———-
0 2
1 3
2 4
3 5
4 new item
5 2
6 3
7 4
In [184]:
“””
Tuple: hashable (i.e. can use as dictionary key)
fixed size (no insertion or deletion)
“””
# it does not make sense to create empty tuples
atuple = (1,2,3,4,5)
# or you can cast other iterables to tuple
atuple = tuple([1,2,3])

# indexing and traversal are same as list
In [185]:
“””
Named tuples for readibility
“””
from collections import namedtuple
Point = namedtuple(‘Point’, ‘x y’)
pt1 = Point(1.0, 5.0)
pt2 = Point(2.5, 1.5)
print(pt1.x, pt1.y)

1.0 5.0
In [186]:
“””
Dict: not hashable
dynamic size
no duplicates allowed
hash table implementation which is fast for searching
“””
# dict creation
adict = {} # empty dict, equivalent to dict()
adict = {‘a’:1, ‘b’:2, ‘c’:3}
print(adict)

# get all keys in dictionary
print(adict.keys())

# get value paired with key
print(adict[‘a’])
key = ‘e’

# NOTE: accessing keys not in the dictionary leads to exception
if key in adict:
print(adict[key])

# add or modify dictionary entries
adict[‘e’] = 10 # insert new key
adict[‘e’] = 5 # modify existing keys

print(“-“*10)
# traverse keys only
for key in adict:
print(key, adict[key])

print(“-“*10)
# or traverse key-value pairs together
for key, value in adict.items():
print(key, value)

print(“-“*10)
# NOTE: Checking if a key exists
key = ‘e’
if key in adict: # NO .keys() here please!
print(adict[key])
else:
print(“Not found!”)

{‘a’: 1, ‘b’: 2, ‘c’: 3}
dict_keys([‘a’, ‘b’, ‘c’])
1
———-
a 1
b 2
c 3
e 5
———-
a 1
b 2
c 3
e 5
———-
5
In [187]:
“””
Special dictionaries
“””
# set is a dictionary without values
aset = set()
aset.add(‘a’)

# deduplication short-cut using set
alist = [1,2,3,3,3,4,3]
alist = list(set(alist))
print(alist)

# default_dictionary returns a value computed from a default function
# for non-existent entries
from collections import defaultdict
adict = defaultdict(lambda: ‘unknown’)
adict[‘cat’] = ‘feline’
print(adict[‘cat’])
print(adict[‘dog’])

[1, 2, 3, 4]
feline
unknown
In [188]:
# counter is a dictionary with default value of 0
# and provides handy iterable counting tools
from collections import Counter

# initialize and modify empty counter
counter1 = Counter()
counter1[‘t’] = 10
counter1[‘t’] += 1
counter1[‘e’] += 1
print(counter1)
print(“-“*10)

# initialize counter from iterable
counter2 = Counter(“letters to be counted”)
print(counter2)
print(“-“*10)

# computations using counters
print(“1”, counter1 + counter2)
print(“2,”, counter1 – counter2)
print(“3”, counter1 or counter2) # or for intersection, and for union

Counter({‘t’: 11, ‘e’: 1})
———-
Counter({‘e’: 4, ‘t’: 4, ‘ ‘: 3, ‘o’: 2, ‘l’: 1, ‘r’: 1, ‘s’: 1, ‘b’: 1, ‘c’: 1, ‘u’: 1, ‘n’: 1, ‘d’: 1})
———-
1 Counter({‘t’: 15, ‘e’: 5, ‘ ‘: 3, ‘o’: 2, ‘l’: 1, ‘r’: 1, ‘s’: 1, ‘b’: 1, ‘c’: 1, ‘u’: 1, ‘n’: 1, ‘d’: 1})
2, Counter({‘t’: 7})
3 Counter({‘t’: 11, ‘e’: 1})
In [189]:
# sorting
a = [4,6,1,7,0,5,1,8,9]
a = sorted(a)
print(a)
a = sorted(a, reverse=True)
print(a)

[0, 1, 1, 4, 5, 6, 7, 8, 9]
[9, 8, 7, 6, 5, 4, 1, 1, 0]
In [190]:
# sorting
a = [(“cat”,1), (“dog”, 3), (“bird”, 2)]
a = sorted(a)
print(a)
a = sorted(a, key=lambda x:x[1])
print(a)

[(‘bird’, 2), (‘cat’, 1), (‘dog’, 3)]
[(‘cat’, 1), (‘bird’, 2), (‘dog’, 3)]
In [191]:
# useful in dictionary sorting
adict = {‘cat’:3, ‘bird’:1}
print(sorted(adict.items(), key=lambda x:x[1]))

[(‘bird’, 1), (‘cat’, 3)]
In [192]:
# Syntax sugar: one-line control flow + list operation
x = [1,2,3,5,3]
“””
for i in range(len(sent)):
sent[i] = sent[i].lower().split(” “)
“””
x1 = [xx*3 + 5 for xx in x]
print(x1)

x2 = [xx*3 + 5 for xx in x if xx < 3] print(x2) # Use this for deep copy! # copy = [obj.copy() for obj in original] [8, 11, 14, 20, 14] [8, 11] In [193]: # Syntax sugar: * operator for repeating iterable elements print("-"*10) print([1]*10) # Note: This only repeating by value # So you cannot apply the trick on reference types # To create a double list # DONT doublelist = [[]]*10 doublelist[0].append(1) print(doublelist) # DO doublelist = [[] for _ in range(10)] doublelist[0].append(1) print(doublelist) ---------- [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] [[1], [1], [1], [1], [1], [1], [1], [1], [1], [1]] [[1], [], [], [], [], [], [], [], [], []] 4. Numpy Very powerful python tool for handling matrices and higher dimensional arrays In [194]: import numpy as np In [200]: # create arrays a = np.array([[1,2],[3,4],[5,6]]) print(a) print(a.shape) # create all-zero/one arrays b = np.ones((3,4)) # np.zeros((3,4)) print(b) print(b.shape) # create identity matrix c = np.eye(5) print(c) print(c.shape) # create random matrix with standard normal init d = np.random.normal(size=(5,5)) print(d) [[1 2] [3 4] [5 6]] (3, 2) [[1. 1. 1. 1.] [1. 1. 1. 1.] [1. 1. 1. 1.]] (3, 4) [[1. 0. 0. 0. 0.] [0. 1. 0. 0. 0.] [0. 0. 1. 0. 0.] [0. 0. 0. 1. 0.] [0. 0. 0. 0. 1.]] (5, 5) [[-0.16367035 -0.87855847 0.7961741 0.26598743 -1.75846406] [-0.09106335 -0.95040985 -0.84240584 0.5022866 0.40741974] [-0.6448735 -0.94000292 -0.63470733 0.3198772 0.20179754] [ 3.87482256 -2.01679666 1.06469451 0.75220559 0.8659874 ] [ 1.86533616 1.41129369 0.74469198 0.56709733 0.33023962]] In [201]: # reshaping arrays a = np.arange(8) # [8,] all vectors are column by default b = a.reshape(1,-1) # [1,8] row vector -- -1 for auto-fill c = a.reshape((4,2)) # shape [4,2] d = a.reshape((2,2,-1)) # shape [2,2,2] e = c.flatten() # shape [8,] f = np.expand_dims(a, 0) # [1,8] g = np.expand_dims(a, 1) # [8,1] h = e.squeeze() # shape[8, ] -- remove all unnecessary dimensions print(a) print(b) [0 1 2 3 4 5 6 7] [[0 1 2 3 4 5 6 7]] In [202]: # be careful about vectors! a = np.array([1,2,3]) # this is a 3-d column vector, which you cannot transpose print(a) print(a.shape) print(a.T.shape) a = a.reshape(-1, 1) # this is a 3x1 matrix, which you can transpose print(a) print(a.shape) print(a.T.shape) [1 2 3] (3,) (3,) [[1] [2] [3]] (3, 1) (1, 3) In [203]: # concatenating arrays a = np.ones((4,3)) b = np.ones((4,3)) c = np.concatenate([a,b], 0) print(c.shape) d = np.concatenate([a,b], 1) print(d.shape) (8, 3) (4, 6) In [204]: # access array slices by index a = np.zeros([10, 10]) a[:3] = 1 a[:, :3] = 2 a[:3, :3] = 3 rows = [4,6,7] cols = [9,3,5] a[rows, cols] = 4 print(a) [[3. 3. 3. 1. 1. 1. 1. 1. 1. 1.] [3. 3. 3. 1. 1. 1. 1. 1. 1. 1.] [3. 3. 3. 1. 1. 1. 1. 1. 1. 1.] [2. 2. 2. 0. 0. 0. 0. 0. 0. 0.] [2. 2. 2. 0. 0. 0. 0. 0. 0. 4.] [2. 2. 2. 0. 0. 0. 0. 0. 0. 0.] [2. 2. 2. 4. 0. 0. 0. 0. 0. 0.] [2. 2. 2. 0. 0. 4. 0. 0. 0. 0.] [2. 2. 2. 0. 0. 0. 0. 0. 0. 0.] [2. 2. 2. 0. 0. 0. 0. 0. 0. 0.]] In [205]: # transposition a = np.arange(24).reshape(2,3,4) print(a.shape) print(a) a = np.transpose(a, (2,1,0)) # swap 0th and 2nd axes print(a.shape) print(a) (2, 3, 4) [[[ 0 1 2 3] [ 4 5 6 7] [ 8 9 10 11]] [[12 13 14 15] [16 17 18 19] [20 21 22 23]]] (4, 3, 2) [[[ 0 12] [ 4 16] [ 8 20]] [[ 1 13] [ 5 17] [ 9 21]] [[ 2 14] [ 6 18] [10 22]] [[ 3 15] [ 7 19] [11 23]]] In [227]: c = np.array([[1,2],[3,4]]) print(np.linalg.inv(c)) # pinv is pseudo inversion for stability print(np.linalg.pinv(c)) # To compute c^-1 b b = np.array([1, 1]) print(np.linalg.inv(c)@b) print(np.linalg.solve(c,b)) # preferred! [[-2. 1. ] [ 1.5 -0.5]] [[-2. 1. ] [ 1.5 -0.5]] [-1. 1.] [-1. 1.] In [206]: # vector dot product v1 = np.array([1,2]) v2 = np.array([3,4]) print(v1.dot(v2)) print(np.dot(v1,v2)) print(v1@v2) 11 11 11 In [207]: # vector outer product print(np.outer(v1,v2)) print(v1.reshape(-1,1).dot(v2.reshape(1,-1))) [[3 4] [6 8]] [[3 4] [6 8]] In [208]: # Matrix multiply vector (Ax) m = np.array([1,2,3,4]).reshape(2,2) print(m@v1) print(m.dot(v1)) print(np.matmul(m, v1)) [ 5 11] [ 5 11] [ 5 11] In [209]: # matrix multiplication a = np.ones((4,3)) # 4,3 b = np.ones((3,2)) # 3,2 --> 4,2
print(a @ b) # same as a.dot(b)
print(np.matmul(a,b))

[[3. 3.]
[3. 3.]
[3. 3.]
[3. 3.]]
[[3. 3.]
[3. 3.]
[3. 3.]
[3. 3.]]
In [210]:
# broadcasting
c = np.ones([4,4])
# automatic repetition along axis
d = np.array([1,2,3,4]).reshape(4,1)
print(c.shape)
print(d.shape)
print(c + d)

(4, 4)
(4, 1)
[[2. 2. 2. 2.]
[3. 3. 3. 3.]
[4. 4. 4. 4.]
[5. 5. 5. 5.]]
In [211]:
# computing pairwise distance (using broadcasting)
samples = np.random.random([15, 5])
diff=samples[:,np.newaxis,:]-samples[np.newaxis]
print(samples[:,np.newaxis,:].shape)
print(samples[np.newaxis,:,:].shape)
print(diff.shape)

(15, 1, 5)
(1, 15, 5)
(15, 15, 5)
In [212]:
# speed test: numpy vs list
a = np.ones((100,100))
b = np.ones((100,100))

def matrix_multiplication(X, Y):
result = [[0]*len(Y[0]) for _ in range(len(X))]
for i in range(len(X)):
for j in range(len(Y[0])):
for k in range(len(Y)):
result[i][j] += X[i][k] * Y[k][j]
return result

import time

# run numpy matrix multiplication for 10 times
start = time.time()
for _ in range(10):
a @ b
end = time.time()
print(“numpy spends {} seconds”.format(end-start))

# run list matrix multiplication for 10 times
start = time.time()
for _ in range(10):
matrix_multiplication(a,b)
end = time.time()
print(“list operation spends {} seconds”.format(end-start))

# the difference gets more significant as matrices grow in size!

numpy spends 0.003999471664428711 seconds
list operation spends 8.870983362197876 seconds
In [213]:
# other common operations
a = np.ones((4,4))
print(np.linalg.norm(a, axis=0))
print(np.linalg.norm(a))
print(np.sum(a)) # sum all elements in matrix
print(np.sum(a, axis=0)) # sum along axis 0
print(np.sum(a, axis=1)) # sum along axis 1
# element-wise operations, for examples
print(np.log(a))
print(np.exp(a))
print(np.sin(a))
# operation with scalar is interpreted as element-wise
print(a * 3)

[2. 2. 2. 2.]
4.0
16.0
[4. 4. 4. 4.]
[4. 4. 4. 4.]
[[0. 0. 0. 0.]
[0. 0. 0. 0.]
[0. 0. 0. 0.]
[0. 0. 0. 0.]]
[[2.71828183 2.71828183 2.71828183 2.71828183]
[2.71828183 2.71828183 2.71828183 2.71828183]
[2.71828183 2.71828183 2.71828183 2.71828183]
[2.71828183 2.71828183 2.71828183 2.71828183]]
[[0.84147098 0.84147098 0.84147098 0.84147098]
[0.84147098 0.84147098 0.84147098 0.84147098]
[0.84147098 0.84147098 0.84147098 0.84147098]
[0.84147098 0.84147098 0.84147098 0.84147098]]
[[3. 3. 3. 3.]
[3. 3. 3. 3.]
[3. 3. 3. 3.]
[3. 3. 3. 3.]]
In [2]:
# invalid operations result in an NaN
a = np.array(0)
b = np.array(0)
print(a/b)

nan

:4: RuntimeWarning: invalid value encountered in true_divide
print(a/b)

5. Matplotlib
Powerful tool for visualization 
Many tutorials online. We only go over the basics here 

In [214]:
import matplotlib.pyplot as plt
In [215]:
# line plot
x = np.arange(0, 2, 0.01)
y = 1+np.sin(2*np.pi*x)
plt.plot(x,y)
Out[215]:
[]


In [216]:
# scatter plot
x = [1,3,2]
y = [1,2,3]
plt.scatter(x,y)
Out[216]:


In [217]:
# bar plots
plt.bar(x,y)
Out[217]:


In [218]:
# plot configurations
x = [1,2,3]
y1 = [1,3,2]
y2 = [4,0,4]

# set figure size
plt.figure(figsize=(5,5))

# set axes
plt.xlim(0,5)
plt.ylim(0,5)
plt.xlabel(“x label”)
plt.ylabel(“y label”)

# add title
plt.title(“My Plot”)

plt.plot(x,y1, label=”data1″, color=”red”, marker=”*”, dashes=[5,1])
plt.plot(x,y2, label=”data2″, color=”green”, marker=”.”)
plt.grid()
plt.legend()
Out[218]:


In [219]:
# subplots
f, ax = plt.subplots(2,2,figsize=(5,5))
ax[0][0].plot(x,y)
ax[0][1].scatter(x,y)
ax[1][0].bar(x,y)
ax[1][1].hist(x,y)
plt.show()


In [220]:
# plot area under curve
probs = [1, 1, 0.95, 0.9, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4]
thres = np.arange(0,1,0.1)
plt.fill_between(x=thres, y1=probs, y2=0, step=’post’)
Out[220]:


In [221]:
import seaborn as sn
import matplotlib.pyplot as plt

array = [[13,1,1,0,2,0],
[3,9,6,0,1,0],
[0,0,16,2,0,0],
[0,0,0,13,0,0],
[0,0,0,0,15,0],
[0,0,1,0,0,15]]
labels = ‘A B C D E F’.split(‘ ‘)
sn.heatmap(array, annot=True, annot_kws={“size”: 16}, cmap=”rocket_r”)
plt.xticks(ticks=np.arange(len(labels))+0.5,labels=labels)
plt.yticks(ticks=np.arange(len(labels))+0.5,labels=labels,rotation=0)
plt.show()


In [ ]: