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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Python Data Structures
Data structure in computing
Data structures are how computer programs store information. Theses information can be processed, analyzed 
and visualized easily from the programme. Scientific data can be large and complex and may require data structures appropriate for scientific programming. In Astronomy, the fits file is one of the most widely used data-storing medium, it can store a lot of information including the coordinates, the precious time, a very large cataelog table, multi-dimension data cube, etc.. These data, when it is opened by the programme, shall be recognised and easily managed by the programme.
In Python, there are pre-defined advanced data structure depending on the kind of data you wish to store. 
You will have to choose data structures that best meet your requirements for the problem you are trying to solve. In this section, I will go through specifically examine three Python data structures
Step1:  Arithmetic Operations
Python implements seven basic binary arithmetic operators, two of which can double as unary operators.
They are summarized in the following table
Step2:  Strings in Python 2 and 3
```Python
Python 2
print type("Hello World!")
<type 'str'> 
this is a byte string
print type(u"Hello World!")
<type 'unicode'>
this is a Unicode string
```
```Python
Python 3
print(type("Hello World!"))
<class 'str'>
this is a Unicode string
print(type(b"Hello World!"))
<class 'bytes'>
this is a byte string
```
Built-In Data Structures
| Type Name | Example                   | Add Element                                | Get Element | Set Element | Description                           |
|-----------|---------------------------|--------------------------------------------|-------------|-------------|---------------------------------------|
| list  | [1, 2, 3]             | x.append(1)                                | x[0]        | x[0]=2      | Ordered collection                    |
| tuple | (1, 2, 3)             | no altering                                | x[0]        | no altering | Immutable ordered collection          |
| dict  | {'a'
Step3:  Definition
It is defined with parentheses 
Step4:  A single colon a[
Step5:  more interestingly, they have negative index
a[-1] means last item in the array
a[-2
Step6:  You may reversed a list with xxx[
Step7:  Concatenate
You may add up two list or we say concatenate, and multiply to duplicate the items.
Step8:  Sorting
You may sort a list with sorted(x). Noted that it returns a new list.
Step9:  Add element (append); Remove element (pop); Insert element (insert)
These functions are modified in-place, i.e. the original list will be changed
Step10:  Tuple
A Python tuple is similar to a list. The elements are in order but fixed once they are created. In other words, they are immutable. The tuple can store differently type of elements. 
Definition
It is defined with parentheses 
Step11:  Dictionary
Dictionary is more flexible than list and its index is a string, it is defined with curly bracket
Step12:  Extra reading
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Python Code:
a = 1 # integer
b = 1.1 #floating point numbers
c = True; d = False # Boolean (logical expression)
e = "Hello" # Strings
Explanation: Python Data Structures
Data structure in computing
Data structures are how computer programs store information. Theses information can be processed, analyzed 
and visualized easily from the programme. Scientific data can be large and complex and may require data structures appropriate for scientific programming. In Astronomy, the fits file is one of the most widely used data-storing medium, it can store a lot of information including the coordinates, the precious time, a very large cataelog table, multi-dimension data cube, etc.. These data, when it is opened by the programme, shall be recognised and easily managed by the programme.
In Python, there are pre-defined advanced data structure depending on the kind of data you wish to store. 
You will have to choose data structures that best meet your requirements for the problem you are trying to solve. In this section, I will go through specifically examine three Python data structures: datetime, lists, tuples, sets, and dictionaries.
<a href="https://colab.research.google.com/github/ryan-leung/PHYS4650_Python_Tutorial/blob/master/notebooks/02-Python-Data-Structures.ipynb"><img align="right" src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open in Colab" title="Open and Execute in Google Colaboratory">
</a>
Built-In Types
Python's simple types are summarized in the following table:
| Type        | Example        | Description                                                  |
|-------------|----------------|--------------------------------------------------------------|
| int     | x = 1      | integers (i.e., whole numbers)                               |
| float   | x = 1.0    | floating-point numbers (i.e., real numbers)                  |
| complex | x = 1 + 2j | Complex numbers (i.e., numbers with real and imaginary part) |
| bool    | x = True   | Boolean: True/False values                                   |
| str     | x = 'abc'  | String: characters or text                                   |
| NoneType| x = None   | Special object indicating nulls                              |
We'll take a quick look at each of these in turn.
End of explanation
# addition, subtraction, multiplication
(4 + 8) * (6.5 - 3)
Explanation: Arithmetic Operations
Python implements seven basic binary arithmetic operators, two of which can double as unary operators.
They are summarized in the following table:
| Operator     | Name           | Description                                            |
|--------------|----------------|--------------------------------------------------------|
| a + b    | Addition       | Sum of a and b                                 |
| a - b    | Subtraction    | Difference of a and b                          |
| a * b    | Multiplication | Product of a and b                             |
| a / b    | True division  | Quotient of a and b                            |
| a // b   | Floor division | Quotient of a and b, removing fractional parts |
| a % b    | Modulus        | Integer remainder after division of a by b     |
| a ** b   | Exponentiation | a raised to the power of b                     |
| -a       | Negation       | The negative of a                                  |
| +a       | Unary plus     | a unchanged (rarely used)                          |
These operators can be used and combined in intuitive ways, using standard parentheses to group operations.
For example:
End of explanation
x = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
Explanation: Strings in Python 2 and 3
```Python
Python 2
print type("Hello World!")
<type 'str'> 
this is a byte string
print type(u"Hello World!")
<type 'unicode'>
this is a Unicode string
```
```Python
Python 3
print(type("Hello World!"))
<class 'str'>
this is a Unicode string
print(type(b"Hello World!"))
<class 'bytes'>
this is a byte string
```
Built-In Data Structures
| Type Name | Example                   | Add Element                                | Get Element | Set Element | Description                           |
|-----------|---------------------------|--------------------------------------------|-------------|-------------|---------------------------------------|
| list  | [1, 2, 3]             | x.append(1)                                | x[0]        | x[0]=2      | Ordered collection                    |
| tuple | (1, 2, 3)             | no altering                                | x[0]        | no altering | Immutable ordered collection          |
| dict  | {'a':1, 'b':2, 'c':3} | x['new_key'] = 4 or x.update({'new_key'=4} | x['a']      | x['a']=2    | Unordered (key,value) mapping         |
| set   | {1, 2, 3}             | x.add(4)                                   | no indexing | no indexing | Unordered collection of unique values |
list
A Python list is a sequence of values (elements) that are usually the same kind of item. They are in order and mutable. Mutable means they can be changed after they are created, of course, this implies you can exchange the order of the elements inside it. This is a Python list of prime numbers smaller than 50:
End of explanation
print(x)
print(x[0])
Explanation: Definition
It is defined with parentheses : [xx,xx,xx]. 
Get Element
The elements are called using a square bracket with an index starting from zero : x[y], 0..N. 
Slice (sub-array)
You can slice the array using colon, in this case a[start:end] means items start up to end-1.
End of explanation
print(x[1:2])
print(x[:])
print(x[:2])
print(x[1:])
Explanation: A single colon a[:] means a copy of the whole array.
a[start:] return tuple of items start through the rest of the array.
a[:end]return tuple of items from the beginning through end-1.
End of explanation
print(x[-1])
print(x[-2])
print(x[-2:])
print(x[:-2])
Explanation: more interestingly, they have negative index
a[-1] means last item in the array
a[-2:] means last two items in the array
a[:-2] means everything except the last two items
End of explanation
print(x[::-1])
Explanation: You may reversed a list with xxx[::-1].
End of explanation
print(x + [0,1])
print([0,1] + x)
print([0,1] * 5)
Explanation: Concatenate
You may add up two list or we say concatenate, and multiply to duplicate the items.
End of explanation
print(x[::-1])
y = sorted(x[::-1])
print(y)
Explanation: Sorting
You may sort a list with sorted(x). Noted that it returns a new list.
End of explanation
print(x)
x.append('A')
print(x)
print(x)
x.insert(5,'B') # insert 'B' between x[4] and x[5], results in x[5] = 'B'
print(x)
print(x); 
x.pop(5); # Removed the x[5] item and return it
print(x); 
x.pop(-1); # Removed the last item and return it
print(x)
Explanation: Add element (append); Remove element (pop); Insert element (insert)
These functions are modified in-place, i.e. the original list will be changed
End of explanation
corr = (22.28552, 114.15769)
print(corr)
corr[0] = 10
Explanation: Tuple
A Python tuple is similar to a list. The elements are in order but fixed once they are created. In other words, they are immutable. The tuple can store differently type of elements. 
Definition
It is defined with parentheses : (xx,xx,xx). 
Get Element
The elements are called using a square bracket with an index starting from zero : x[y], 0..N. 
Slice (sub-array)
You can slice the array using colon, in this case a[start:end] means items start up to end-1.
End of explanation
# Creating an empty dictionary
location = {}
print(location)
# Defined with a curly bracket
location = {
            'Berlin': (52.5170365, 13.3888599),
            'London': (51.5073219, -0.1276474),
            'Sydney': (-33.8548157, 151.2164539),
            'Tokyo': (34.2255804, 139.294774527387),
            'Paris': (48.8566101, 2.3514992),
            'Moscow': (46.7323875, -117.0001651)
           }
print(location)
# Update
location.update({'Hong Kong': (22.2793278, 114.1628131)})
print(location)
# Call element
location['Tokyo']
# Delete element
del location['Hong Kong']
location
for key, value in location.items():
    print(key, value)
Explanation: Dictionary
Dictionary is more flexible than list and its index is a string, it is defined with curly bracket: 
data = {'k1' : y1 , 'k2' : y2 , 'k3' : y3 }
k1, k2, k3 are called keys while y1,y2 and y3 are elements.
Creating an empty dictionary
It is defined with a pair of curly bracket or the dict() fuction: data = {} or data = dict()
Creating a dictionary with initial values
It could be defined with a curly bracket with index:element pairs : data = {'k1' : y1 , 'k2' : y2 , 'k3' : y3 }. 
It could also be defined with the dict() function : data = dict(k1=y1, k2=y2, k3=y3).
It could also be defined with tuples : data = {k: v for k, v in (('k1', y1),('k2',y2),('k3',y3))}.
Get Element
The elements are called using a square bracket with an index string : data[key]. 
Inserting/Updating a single value / multiple values
data['k1']=1  # Updates if 'k1' exists, else adds the element with index 'k1'
data.update({'k1':1})
data.update(dict(k1=1))
data.update(k1=1)
Multiple values : data.update({'k3':3,'k4':4})  # Updates 'k3' and adds 'k4'
Merged dictionary without modifying originals
data3 = {}
data3.update(data)  # Modifies data3, not data
data3.update(data2)  # Modifies data3, not data2
Delete an item
del data[key]  # Removes specific element in a dictionary
data.pop(key)  # Removes the key & returns the value
data.clear()  # Clears entire dictionary
Check if a key is existed
key in data # Return a boolean
Iterate through pairs
for key in data: # Iterates just through the keys, ignoring the values
for key, value in d.items(): # Iterates through the pairs
End of explanation
### More on slicing in list and tuple
start=2
end=5
step=2
print("Original:", x)
print("items start through end-1 :", x[start:end]) # items start through end-1
print("items start through the rest of the array :", x[start:])    # items start through the rest of the array
print("items from the beginning through end-1 :", x[:end])      # items from the beginning through end-1
print("whole array :", x[:])         # whole array
print("last item in the array :", x[-1])    # last item in the array
print("last two items in the array :", x[-2:])   # last two items in the array
print("everything except the last two items :", x[:-2])   # everything except the last two items
print("start through not past end, by step", x[start:end:step]) # start through no01-Python-Syntaxt past end, by step
Explanation: Extra reading:
End of explanation
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