Python Two-Dimensional Dictionary

In Python, the dictionary (dict) is a very useful data type. Essentially, it’s a mapping of key-value pairs, allowing for efficient data organization and querying. Typically, the keys and values of a Python dictionary are single data types, such as strings, integers, and floating-point numbers. However, sometimes, we need to expand a dictionary’s keys or values to composite types, such as tuples, lists, and dictionaries. This is where two-dimensional dictionaries come in handy.

Definition of a Two-Dimensional Dictionary

A two-dimensional dictionary is a dictionary whose keys or values are another dictionary. Its definition is simple: simply use nested dictionaries. For example, the following code defines a two-dimensional dictionary:

>>> d = {'a': {'x': 1, 'y': 2}, 'b': {'x': 3, 'y': 4}}
>>> print(d)
{'a': {'x': 1, 'y': 2}, 'b': {'x': 3, 'y': 4}}

In this two-dimensional dictionary, the values corresponding to the entries with keys ‘a’ and ‘b’ are both dictionaries with two key-value pairs: ‘x’: 1, ‘y’: 2 and ‘x’: 3, ‘y’: 4, respectively. In addition to nested dictionaries, two-dimensional dictionaries can also have other types of keys and values, such as strings and integers. For example:

>>> d = {'a': 1, 'b': {'x': 3, 'y': 4}}
>>> print(d)
{'a': 1, 'b': {'x': 3, 'y': 4}}

In this two-dimensional dictionary, the value corresponding to the key ‘b’ is a dictionary with two key-value pairs: ‘x’: 3, ‘y’: 4. The value corresponding to the key ‘a’ is the integer 1.

Two-Dimensional Dictionary Operations

Two-dimensional dictionaries operate similarly to regular dictionaries, but special attention must be paid to the data types of the keys and values, as well as how nested dictionaries are accessed. The following are some common operation examples:

Accessing Elements of a Two-Dimensional Dictionary

Accessing elements of a two-dimensional dictionary requires two levels of key names. The first level corresponds to the outer dictionary’s key, and the second level corresponds to the inner dictionary’s key. For example, to access the value of the key ‘y’ in the dictionary corresponding to the element ‘b’ in the two-dimensional dictionary {‘a’: {‘x’: 1, ‘y’: 2}, ‘b’: {‘x’: 3, ‘y’: 4}}, you can use the following code:

>>> d = {'a': {'x': 1, 'y': 2}, 'b': {'x': 3, 'y': 4}}
>>> print(d['b']['y'])
4

Modifying Elements in a Two-Dimensional Dictionary

Modifying elements in a two-dimensional dictionary also requires using two levels of key names. For example, to change the value of the key ‘y’ in the dictionary corresponding to element ‘b’ in the two-dimensional dictionary above to 5, you can use the following code:

>>> d = {'a': {'x': 1, 'y': 2}, 'b': {'x': 3, 'y': 4}}
>>> d['b']['y'] = 5
>>> print(d)
{'a': {'x': 1, 'y': 2}, 'b': {'x': 3, 'y': 5}}

Traversing the Elements of a Two-Dimensional Dictionary

Traversing the elements of a two-dimensional dictionary requires two loops. The outer loop iterates over the keys of the outer dictionary, while the inner loop iterates over both the keys and values of the inner dictionary. For example, to iterate over all elements in a two-dimensional dictionary {‘a’: {‘x’: 1, ‘y’: 2}, ‘b’: {‘x’: 3, ‘y’: 4}}, you can use the following code:

>>> d = {'a': {'x': 1, 'y': 2}, 'b': {'x': 3, 'y': 4}}
>>> for k1, v1 in d.items():
... print(k1)
... for k2, v2 in v1.items():
... print(k2, v2)
...
a
x 1
y 2
b
x 3
y 4

The above code first uses an outer loop to iterate over all keys in the two-dimensional dictionary, and then uses an inner loop to iterate over the keys and values in each inner dictionary.

Length of a Two-Dimensional Dictionary

The length of a two-dimensional dictionary refers to the total number of key-value pairs within it, including the outer and inner dictionaries. To find the length of a two-dimensional dictionary, use the following code:

>>> d = {'a': {'x': 1, 'y': 2}, 'b': {'x': 3, 'y': 4}}
>>> print(len(d))
2
>>> count = 0
>>> for k1, v1 in d.items():
... count += len(v1)
...
>>> print(count)
4

In the code above, the first print statement outputs the length of the outer dictionary, which is 2; the second print statement uses a loop to add up the lengths of all the inner dictionaries, which is 4.

Practical Applications of Two-Dimensional Dictionaries

Two-dimensional dictionaries are very useful in real-world applications. They are often used to record complex data structures such as tables and graphs. For example, we can use a two-dimensional dictionary to store a set of student grades. Each student has a corresponding dictionary, which stores key-value pairs for each subject’s grades:

>>> scores = {'Tom': {'Math': 98, 'English': 87, 'Science': 94},
... 'Lucy': {'Math': 85, 'English': 92, 'Science': 88},
... 'Lily': {'Math': 78, 'English': 83, 'Science': 79}}
>>> print(scores['Tom']['English'])
87

In the above code, we define a two-dimensional dictionary, scores, that records the math, English, and science scores of three students. Indexing allows for easy access to any student’s score in any subject.

In addition, two-dimensional dictionaries are often used to record edge and node data of graphs. For example, we can use a two-dimensional dictionary to record the edge data of a directed graph. Each node corresponds to a dictionary that stores key-value pairs of all adjacent nodes:

>>> graph = {'A': {'B': 3, 'C': 4},
... 'B': {'D': 2, 'E': 4},
... 'C': {'F': 5},
... 'D': {'F': 1, 'G': 2},
... 'E': {'G': 4},
... 'F': {'G': 1}}
>>> print(graph['A']['C'])
4

In the above code, we define a two-dimensional dictionary, graph, to record the edge data of a directed graph. Indexing allows convenient access to any node’s adjacent nodes and edge weights.

Conclusion

Two-dimensional dictionaries are a very useful data type in Python, used for storing complex data structures and querying them. Defining a two-dimensional dictionary is simple: simply nest dictionaries within a dictionary. Two-dimensional dictionaries operate similarly to regular dictionaries, but require special attention to the data types of keys and values, as well as how nested dictionaries are accessed. In practical applications, two-dimensional dictionaries are often used to store complex data structures, such as tables and graph edge and node data. Mastering the use of two-dimensional dictionaries can provide greater flexibility and scalability in data processing and algorithm design.