Dictionaries：練習問題

Which of the following describes a dictionary as an abstract data type?

A 4-vector over \( \mathbb{R} \) is represented as a dictionary mapping indices to values. Given the vector:
\( 0 \mapsto 2.0 \)
\( 1 \mapsto 3.14 \)
\( 2 \mapsto -1.0 \)
\( 3 \mapsto 2.72 \)
Which of the following is the correct representation of this vector in Python dictionary syntax?

A dictionary is used to represent a sparse vector in a high-dimensional space. If a vector in \( \mathbb{R}^5 \) is defined as \( v = [0, 1.5, 0, 0, -3.2] \), which dictionary representation is both memory-efficient and logically correct based on the index-to-value mapping?

A programmer is representing a document containing the words 'The green, green grass grows' as a dictionary by mapping each unique word to its frequency of occurrence. What would be the correctly formatted dictionary representation, ignoring letter case?

A dictionary is a data structure consisting of key-value pairs. Describe the primary method used to access a value within a dictionary.

Explain why a dictionary can be considered a valid representation of a vector, and provide an example of the vector \([0.5, 0.0, 1.2]\) represented as a dictionary.

A Dictionary is used to represent the sparse vector \( [0, 0, 4.5, 0, -1.2] \) where indices map to values. Provide the dictionary representation and explain why this is more efficient than a 1D array for very large sparse vectors.

A Dictionary is an abstract data type that stores key-value pairs. Consider the following dictionary representing the inventory of a small store:
Inventory = {"Apple": 50, "Banana": 20, "Orange": 30}

a. What is the value associated with the key "Banana"? (1 point)
b. Describe the logical result of performing the operation Update(Inventory, "Apple", 45). (1 point)
c. What occurs if a programmer attempts to add a new key "Apple" with a different value? (1 point)