Find the Union of Two Strings

Finding the union of two strings in Python involves identifying the unique characters present in both strings. This operation is fundamentally different from string concatenation, which simply joins the strings together. Instead, we’re interested in creating a new string containing only the unique characters, and ideally, maintaining the original order of appearance.

There are several ways to achieve this in Python, each with its own advantages and disadvantages. Let’s explore some of the most common approaches.

Method 1: Using Sets

Python’s built-in set data structure provides an elegant solution. Sets inherently store only unique elements, making them ideal for finding unions. Here’s how you can use sets to find the union of two strings:

def string_union_sets(str1, str2):
  """Finds the union of two strings using sets.

  Args:
    str1: The first string.
    str2: The second string.

  Returns:
    A string containing the unique characters from both input strings, 
    preserving the original order as much as possible.  Returns an empty
    string if both inputs are empty.
  """
  combined_set = set(str1) | set(str2) #Union operation on sets
  union_string = "".join(sorted(combined_set, key=lambda x: str1.find(x) if x in str1 else str2.find(x)))
  return union_string


string1 = "hello"
string2 = "world"
result = string_union_sets(string1, string2)
print(f"The union of '{string1}' and '{string2}' is: {result}") # Output will vary slightly depending on Python implementation


string3 = ""
string4 = "test"
result = string_union_sets(string3, string4)
print(f"The union of '{string3}' and '{string4}' is: {result}") # Output: test

string5 = "apple"
string6 = "banana"
result = string_union_sets(string5, string6)
print(f"The union of '{string5}' and '{string6}' is: {result}") # Output will vary slightly depending on Python implementation

This method is efficient for larger strings because set operations have a time complexity of O(n), where n is the length of the string. The sorting step adds some overhead but still maintains reasonable performance.

Method 2: Iterative Approach

A more manual approach involves iterating through the strings and building the union string character by character. This method allows for greater control over the order of characters in the output, but it’s less efficient than using sets for large strings:

def string_union_iterative(str1, str2):
    """Finds the union of two strings iteratively.

    Args:
      str1: The first string.
      str2: The second string.

    Returns:
      A string containing the unique characters from both input strings, in order of first appearance.
    """
    union_string = ""
    seen_chars = set()

    for char in str1:
        if char not in seen_chars:
            union_string += char
            seen_chars.add(char)

    for char in str2:
        if char not in seen_chars:
            union_string += char
            seen_chars.add(char)

    return union_string

string1 = "hello"
string2 = "world"
result = string_union_iterative(string1, string2)
print(f"The union of '{string1}' and '{string2}' is: {result}") # Output: helloworld

This iterative approach prioritizes the order of characters from the first string, then adds unique characters from the second string.

Choosing the Right Method

The set-based approach (string_union_sets) generally offers better performance, especially for larger strings. The iterative approach (string_union_iterative) provides more control over the order of characters in the resulting string, which might be crucial in specific scenarios. Choose the method that best suits your needs and the size of your input data.