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Set Operations

Introduction

Python sets support mathematical set operations like Union, Intersection, and Difference. These operations are highly optimized in C and are extremely useful for solving problems that ask you to compare two collections of data.

Intersection (&)

Returns a new set containing only the elements found in both sets.

a = {1, 2, 3, 4}
b = {3, 4, 5, 6}

print(a & b) # {3, 4}

When to use

Use intersection when a problem asks you to find "common elements" between two arrays.

  • Time Complexity: \(O(\min(\text{len}(a), \text{len}(b)))\)

Union (|)

Returns a new set containing all unique elements from both sets.

a = {1, 2, 3}
b = {3, 4, 5}

print(a | b) # {1, 2, 3, 4, 5}

When to use

Use union when combining multiple lists of results and you need to ensure no duplicates exist in the final output.

  • Time Complexity: \(O(\text{len}(a) + \text{len}(b))\)

Difference (-)

Returns a new set containing elements that are in the first set, but not in the second set.

a = {1, 2, 3, 4}
b = {3, 4}

print(a - b) # {1, 2}

When to use

Use difference when you need to filter a collection against a list of "invalid" or "seen" items.

  • Time Complexity: \(O(\text{len}(a))\)

Symmetric Difference (^)

Returns a new set containing elements that are in either set, but not both.

a = {1, 2, 3}
b = {2, 3, 4}

print(a ^ b) # {1, 4}

When to use

Use symmetric difference when a problem asks you to find elements that appear exactly once across two arrays.

  • Time Complexity: \(O(\text{len}(a) + \text{len}(b))\)

In-Place Updates

All of the above operators create a new set. If you want to modify an existing set in place to save memory, use the assignment versions:

  • &= (intersection_update)
  • |= (update)
  • -= (difference_update)
  • ^= (symmetric_difference_update)
a = {1, 2, 3}
b = {3, 4, 5}

a &= b # Modifies 'a' directly
print(a) # {3}

Summary

  • Use & (Intersection) for common elements.
  • Use | (Union) to combine uniquely.
  • Use - (Difference) to remove specific elements.
  • Use ^ (Symmetric Difference) for exclusively unique elements.
  • Use the x= versions for in-place modifications to save memory.