Visualized DSA Strategies

Episode 3 Prefix Sums

1 h 6 min · Python · Quiz

Episode 3Prefix Sums

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The complete guide to prefix sums for coding interviews, in Python. First how a prefix array is built and why it has one extra slot; the four questions a running total answers; what each approach costs; the Python for prefix and difference arrays; and five traps. Then nine types, each worked as a small problem in full: examples, the brute force animated beside the running line of code, the complete code, every line explained, and the prefix-sum solution the same way.

What you'll learn

  • How a prefix array turns any range sum into one subtraction
  • Why the array has n + 1 slots and starts with 0
  • Left total against right total with a running sum
  • Counting subarrays that sum to k with a prefix map
  • Prefix remainders and balances: the same prefix twice means a range between
  • Prefix and suffix products without division
  • A difference array for many range updates
  • 2D prefix sums and the four-corner formula
  • Running maximums from both sides: trapping rain water

Chapters

  1. 0:00Intro
  2. 0:24Build a prefix array
  3. 1:46Four questions prefix sums answer
  4. 2:23What each approach costs
  5. 3:08Prefix sums in Python
  6. 4:34Five traps
  7. 5:32Nine prefix-sum types
  8. 6:15Type 1 · Sum of a range, many times
  9. 11:53Type 2 · Where the two sides balance
  10. 18:06Type 3 · Count subarrays that add to k
  11. 24:24Type 4 · A subarray that's a multiple of k
  12. 30:56Type 5 · Equal zeros and ones
  13. 37:45Type 6 · Product of everything else
  14. 44:20Type 7 · Many range updates, one sweep
  15. 50:35Type 8 · The sum of a rectangle
  16. 57:19Type 9 · How much rain is trapped
  17. 1:03:52Spot the type
  18. 1:04:41Quiz: which type?
  19. 1:05:28Recap

Quiz: test yourself

The 5 questions from the end of the episode. Pick an answer to see why it's right.