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Prefix Sum technique - more useful than you think

Smriti BansalSmriti Bansal
10 months ago
403

Prefix sum is one of those techniques that seems too simple to be useful, but it solves a lot of problems elegantly:

Basic idea: Precompute cumulative sums so any range sum is O(1).

Problems it solves:

  • Subarray sum equals K
  • Range sum query
  • Contiguous array (with hashmap)
  • Product of array except self (prefix + suffix products)
  • Maximum subarray (Kadane's is basically a prefix sum variant)

2D extension: Prefix sum on matrix for area queries.

Once you recognize the pattern, these problems become trivial. Highly recommend practicing 5-10 prefix sum problems.

prefix-sumtechniquetutorialdsa

Comments (4)

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Tanvi Batra
Tanvi Batra6 months ago

This is a solid breakdown, Smriti! I used prefix sums for the first time to solve a range sum query problem and it blew my mind how fast it made everything. Curious though, how often do you actually use the 2D prefix sum in competitive programming?

Garima Chauhan
Garima Chauhan8 months ago

I used to think prefix sums were boring until they helped me optimize my code from O(n^2) to O(n) 😂. Anyone else had a similar eureka moment?

Katya Kozlov
Katya Kozlov9 months ago

I’m not sure I fully get how the 'Product of array except self' fits into the prefix sum idea. Isn’t that more about separate product arrays?

Urvi Iyer
Urvi Iyer9 months ago

Does anyone know a good resource for practicing 2D prefix sum problems? I grasp the concept but finding practical applications would be helpful.