From Naive Loops to O(1) Brilliance: The Power of Prefix Sums &
Difference Arrays
When I first started solving array problems, I always reached for loops. Want to find the sum of a subarray? Loop. Want to update a range of elements? Loop again.
But then I discovered something that changed everything — prefix sums and difference arrays. These techniques are all about one thing: Do a little work up front to save a lot of time later.
The Problem
Given an array, you’re asked repeatedly:
“What’s the sum of elements between index L and R?”
The naive approach:
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let sum = 0;
for (let i = L; i <= R; i++) sum += arr[i];
But that’s O(n) per query — not scalable.
Enter: Prefix Sums
One pass builds a prefix array:
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prefix[0] = arr[0];
for (let i = 1; i < arr.length; i++) {
prefix[i] = prefix[i - 1] + arr[i];
}
Now range sum is O(1):
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sum = prefix[R] - (L > 0 ? prefix[L - 1] : 0);
Range Updates with Difference Arrays
Need to add +10 to every number from index 2 to 5?
Instead of looping:
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diff[2] += 10;
diff[6] -= 10;
Apply a prefix sum to diff at the end to get the final array.
This is how we update ranges in O(1) time.
Real-Life Applications
Used in:
Range-based scoring in games 
Bulk financial transactions 
Efficient spreadsheet operations 
Why It Matters
Prefix sums and diff arrays teach you to solve smarter, not harder.
They’re not just coding tricks — they’re a mindset:
Minimize repetition
Maximize efficiency
Think in preprocess → query cycles
Curious to Try?
Next time you’re about to loop through a subarray — pause.
There might be a better way waiting for you.
Let’s write code that thinks ahead.
#DSA #Arrays #CodingTips #BigO #LearningByDoing