Prefix Sum Pattern for Coding Interviews: 2026 Guide

Some coding interview patterns announce themselves loudly: a sorted array screams binary search, a dependency graph screams topological sort. The prefix sum pattern is quieter. It hides inside questions about subarrays, ranges, running balances and “how many ways” — and candidates who don’t recognise it end up writing an O(n²) double loop while the interviewer waits for the O(n) insight.

This guide covers how prefix sums work, the three variants that show up most often in 2026 coding interviews, and a repeatable way to spot them under pressure. Code samples are in Java, but the ideas translate directly to Python, C++ or JavaScript.

What Is the Prefix Sum Pattern?

A prefix sum array stores the cumulative total of every element up to each index. For an input array nums, define prefix[i] as the sum of the first i elements, with prefix[0] = 0. Once that array exists, the sum of any subarray nums[l..r] is a single subtraction:

sum(l, r) = prefix[r + 1] - prefix[l]

That one identity is the whole pattern. You pay O(n) once to build the array, and every range query afterwards costs O(1). The leading zero is not decoration — it removes an entire class of off-by-one bugs by letting subarrays that start at index 0 use the same formula as everything else.

Variant 1: Range Sum Queries

The textbook version is LeetCode 303, Range Sum Query – Immutable. The array never changes, but you’re asked for the sum between two indices thousands of times. Recomputing each sum is O(n) per query; a prefix array makes it O(1).

class NumArray {
    private final int[] prefix;

    public NumArray(int[] nums) {
        prefix = new int[nums.length + 1];
        for (int i = 0; i < nums.length; i++) {
            prefix[i + 1] = prefix[i] + nums[i];
        }
    }

    public int sumRange(int left, int right) {
        return prefix[right + 1] - prefix[left];
    }
}

Interviewers rarely stop here. Expect follow-ups such as “What if the array is two-dimensional?” (LeetCode 304) or “What if values can be updated?” For the 2D case, extend the idea so prefix[r][c] holds the sum of the rectangle from the origin, and use inclusion–exclusion to query any sub-rectangle. For frequent updates, say clearly that a plain prefix array breaks down and a Fenwick tree or segment tree is the right tool — naming the trade-off is often worth more than coding it.

Variant 2: Prefix Sum + Hash Map

This is the variant that separates prepared candidates from everyone else. The classic problem is LeetCode 560, Subarray Sum Equals K: count the contiguous subarrays whose sum equals k. Because the array can contain negative numbers, a sliding window does not work — the window sum is not monotonic.

The insight: a subarray ending at index j sums to k exactly when some earlier prefix equals currentPrefix - k. So as you scan, keep a hash map from prefix value to how many times you’ve seen it.

public int subarraySum(int[] nums, int k) {
    Map<Integer, Integer> seen = new HashMap<>();
    seen.put(0, 1);          // empty prefix
    int sum = 0, count = 0;

    for (int num : nums) {
        sum += num;
        count += seen.getOrDefault(sum - k, 0);
        seen.merge(sum, 1, Integer::sum);
    }
    return count;
}

Three details interviewers watch for:

• Seeding the map with {0: 1}. Without it, subarrays that start at index 0 are silently missed.
• Querying before inserting. Look up sum - k before adding the current sum, otherwise k = 0 counts empty subarrays.
• Overflow awareness. In Java, mention that you’d switch to long if inputs could push the running sum past Integer.MAX_VALUE.

The same template solves a surprising number of problems once you change what the map stores:

• Contiguous Array (LeetCode 525): treat 0 as -1, then find the longest subarray with sum 0. Store the first index each prefix appears instead of a count.
• Continuous Subarray Sum (LeetCode 523): store prefix % k. Two equal remainders at least two indices apart mean a multiple of k.
• Subarray Sums Divisible by K (LeetCode 974): count equal remainders, normalising negatives with ((sum % k) + k) % k.

Variant 3: Prefix Products and Difference Arrays

“Prefix” does not have to mean addition. LeetCode 238, Product of Array Except Self, forbids division and asks for O(n) time. The answer at each index is the product of everything to its left multiplied by everything to its right — a prefix product and a suffix product. Candidates who already think in prefixes usually solve it in minutes, and can then optimise to O(1) extra space by reusing the output array for the left pass.

The inverse idea is the difference array. When a problem applies many range updates (“add 5 to every index from 2 to 7”) and asks for the final state, record +v at the start of each range and -v just past its end. A single prefix-sum pass at the end reconstructs every value. This handles problems like Corporate Flight Bookings (LeetCode 1109) and Car Pooling (LeetCode 1094), and it maps neatly to real systems: counting concurrent sessions or overlapping reservations from start/end events.

How to Recognise a Prefix Sum Problem

Under interview pressure, pattern recognition matters more than memorised solutions. Reach for prefix sums when you notice these signals:

1. The word “subarray” or “contiguous” combined with a sum, count, average or balance condition.
2. Repeated range queries on data that doesn’t change between queries.
3. Negative numbers are allowed, which rules out a sliding window and points toward prefix sum plus hash map.
4. “Equal number of X and Y” — map one to +1 and the other to -1, then look for a zero-sum subarray.
5. Many range updates, one final read — that’s a difference array.

A useful habit: whenever your first idea is a nested loop over (start, end) pairs, pause and ask whether the inner loop is just recomputing a running total. If it is, a prefix array or hash map almost always removes it.

Common Mistakes to Avoid

• Using sliding window with negatives. It’s the most frequent wrong turn on LeetCode 560. State why it fails before switching approaches — interviewers reward the reasoning.
• Mixing inclusive and exclusive indices. Pick the prefix[i + 1] = prefix[i] + nums[i] convention and stick with it.
• Storing the wrong thing in the map. Counting problems store frequencies; “longest subarray” problems store the earliest index and never overwrite it.
• Forgetting complexity analysis. Always close with time O(n) and space O(n), and mention when the space can drop to O(1).

A One-Week Prefix Sum Practice Plan

If prefix sums are a gap in your preparation, this short plan builds the pattern from fundamentals to interview-ready:

• Day 1: Range Sum Query – Immutable (303) and Running Sum of 1D Array (1480).
• Day 2: Range Sum Query 2D (304). Draw the inclusion–exclusion diagram by hand.
• Day 3: Subarray Sum Equals K (560). Solve it, then explain it aloud as if to an interviewer.
• Day 4: Contiguous Array (525) and Continuous Subarray Sum (523).
• Day 5: Subarray Sums Divisible by K (974) and Product of Array Except Self (238).
• Day 6: Corporate Flight Bookings (1109) and Car Pooling (1094) for difference arrays.
• Day 7: Re-solve three problems from memory under a 20-minute timer, narrating your approach.

The narration step matters. In a live interview, the candidate who says “the running sum is monotonic only for non-negative inputs, so I’ll use a prefix-sum map instead of a window” demonstrates far more than one who silently produces working code.

Start Practising Today

Prefix sums are one of the highest-leverage patterns you can learn: a single identity unlocks range queries, subarray counting, divisibility checks and bulk range updates. Pick one problem from the plan above and solve it today, then explain your solution out loud before you look at any editorial. If you want structured support while you practise, explore Niraswa AI and keep building the habits that turn a quiet pattern into an obvious one in your next interview.