DSA TrainerRange Sum Query - Immutable
Design a data structure that handles repeated range sum queries on an immutable array. Given array `nums`, each call to `sumRange(left, right)` should return the sum of elements between indices left and right (inclusive). Optimize for multiple query calls.
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Problem
Given an integer array nums, handle multiple queries of the following type: calculate the sum of the elements of nums between indices left and right inclusive.
Input
An integer array `nums` and multiple `sumRange(left, right)` queries.
Output
The sum of `nums[left..right]` for each query.
Examples
Input: nums = [-2,0,3,-5,2,-1], queries: sumRange(0,2), sumRange(2,5), sumRange(0,5)
Output: 1, -1, -3
Precompute prefix sums. sumRange(0,2) = prefix[3] - prefix[0] = 1.
The brute-force approach
For each query, loop from left to right and sum the elements.
def sumRange(left, right):
return sum(nums[left:right+1])O(n) per query. With many queries, this is O(n × queries) total.
Spotting the pattern
This is a Prefix Sum problem. The key question to ask yourself:
If you know the running total up to index right+1 and the running total up to index left, how do you isolate the sum of the range [left, right] from those two numbers?
Answering that is where it clicks, and it's exactly what the guided walkthrough below builds with you: the pattern reasoning, a progressive hint ladder that never spoils the answer, a row-by-row dry run, the optimized solution, and an in-browser editor to run your code against real test cases.
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