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Solution: Range Sum Query - Immutable

Explore how to efficiently compute the sum of array elements within a given range by using an immutable prefix sum approach. This lesson guides you through implementing the NumArray class that precomputes cumulative sums to enable constant-time sumRange queries, helping you solve complex coding challenges with optimal time and space complexity.

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Statement

You are given an integer array, nums, and you need to handle multiple queries of the following type:

  • Query: Calculate the sum of elements in nums between indices i and j (inclusive), where i <= j.

Implement the NumArray class to support the following operations efficiently:

  • Constructor: Initializes the object with the integer array nums.

  • sumRange(i, j): Returns the sum of the elements of nums between indices i and j (inclusive), i.e., the sum of nums[i] + nums[i + 1] + ... + nums[j].

Constraints:

  • 1≤1 \leq nums.length ≤103\leq 10^3

  • −105≤-10^5 \leq nums[i] ...