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Solution: Range Sum Query - Immutable

Explore how to design and implement the NumArray class to efficiently handle range sum queries on integer arrays. Understand the use of prefix sum arrays to achieve constant time sum retrieval between indices, improving query performance while managing space complexity effectively.

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:

  • 11 \leq nums.length 103\leq 10^3

  • 105-10^5 \leq nums[i] ...