Solution: Range Sum Query - Immutable

Understand how to design the NumArray class to efficiently handle multiple range sum queries on an integer array. Learn to build and use a prefix sum array in the constructor to enable constant-time sum calculations between indices. This lesson covers algorithm implementation, complexity analysis, and practical usage to solve range sum queries using an immutable approach.

We'll cover the following...

Statement
Solution
- Time complexity
- Space complexity

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:

$1 \leq$ nums.length $\leq 10^3$
$-10^5 \leq$ nums[i] ...