[LeetCode] 303. Range Sum Query - Immutable

Given an integer array nums, find the sum of the elements between indices i and j (i ≤ j), inclusive.
Example:
Given nums = [-2, 0, 3, -5, 2, -1]

sumRange(0, 2) -> 1
sumRange(2, 5) -> -1
sumRange(0, 5) -> -3
Note:
  1. You may assume that the array does not change.
  2. There are many calls to sumRange function.

Thought process:
Use prefix sum (DP): sum(i, j) = prefixSum(j) - prefixSum(i - 1).

Solution:

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class NumArray {
    private int[] prefixSum;
    
    public NumArray(int[] nums) {
        prefixSum = new int[nums.length + 1];
        for (int i = 1; i < prefixSum.length; i++) {
            prefixSum[i] = prefixSum[i - 1] + nums[i - 1];
        }
    }
    
    public int sumRange(int i, int j) {
        return prefixSum[j + 1] - prefixSum[i];
    }
}

/**
 * Your NumArray object will be instantiated and called as such:
 * NumArray obj = new NumArray(nums);
 * int param_1 = obj.sumRange(i,j);
 */

Time complexity: 
  1. Constructor(): O(n).
  2. sumRange(): O(1).
Location: San Jose, CA, USA

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