range_sum_query.rb

class NumArray
  def initialize(nums)
    sum = 0
    @prefix_sums = nums.map do |x|
      sum += x
    end
    @prefix_sums.prepend(0)
  end

  def sum_range(left, right)
    @prefix_sums[right + 1] - @prefix_sums[left]
  end
end

class NumArray
  def initialize(nums)
    @nums = nums

    # instead of [0..i] as prefix, use [i..n] as postfix
    sum = 0
    @postfix_sum = nums.reverse.map do |value|
      sum += value
    end.reverse
  end

  def sum_range(left, right)
    @postfix_sum[left] - @postfix_sum[right] + @nums[right]
  end
end