# Time:  ctor:   O(n),
#        lookup: O(1)
# Space: O(n)
#
#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:
# You may assume that the array does not change.
# There are many calls to sumRange function.
#

class NumArray(object):
    def __init__(self, nums):
        """
        initialize your data structure here.
        :type nums: List[int]
        """
        self.accu = [0]
        for num in nums: 
            self.accu += self.accu[-1] + num,

    def sumRange(self, i, j):
        """
        sum of elements nums[i..j], inclusive.
        :type i: int 
        :type j: int
        :rtype: int 
        """
        return self.accu[j + 1] - self.accu[i]
        

# Your NumArray object will be instantiated and called as such:
# numArray = NumArray(nums)
# numArray.sumRange(0, 1)
# numArray.sumRange(1, 2)

# Time:  ctor:   O(n),
#        lookup: O(1)
# Space: O(n)
#
#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:
# You may assume that the array does not change.
# There are many calls to sumRange function.
#

class NumArray(object):
    def __init__(self, nums):
        """
        initialize your data structure here.
        :type nums: List[int]
        """
        self.accu = [0]
        for num in nums: 
            self.accu.append(self.accu[-1] + num),

    def sumRange(self, i, j):
        """
        sum of elements nums[i..j], inclusive.
        :type i: int 
        :type j: int
        :rtype: int 
        """
        return self.accu[j + 1] - self.accu[i]
        

# Your NumArray object will be instantiated and called as such:
# numArray = NumArray(nums)
# numArray.sumRange(0, 1)
# numArray.sumRange(1, 2)

Update range-sum-query-immutable.py