Range Sum Query - Mutable

Problem: Range Sum Query - Mutable

The general solution is binary-indexed tree. The link refers to a detailed tutorial. Its basic idea is to store partial range sum at an array-implemented tree.

Code in Python:

class NumArray(object):
    def __init__(self, nums):
        """
        initialize your data structure here.
        :type nums: List[int]
        """
        self.length = len(nums) + 1
        self.nums = nums
        self.tree = [0] * self.length
        for i in xrange(1, self.length):
            self.tree[i] = self.sumBefore(i-1) - self.sumBefore(i-(i&(-i))) + self.nums[i-1]

    def sumBefore(self, i):
        return 0 if i == 0 else self.tree[i] + self.sumBefore(i-(i&(-i)))


    def update(self, i, val):
        """
        :type i: int
        :type val: int
        :rtype: int
        """
        diff = val - self.nums[i]
        self.nums[i] = val
        i += 1
        while i < self.length:
            self.tree[i] += diff
            i += (i&(-i))


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