LeetCode 307. Range Sum Query - Mutable

Given an integer array nums, find the sum of the elements between indices i and j (i ≤ j), inclusive.

The update(i, val) function modifies nums by updating the element at index i to val.

Example:

Given nums = [1, 3, 5]sumRange(0, 2) -> 9update(1, 2)sumRange(0, 2) -> 8

Note:

1. The array is only modifiable by the update function.
2. You may assume the number of calls to update and sumRange function is distributed evenly.

#include <vector>#include <iostream>using namespace std;// this is actually to use binary index tree.int getSum(vector<int>& BITree, int index) {  int sum = 0;  index = index + 1;  while(index > 0) {    sum += BITree[index];    index -= index & (-index); // update to its parent node in getSum view.  }  return sum;}void updateBITree(vector<int>& BITree, int index, int val) {  index = index + 1;  while(index < BITree.size()) {    BITree[index] += val;    index += index & (-index); // update to its parent node in update view  }}vector<int> createBITree(vector<int>& nums) {  int n = nums.size();  vector<int> BITree(n + 1, 0);  for(int i = 0; i < n; ++i) {    updateBITree(BITree, i, nums[i]);  }  return BITree;}int main(void) {  vector<int> nums{1, 3, 5};  vector<int> BITree = createBITree(nums);  updateBITree(BITree, 1, 2);  cout << getSum(BITree, 2) << endl;}

Binary Index Tree: See explain here: Binary Index Tree However, how the index is organized is not clear.

Let's use an example to help explain how to organize a binary index tree.

Suppose we have a 10 size array [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

Our target tree will be like this:

The picture above shows how is the binary index tree organized. There are several things to pay attentions to:

1: Update parent node is index += index & (-index)

2: GetSum parent node is index -= index &(-index)

3: BITree's first index is empty.

4: The parent index equals to change the child index's rightmost bit '1' into '0'.