Nov 9, 2025
diff --git a/src/data_structures/fenwick.md b/src/data_structures/fenwick.md

 We can find arbitrary range sums by computing the prefix sums for $l-1$ and $r$ and taking the difference of them again.

 ```python
 def add(b, idx, x):
    while idx <= N:
        b[idx] += x
        idx += idx & -idx
 ```cpp
 void add(std::vector<int> b, int idx, int x) {
    while (idx <= n) {
        b[idx] += x;
        idx += idx & -idx;
    }
 }

 def range_add(l,r,x):
 void range_add(int l, int r, int x) {
    add(B1, l, x)
    add(B1, r+1, -x)
    add(B2, l, x*(l-1))
    add(B2, r+1, -x*r)
    add(B1, r + 1, -x)
    add(B2, l, x * (l - 1))
    add(B2, r + 1, -x * r)
 }

 def sum(b, idx):
    total = 0
    while idx > 0:
        total += b[idx]
        idx -= idx & -idx
    return total
 int sum(std::vector<int> b, int idx) {
    int total = 0;
    while (idx > 0) {
        total += b[idx];
        idx -= idx & -idx;
    }
    return total;
 }

 def prefix_sum(idx):
    return sum(B1, idx)*idx -  sum(B2, idx)
 int prefix_sum(int idx) {
    return sum(B1, idx) * idx - sum(B2, idx);
 }

 def range_sum(l, r):
    return prefix_sum(r) - prefix_sum(l-1)
 int range_sum(int l, int r) {
    return prefix_sum(r) - prefix_sum(l - 1);
 }
 ```

 ## Practice Problems
Original file line number	Diff line number	Diff line change
Expand Up		@@ -431,30 +431,37 @@ Thus we can use $B_2$ for shaving off extra terms when we multiply $B_1[i]\times

		We can find arbitrary range sums by computing the prefix sums for $l-1$ and $r$ and taking the difference of them again.

		```python
		def add(b, idx, x):
		while idx <= N:
		b[idx] += x
		idx += idx & -idx
		```cpp
		void add(std::vector<int> b, int idx, int x) {
		while (idx <= n) {
		b[idx] += x;
		idx += idx & -idx;
		}
		}

		def range_add(l,r,x):
		void range_add(int l, int r, int x) {
		add(B1, l, x)
		add(B1, r+1, -x)
		add(B2, l, x*(l-1))
		add(B2, r+1, -x*r)
		add(B1, r + 1, -x)
		add(B2, l, x * (l - 1))
		add(B2, r + 1, -x * r)
		}

		def sum(b, idx):
		total = 0
		while idx > 0:
		total += b[idx]
		idx -= idx & -idx
		return total
		int sum(std::vector<int> b, int idx) {
		int total = 0;
		while (idx > 0) {
		total += b[idx];
		idx -= idx & -idx;
		}
		return total;
		}

		def prefix_sum(idx):
		return sum(B1, idx)*idx - sum(B2, idx)
		int prefix_sum(int idx) {
		return sum(B1, idx) * idx - sum(B2, idx);
		}

		def range_sum(l, r):
		return prefix_sum(r) - prefix_sum(l-1)
		int range_sum(int l, int r) {
		return prefix_sum(r) - prefix_sum(l - 1);
		}
		```

		## Practice Problems
Expand Down