Fenwick trees (Binary Indexed Trees) in Data Structures Theory - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize a Fenwick tree array of size n+1.

Data Structures Theory

fenwicks = [0] * [1]

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An+1

Bn-1

Cn

D2*n

Attempts:

3 left

💡 Hint

Common Mistakes

Using size n causes index errors because index 0 is unused.

Using size n-1 is too small and misses elements.

The Fenwick tree uses 1-based indexing, so the array size is n+1 to include index n.

2fill in blank

medium

Complete the code to get the least significant bit (LSB) of an integer x.

Data Structures Theory

lsb = x & [1]

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A-x

B1

Cx

D~x

Attempts:

3 left

💡 Hint

Common Mistakes

Using x & x returns x itself, not the LSB.

Using x & 1 only checks the last bit, not the full LSB.

The expression x & (-x) isolates the least significant bit set to 1 in x.

3fill in blank

hard

Fix the error in the Fenwick tree update function to correctly move to the next index.

Data Structures Theory

def update(i, delta):
    while i < len(fenwicks):
        fenwicks[i] += delta
        i += [1]

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Ai | (-i)

Bi + 1

Ci & i

Di & (-i)

Attempts:

3 left

💡 Hint

Common Mistakes

Adding 1 instead of the LSB causes incorrect updates.

Using bitwise OR or AND with wrong operands breaks the logic.

To move to the next index in Fenwick tree update, add the least significant bit (i & -i) to i.

4fill in blank

hard

Fill both blanks to compute the prefix sum up to index i in a Fenwick tree.

Data Structures Theory

def prefix_sum(i):
    result = 0
    while i > 0:
        result += fenwicks[[1]]
        i -= [2]
    return result

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Ai

Bi & (-i)

Ci + 1

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using i + 1 as index causes out-of-range errors.

Adding or subtracting wrong values breaks the prefix sum logic.

To get the prefix sum, add fenwicks[i] and then move to the parent by subtracting the LSB (i & -i).

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps each index to its Fenwick tree prefix sum if the sum is positive.

Data Structures Theory

result = [1]: prefix_sum([2]) for [3] in range(1, n+1) if prefix_sum([2]) > 0}

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Ai

Dindex

Attempts:

3 left

💡 Hint

Common Mistakes

Using different variable names causes NameError.

Using index instead of i breaks the comprehension.

The comprehension uses i as the key and argument to prefix_sum, iterating i from 1 to n.