Priority queue with heaps in Data Structures Theory - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to identify the root element in a max-heap.

Data Structures Theory

root = heap[[1]]

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A1

B0

C-1

Dlen(heap)

Attempts:

3 left

💡 Hint

Common Mistakes

Using 1 as the root index, which is incorrect for zero-based arrays.

Using -1 or len(heap), which do not point to the root.

In a max-heap stored as an array, the root element is always at index 0.

2fill in blank

medium

Complete the formula to find the left child index of a node at index i in a heap.

Data Structures Theory

left_child_index = 2 * [1] + 1

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A2

Bi + 1

Ci

Di - 1

Attempts:

3 left

💡 Hint

Common Mistakes

Adding 1 to i before multiplying, which shifts the index incorrectly.

Using i - 1 or a fixed number instead of the node index.

The left child of a node at index i in a zero-based heap array is at index 2*i + 1.

3fill in blank

hard

Fix the error in the code to get the parent index of a node at index i in a heap.

Data Structures Theory

parent_index = ([1] - 1) // 2

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Ai

Bi + 1

Ci - 1

D2 * i

Attempts:

3 left

💡 Hint

Common Mistakes

Adding 1 to i before subtracting, which gives wrong parent index.

Using multiplication instead of division.

The parent of a node at index i is at (i - 1) // 2 in a zero-based heap array.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps each node to its depth in a heap of size n.

Data Structures Theory

{node: [1] for node in range(n) if node [2] n}

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Anode.bit_length() - 1

B<

C>=

Dnode

Attempts:

3 left

💡 Hint

Common Mistakes

Using '>=' instead of '<' in the condition.

Using 'node' directly instead of calculating depth.

The depth of a node in a heap can be found using the bit length of its index minus one. The comprehension includes nodes with index less than n.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps each node to its parent index in a heap of size n, excluding the root.

Data Structures Theory

{node: ([1] - 1) // 2 for node in range(1, [2]) if node [3] n}

Drag options to blanks, or click blank then click option'

Anode

Bn + 1

C<

Dnode + 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'node + 1' instead of 'node' for parent calculation.

Using '>=' instead of '<' in the condition.

This comprehension calculates the parent index for each node from 1 up to n, excluding the root at index 0. The condition ensures nodes are less than n.