Heap Concept Structure and Properties in DSA Rust - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a heap in data structures?

A heap is a special tree-based data structure that satisfies the heap property: in a max-heap, each parent node is greater than or equal to its children; in a min-heap, each parent node is less than or equal to its children.

beginner

What is the shape property of a heap?

The shape property means the heap is a complete binary tree. This means all levels are fully filled except possibly the last level, which is filled from left to right without gaps.

beginner

Explain the heap property with an example.

In a max-heap, if a parent node has value 10, its children can have values like 7 and 5 but not 12. This ensures the parent is always larger or equal to its children.

intermediate

How is a heap usually stored in memory?

A heap is often stored as an array where the parent and children positions follow simple formulas: for a node at index i, left child is at 2*i + 1, right child at 2*i + 2, and parent at (i-1)/2 (integer division).

beginner

Why is the heap structure useful?

Heaps allow quick access to the largest or smallest element, making them useful for priority queues, sorting algorithms like heapsort, and efficient selection problems.

What does the shape property of a heap ensure?

A The heap is a balanced binary search tree

B All nodes have two children

C The heap is a complete binary tree

D The heap nodes are sorted in ascending order

The shape property means the heap is a complete binary tree, fully filled except possibly the last level filled from left to right.

In a max-heap, which of the following is true?

A Parent nodes are smaller than children

B Heap is sorted in ascending order

C Children nodes are always equal

D Parent nodes are greater than or equal to children

In a max-heap, each parent node is greater than or equal to its children.

How is the left child index calculated in an array-based heap for a node at index i?

A 2 * i

B 2 * i + 1

C i / 2

D i - 1

Left child index = 2 * i + 1 in array representation of a heap.

Which data structure is a heap NOT guaranteed to be?

A Binary search tree

B Array

C Complete binary tree

D Tree

A heap is not a binary search tree; it only satisfies the heap property, not the BST ordering.

What is a common use of heaps?

A Implementing priority queues

B Storing sorted data

C Hashing keys

D Linked list traversal

Heaps are commonly used to implement priority queues for efficient access to highest or lowest priority elements.

Describe the two main properties that define a heap data structure.

Think about the tree shape and how parent and child values relate.

Explain how a heap can be stored in an array and how to find parent and child nodes using indices.

Remember the formulas for navigating the heap in an array.

Practice

1. What is the main property of a max-heap data structure?

easy

A. Every parent node is less than or equal to its children

B. Every parent node is greater than or equal to its children

C. All leaf nodes are at the same level

D. It is a balanced binary search tree

Solution

1. Step 1: Understand max-heap property

   A max-heap requires that each parent node's value is greater than or equal to its children.

2. Step 2: Compare options with definition

   Every parent node is greater than or equal to its children matches the max-heap property exactly; others describe different structures or properties.

3. Final Answer:

   Every parent node is greater than or equal to its children -> Option B

4. Quick Check:

   Max-heap property = parent ≥ children [OK]

Hint: Max-heap means parent is always bigger or equal [OK]

Common Mistakes:

• Confusing max-heap with min-heap property
• Thinking heap is a binary search tree
• Assuming all leaves are at the same level

2. Which of the following Rust code snippets correctly creates a max-heap using the standard library?

easy

A. let mut heap = std::collections::BinaryHeap::new();

B. let mut heap = std::collections::VecDeque::new();

C. let mut heap = std::collections::HashMap::new();

D. let mut heap = std::collections::BinaryHeap::new(0);

Solution

1. Step 1: Identify Rust heap creation syntax

   Rust's standard max-heap is created using BinaryHeap::new() for an empty heap.

2. Step 2: Check each option

   A: let mut heap = std::collections::BinaryHeap::new(); uses BinaryHeap::new(), which is correct. B: let mut heap = std::collections::VecDeque::new(); uses VecDeque (not a heap). C: uses HashMap (not a heap). D: uses BinaryHeap::new(0) which is invalid syntax since new() takes no arguments.

3. Final Answer:

   let mut heap = std::collections::BinaryHeap::new(); -> Option A

4. Quick Check:

   BinaryHeap::new() creates max-heap [OK]

Hint: Use BinaryHeap::new() to create max-heap in Rust [OK]

Common Mistakes:

• Using VecDeque or HashMap instead of BinaryHeap
• Confusing with capacity initialization
• Passing arguments to BinaryHeap::new()

3. What will be the output of the following Rust code using a max-heap?

use std::collections::BinaryHeap;

fn main() {
    let mut heap = BinaryHeap::new();
    heap.push(10);
    heap.push(5);
    heap.push(20);
    println!("{}", heap.pop().unwrap());
}

medium

A. 5

B. None

C. 10

D. 20

Solution

1. Step 1: Understand BinaryHeap behavior

   BinaryHeap in Rust is a max-heap by default, so pop() returns the largest element.

2. Step 2: Trace the pushed values and pop result

   Values pushed: 10, 5, 20. The largest is 20, so pop() returns 20.

3. Final Answer:

   20 -> Option D

4. Quick Check:

   Max-heap pop() returns max value 20 [OK]

Hint: pop() returns max value in Rust BinaryHeap [OK]

Common Mistakes:

• Thinking pop() returns smallest value
• Confusing push order with pop order
• Assuming pop() returns None if heap not empty

4. Identify the error in the following Rust code that tries to create a min-heap using BinaryHeap:

use std::collections::BinaryHeap;

fn main() {
    let mut heap = BinaryHeap::new();
    heap.push(3);
    heap.push(1);
    heap.push(2);
    println!("{}", heap.peek().unwrap());
}

medium

A. BinaryHeap is a max-heap by default, not min-heap

B. Missing import for min-heap

C. Cannot push integers into BinaryHeap

D. BinaryHeap does not support peek() method

Solution

1. Step 1: Check BinaryHeap default behavior

   Rust's BinaryHeap is a max-heap by default, so peek() returns the largest element, not the smallest.

2. Step 2: Identify why min-heap is not created

   The code pushes 3,1,2 but peek() returns 3 (max), not 1 (min). To create min-heap, a wrapper or Reverse is needed.

3. Final Answer:

   BinaryHeap is a max-heap by default, not min-heap -> Option A

4. Quick Check:

   BinaryHeap default = max-heap, not min-heap [OK]

Hint: BinaryHeap is max-heap by default; use Reverse for min-heap [OK]

Common Mistakes:

• Assuming peek() returns smallest element
• Thinking BinaryHeap can't store integers
• Believing peek() method is missing

5. You want to implement a priority queue in Rust that always returns the smallest element first. Which approach correctly achieves this using the standard library's BinaryHeap?

hard

A. Use Vec and sort it after every insertion

B. Use BinaryHeap directly as it is a min-heap by default

C. Use BinaryHeap with std::cmp::Reverse wrapper for elements

D. Use BinaryHeap and negate all values before pushing

Solution

1. Step 1: Understand BinaryHeap default behavior

   BinaryHeap is a max-heap by default, so it returns the largest element first.

2. Step 2: Find correct way to get min-heap behavior

   Wrapping elements with std::cmp::Reverse reverses ordering, making BinaryHeap behave like a min-heap.

3. Step 3: Evaluate other options

   Use BinaryHeap directly as it is a min-heap by default is wrong because BinaryHeap is max-heap by default. Use Vec and sort it after every insertion is inefficient. Use BinaryHeap and negate all values before pushing is a hack but not recommended.

4. Final Answer:

   Use BinaryHeap with std::cmp::Reverse wrapper for elements -> Option C

5. Quick Check:

   Reverse wrapper makes max-heap behave like min-heap [OK]

Hint: Wrap with Reverse to get min-heap from BinaryHeap [OK]

Common Mistakes:

• Assuming BinaryHeap is min-heap by default
• Sorting Vec after every insertion is inefficient
• Negating values is error-prone and not idiomatic