Insertion Sort Algorithm in DSA Rust - Build from Scratch

Insertion Sort Algorithm

📖 Scenario: You have a list of numbers that you want to arrange from smallest to largest, just like organizing books by height on a shelf.

🎯 Goal: Build a Rust program that sorts a list of numbers using the insertion sort method, which places each number in its correct spot one by one.

📋 What You'll Learn

Create a vector called numbers with the exact values: 8, 3, 5, 1, 9

Create a variable called n that stores the length of numbers

Use a for loop with variable i from 1 to n to perform insertion sort

Inside the loop, use a while loop with variable j to move elements and insert the current number

Print the sorted numbers vector at the end

💡 Why This Matters

🌍 Real World

Sorting is used in many places like organizing data, searching faster, and making lists easier to understand.

💼 Career

Understanding sorting algorithms like insertion sort helps in coding interviews and building efficient software.

1

Create the initial list of numbers

Create a vector called numbers with the exact values 8, 3, 5, 1, 9.

DSA Rust

# Create a vector called numbers with values 8, 3, 5, 1, 9
# Your code here

Hint

Use let mut numbers = vec![8, 3, 5, 1, 9]; to create a mutable vector.

2

Create a variable for the length of the list

Create a variable called n that stores the length of the numbers vector.

DSA Rust

fn main() {
    let mut numbers = vec![8, 3, 5, 1, 9];
    // Create a variable n to store the length of numbers
    // Your code here
}

Hint

Use let n = numbers.len(); to get the length of the vector.

3

Implement the insertion sort algorithm

Use a for loop with variable i from 1 to n to perform insertion sort. Inside the loop, use a while loop with variable j to move elements and insert the current number.

DSA Rust

fn main() {
    let mut numbers = vec![8, 3, 5, 1, 9];
    let n = numbers.len();
    // Implement insertion sort using for and while loops
    // Your code here
}

Hint

Use a for loop from 1 to n, and inside it a while loop to shift elements until the correct position is found.

4

Print the sorted list

Print the sorted numbers vector using println!.

DSA Rust

fn main() {
    let mut numbers = vec![8, 3, 5, 1, 9];
    let n = numbers.len();
    for i in 1..n {
        let key = numbers[i];
        let mut j = i;
        while j > 0 && numbers[j - 1] > key {
            numbers[j] = numbers[j - 1];
            j -= 1;
        }
        numbers[j] = key;
    }
    // Print the sorted numbers vector
    // Your code here
}

Hint

Use println!("{:?}", numbers); to print the vector in debug format.

Practice

1. What is the main idea behind the Insertion Sort algorithm?

easy

A. Divide the array into halves and sort each half recursively

B. Build the sorted array one element at a time by inserting elements in their correct position

C. Swap adjacent elements if they are in the wrong order repeatedly

D. Select the smallest element and swap it with the first unsorted element

Solution

1. Step 1: Understand insertion sort process

   Insertion sort builds the sorted list by taking one element at a time and placing it in the correct position among the already sorted elements.

2. Step 2: Compare with other sorting methods

   Unlike divide and conquer (merge sort) or swapping adjacent elements (bubble sort), insertion sort inserts elements directly into their correct place.

3. Final Answer:

   Build the sorted array one element at a time by inserting elements in their correct position -> Option B

4. Quick Check:

   Insertion sort = Insert elements correctly one by one [OK]

Hint: Insertion sort inserts elements into sorted part step-by-step [OK]

Common Mistakes:

• Confusing insertion sort with bubble sort
• Thinking it divides array like merge sort
• Assuming it swaps only smallest elements

2. Which of the following Rust code snippets correctly starts the insertion sort outer loop?

easy

A. for i in 1..arr.len() {

B. for i in 0..arr.len() {

C. for i in (1..arr.len()).rev() {

D. for i in 0..arr.len()-1 {

Solution

1. Step 1: Identify insertion sort loop start

   Insertion sort starts from the second element (index 1) because the first element is considered sorted.

2. Step 2: Check Rust range syntax

   The range 1..arr.len() correctly iterates from index 1 to the last index (exclusive of arr.len()).

3. Final Answer:

   for i in 1..arr.len() { -> Option A

4. Quick Check:

   Start loop at 1 for insertion sort [OK]

Hint: Insertion sort outer loop starts at index 1 [OK]

Common Mistakes:

• Starting loop at 0 instead of 1
• Using reversed range incorrectly
• Off-by-one errors in range

3. What will be the output of the following Rust code after running insertion sort on arr = [4, 3, 1, 5]?

let mut arr = vec![4, 3, 1, 5];
for i in 1..arr.len() {
    let key = arr[i];
    let mut j = i;
    while j > 0 && arr[j - 1] > key {
        arr[j] = arr[j - 1];
        j -= 1;
    }
    arr[j] = key;
}
println!("{:?}", arr);

medium

A. [3, 4, 1, 5]

B. [4, 3, 1, 5]

C. [1, 3, 4, 5]

D. [1, 4, 3, 5]

Solution

1. Step 1: Trace first iteration (i=1)

   key=3, compare with 4; 4 > 3 so shift 4 right, insert 3 at index 0. Array: [3,4,1,5]

2. Step 2: Trace second iteration (i=2)

   key=1, compare with 4 and 3; both >1 so shift them right, insert 1 at index 0. Array: [1,3,4,5]

3. Step 3: Trace third iteration (i=3)

   key=5, compare with 4; 4 < 5 so no shift, insert 5 at index 3. Array unchanged: [1,3,4,5]

4. Final Answer:

   [1, 3, 4, 5] -> Option C

5. Quick Check:

   Sorted array after insertion sort = [1, 3, 4, 5] [OK]

Hint: Trace each key insertion step-by-step [OK]

Common Mistakes:

• Not shifting elements correctly
• Off-by-one errors in while loop
• Printing original array without sorting

4. Identify the bug in this Rust insertion sort snippet:

let mut arr = vec![2, 5, 3];
for i in 1..arr.len() {
    let key = arr[i];
    let mut j = i - 1;
    while j >= 0 && arr[j] > key {
        arr[j + 1] = arr[j];
        j -= 1;
    }
    arr[j + 1] = key;
}

medium

A. The key is not assigned correctly

B. The array is not mutable

C. The for loop range is incorrect

D. The variable j is unsigned and j >= 0 check causes infinite loop

Solution

1. Step 1: Analyze variable j type and condition

   In Rust, usize is unsigned, so j >= 0 is always true, causing infinite loop when j underflows.

2. Step 2: Understand while loop behavior

   When j reaches 0 and decrements, it wraps to a large number, so loop never ends.

3. Final Answer:

   The variable j is unsigned and j >= 0 check causes infinite loop -> Option D

4. Quick Check:

   Unsigned j with j >= 0 causes infinite loop [OK]

Hint: Unsigned index can't be checked with j >= 0 safely [OK]

Common Mistakes:

• Ignoring unsigned integer wrap-around
• Assuming j can be negative
• Not using a different loop condition

5. You want to modify insertion sort in Rust to sort a vector of tuples Vec<(i32, String)> by the integer value. Which change is needed in the comparison inside the while loop?

hard

A. Change arr[j - 1] > key to arr[j - 1].0 > key.0

B. Change arr[j - 1] > key to arr[j - 1].1 > key.1

C. No change needed, tuples compare automatically by second element

D. Change arr[j - 1] > key to arr[j - 1].1.len() > key.1.len()

Solution

1. Step 1: Understand tuple sorting by first element

   To sort by the integer part of the tuple, compare the first element (.0) of each tuple.

2. Step 2: Modify comparison in while loop

   Replace arr[j - 1] > key with arr[j - 1].0 > key.0 to compare integers correctly.

3. Final Answer:

   Change arr[j - 1] > key to arr[j - 1].0 > key.0 -> Option A

4. Quick Check:

   Compare tuple first elements for sorting [OK]

Hint: Compare tuple.0 to sort by integer part [OK]

Common Mistakes:

• Comparing string part instead of integer
• Assuming tuples compare by second element automatically
• Using length of string for comparison