Insertion Sort Algorithm in DSA Python - Build from Scratch

Insertion Sort Algorithm

📖 Scenario: You have a small list of numbers that you want to sort in ascending order. Sorting helps you organize data so you can find things faster, like arranging books by their height on a shelf.

🎯 Goal: Build a simple program that sorts a list of numbers using the insertion sort method. You will create the list, set up a helper variable, write the sorting logic, and then print the sorted list.

📋 What You'll Learn

Create a list called numbers with the exact values: [8, 3, 5, 4, 6]

Create a variable called i to use as the index in the sorting loop

Implement the insertion sort algorithm using a for loop with i from 1 to the length of numbers

Print the sorted numbers list after sorting

💡 Why This Matters

🌍 Real World

Sorting is used everywhere, like organizing contacts on your phone or arranging files by date.

💼 Career

Understanding sorting algorithms helps in software development, data analysis, and optimizing performance.

1

Create the list of numbers

Create a list called numbers with these exact values: [8, 3, 5, 4, 6]

DSA Python

# Create the list called numbers with the values [8, 3, 5, 4, 6]
numbers = []  # Your code here

Hint

Use square brackets [] to create a list and separate numbers with commas.

2

Set up the index variable for sorting

Create a variable called i and set it to 1 to start the sorting from the second element

DSA Python

numbers = [8, 3, 5, 4, 6]
# Create the variable i and set it to 1

# Your code here

Hint

The insertion sort starts from the second element, so i should start at 1.

3

Implement the insertion sort logic

Write a for loop with i from 1 to len(numbers) and inside it, use a while loop to move elements greater than key one position ahead. Use variables key for the current value and j for the index to compare.

DSA Python

numbers = [8, 3, 5, 4, 6]
i = 1
# Write the insertion sort algorithm below

# Your code here

Hint

Use a for loop to pick each element starting from index 1. Then use a while loop to shift larger elements to the right and insert the key in the correct position.

4

Print the sorted list

Write a print statement to display the sorted numbers list

DSA Python

numbers = [8, 3, 5, 4, 6]
i = 1
for i in range(1, len(numbers)):
    key = numbers[i]
    j = i - 1
    while j >= 0 and numbers[j] > key:
        numbers[j + 1] = numbers[j]
        j -= 1
    numbers[j + 1] = key

# Print the sorted numbers list
# Your code here

Hint

Use print(numbers) to show the sorted list.

Practice

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

easy

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

B. Divide the list into halves and sort each half separately

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 a 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

   Options A, B, and D describe other sorting algorithms: bubble sort, merge sort, and selection sort respectively.

3. Final Answer:

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

4. Quick Check:

   Insertion sort = Insert elements in order [OK]

Hint: Insertion sort inserts elements one by one in order [OK]

Common Mistakes:

• Confusing insertion sort with bubble sort
• Thinking insertion sort divides the list
• Mixing insertion sort with selection sort

2. Which of the following is the correct syntax to start the outer loop for insertion sort on a list arr of length n in Python?

easy

A. for i in range(0, n-1):

B. for i in range(n):

C. for i in range(1, n):

D. for i in range(n-1, 0, -1):

Solution

1. Step 1: Identify insertion sort loop start

   The outer loop starts from index 1 because the first element (index 0) is considered sorted.

2. Step 2: Check options

   for i in range(1, n): correctly uses range(1, n). Options B and C start from 0 which is incorrect. for i in range(n-1, 0, -1): loops backwards which is not standard for insertion sort.

3. Final Answer:

   for i in range(1, n): -> Option C

4. Quick Check:

   Start loop at 1 for insertion sort [OK]

Hint: Start outer loop from 1, not 0 [OK]

Common Mistakes:

• Starting loop at 0 instead of 1
• Using reverse loop incorrectly
• Confusing loop ranges

3. What will be the output of the following code snippet?

def insertion_sort(arr):
    for i in range(1, len(arr)):
        key = arr[i]
        j = i - 1
        while j >= 0 and arr[j] > key:
            arr[j + 1] = arr[j]
            j -= 1
        arr[j + 1] = key

arr = [4, 3, 2, 1]
insertion_sort(arr)
print(arr)

medium

A. [4, 3, 2, 1]

B. [1, 2, 3, 4]

C. [1, 3, 2, 4]

D. [2, 3, 4, 1]

Solution

1. Step 1: Trace the insertion sort on input

   The list [4, 3, 2, 1] is sorted step-by-step by moving smaller elements leftwards until fully sorted.

2. Step 2: Final sorted list

   After sorting, the list becomes [1, 2, 3, 4].

3. Final Answer:

   [1, 2, 3, 4] -> Option B

4. Quick Check:

   Sorted ascending = [1, 2, 3, 4] [OK]

Hint: Insertion sort outputs sorted ascending list [OK]

Common Mistakes:

• Assuming original list remains unchanged
• Confusing output with partial sorting
• Misreading the while loop condition

4. Find the error in the following insertion sort code:

def insertion_sort(arr):
    for i in range(1, len(arr)):
        key = arr[i]
        j = i
        while j > 0 and arr[j-1] > key:
            arr[j] = arr[j-1]
            j -= 1
        arr[j] = key

arr = [3, 1, 2]
insertion_sort(arr)
print(arr)

medium

A. The for loop should start from 0, not 1

B. The while loop condition should be j >= 0, not j > 0

C. The assignment arr[j] = key should be outside the while loop

D. The variable j should start at i - 1, not i

Solution

1. Step 1: Check initialization of j

   In insertion sort, j should start at i - 1 to compare the key with previous elements using the standard condition arr[j] > key.

2. Step 2: Verify other parts

   The while loop condition and assignment are correct. The for loop correctly starts at 1.

3. Final Answer:

   The variable j should start at i - 1, not i -> Option D

4. Quick Check:

   j = i - 1 to compare previous elements [OK]

Hint: Start j at i-1 to compare with previous elements [OK]

Common Mistakes:

• Using j = i instead of standard j = i-1
• Changing while loop condition incorrectly
• Misplacing key assignment inside loop

5. Given a list arr = [5, 3, 8, 6, 2], how many total shifts (element moves) will insertion sort perform to sort the list in ascending order?

hard

A. 6

B. 8

C. 7

D. 5

Solution

1. Step 1: Trace shifts during sorting

   Insertion sort shifts elements to insert the key in the correct place:
   - i=1 (key=3): shift 5 right (1 shift)
   - i=2 (key=8): no shift (0 shifts)
   - i=3 (key=6): shift 8 right (1 shift)
   - i=4 (key=2): shift 8, 6, 5, 3 right (4 shifts)

2. Step 2: Calculate total shifts

   Total shifts = 1 + 0 + 1 + 4 = 6 shifts. But note that each shift moves one element one position right. Counting carefully:
   At i=1: 1 shift
   At i=3: 1 shift
   At i=4: 4 shifts
   Total = 6 shifts

3. Step 3: Recount carefully

   Actually, at i=4, elements 3,5,6,8 are shifted right one by one (4 shifts). Total shifts = 1 + 0 + 1 + 4 = 6.

4. Final Answer:

   6 -> Option A

5. Quick Check:

   Count shifts per insertion = 6 [OK]

Hint: Count shifts by tracing each insertion step [OK]

Common Mistakes:

• Counting comparisons instead of shifts
• Missing multiple shifts in one insertion
• Confusing shifts with swaps