Array Rotation Techniques in DSA Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is array rotation?

Array rotation means moving the elements of an array to the left or right by a certain number of positions, wrapping around the ends.

beginner

Explain left rotation by 1 on array [1, 2, 3, 4, 5].

Left rotation by 1 moves each element one step to the left. The first element moves to the end. Result: [2, 3, 4, 5, 1]

intermediate

What is the time complexity of rotating an array by d positions using the reversal algorithm?

The reversal algorithm rotates the array in O(n) time, where n is the array length, by reversing parts of the array three times.

intermediate

Describe the reversal algorithm for array rotation.

1. Reverse the first d elements.
2. Reverse the remaining elements.
3. Reverse the whole array.
This rotates the array left by d positions.

beginner

What happens if you rotate an array by its length?

Rotating an array by its length results in the same array because elements wrap around fully and return to original positions.

What is the result of left rotating [10, 20, 30, 40, 50] by 2 positions?

A [40, 50, 10, 20, 30]

B [30, 40, 50, 10, 20]

C [50, 10, 20, 30, 40]

D [20, 30, 40, 50, 10]

Left rotation by 2 moves first two elements to the end: [30, 40, 50, 10, 20]

Which algorithm rotates an array by reversing parts of it?

A Insertion sort

B Bubble sort

C Reversal algorithm

D Selection algorithm

The reversal algorithm rotates arrays by reversing segments.

Rotating an array right by 1 is the same as rotating it left by how many positions?

A Length of array minus 1

B 1

C Length of array

D 0

Right rotation by 1 equals left rotation by (array length - 1).

What is the time complexity of rotating an array by copying elements to a new array?

A O(n)

B O(1)

C O(n^2)

D O(log n)

Copying elements to a new array for rotation takes O(n) time.

If you rotate an array by 0 positions, what is the result?

A Array empty

B Array reversed

C Array sorted

D Array unchanged

Rotating by 0 means no change to the array.

Explain how the reversal algorithm rotates an array left by d positions.

Think about reversing parts step by step.

Describe the difference between left rotation and right rotation of an array.

Consider direction and wrapping.

Practice

1. What does rotating an array to the left by 1 position do to the elements?

easy

A. Moves each element one step to the right, last element goes to the front

B. Moves each element one step to the left, first element goes to the end

C. Reverses the array

D. Sorts the array in ascending order

Solution

1. Step 1: Understand left rotation

   Left rotation by 1 means the element at index 0 moves to the end, and all others shift left by one.

2. Step 2: Visualize the movement

   For example, [1, 2, 3] becomes [2, 3, 1] after left rotation by 1.

3. Final Answer:

   Moves each element one step to the left, first element goes to the end -> Option B

4. Quick Check:

   Left rotation = shift left + wrap first element [OK]

Hint: Left rotation shifts left, first element moves to end [OK]

Common Mistakes:

• Confusing left rotation with right rotation
• Thinking rotation sorts the array
• Assuming rotation reverses the array

2. Which of the following is the correct Python syntax to rotate an array arr to the right by 2 positions using slicing?

easy

A. arr = arr[-2:] + arr[:-2]

B. arr = arr[2:] + arr[:2]

C. arr = arr[:2] + arr[2:]

D. arr = arr[-2:] - arr[:-2]

Solution

1. Step 1: Understand right rotation with slicing

   Right rotation by 2 means last 2 elements move to front, rest shift right.

2. Step 2: Apply slicing syntax

   arr[-2:] gets last 2 elements, arr[:-2] gets all except last 2. Concatenating gives rotated array.

3. Final Answer:

   arr = arr[-2:] + arr[:-2] -> Option A

4. Quick Check:

   Right rotation by 2 = last 2 + rest [OK]

Hint: Right rotation by k = last k elements + rest [OK]

Common Mistakes:

• Using + operator incorrectly with slices
• Confusing left and right rotation slices
• Using subtraction operator instead of concatenation

3. What is the output of the following code?

arr = [10, 20, 30, 40, 50]
k = 3
rotated = arr[k:] + arr[:k]
print(rotated)

medium

A. [50, 10, 20, 30, 40]

B. [30, 40, 50, 10, 20]

C. [20, 30, 40, 50, 10]

D. [40, 50, 10, 20, 30]

Solution

1. Step 1: Identify rotation type

   arr[k:] + arr[:k] rotates array left by k=3 positions.

2. Step 2: Perform slicing and concatenation

   arr[3:] = [40, 50], arr[:3] = [10, 20, 30], combined = [40, 50, 10, 20, 30]

3. Final Answer:

   [40, 50, 10, 20, 30] -> Option D

4. Quick Check:

   Left rotation by 3 = [40,50] + [10,20,30] [OK]

Hint: arr[k:] + arr[:k] = left rotate by k [OK]

Common Mistakes:

• Mixing left and right rotation logic
• Incorrect slicing indices
• Misreading k value

4. The following code is intended to rotate an array arr to the right by k positions. What is the error?

def rotate_right(arr, k):
    n = len(arr)
    k = k % n
    rotated = arr[k:] + arr[:k]
    return rotated

print(rotate_right([1,2,3,4,5], 2))

medium

A. The slicing indices perform left rotation, not right rotation

B. The modulo operation is incorrect

C. The function does not return anything

D. The print statement is missing parentheses

Solution

1. Step 1: Analyze slicing for rotation

   arr[k:] + arr[:k] rotates array left by k, not right.

2. Step 2: Correct right rotation slicing

   Right rotation by k should be arr[-k:] + arr[:-k].

3. Final Answer:

   The slicing indices perform left rotation, not right rotation -> Option A

4. Quick Check:

   Right rotation needs arr[-k:] + arr[:-k] [OK]

Hint: Right rotation uses negative slicing indices [OK]

Common Mistakes:

• Using left rotation slices for right rotation
• Ignoring modulo to handle k > n
• Forgetting to return the rotated array

5. Given an array arr = [3, 8, 9, 7, 6], how would you rotate it to the right by k = 3 positions using a single Python statement without slicing?

hard

A. Use arr.sort() then reverse

B. Use arr.reverse() three times

C. Use a loop to pop last element and insert at front 3 times

D. Use arr.append(arr.pop()) once

Solution

1. Step 1: Understand rotation without slicing

   Rotating right by 3 means moving last element to front 3 times.

2. Step 2: Use loop with pop and insert

   Loop 3 times: pop last element and insert at index 0 to rotate right.

3. Final Answer:

   Use a loop to pop last element and insert at front 3 times -> Option C

4. Quick Check:

   Pop + insert at front repeated k times = right rotation [OK]

Hint: Pop last and insert front k times for right rotation [OK]

Common Mistakes:

• Using reverse instead of rotation
• Sorting array mistakenly
• Only popping once instead of k times