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

Recall & Review

beginner

What is array rotation?

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

beginner

Explain left rotation of an array by 1 position.

Left rotation by 1 moves each element one step to the left. The first element moves to the end of the array.

intermediate

How does the reversal algorithm help in array rotation?

The reversal algorithm rotates an array by reversing parts of the array in steps, then reversing the whole array to achieve rotation efficiently.

intermediate

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

The time complexity is O(n), where n is the number of elements in the array, because each element is reversed at most twice.

beginner

Describe the difference between left rotation and right rotation.

Left rotation moves elements towards the start of the array, wrapping the first elements to the end. Right rotation moves elements towards the end, wrapping the last elements to the front.

What happens to the first element in a left rotation by 1?

A It moves to the second position

B It stays in the same place

C It moves to the end of the array

D It is removed from the array

In left rotation by 1, the first element moves to the end of the array.

Which algorithm rotates an array by reversing parts of it?

A Reversal algorithm

B Bubble sort

C Selection sort

D Insertion sort

The reversal algorithm rotates an array by reversing segments and then the whole array.

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

A O(n)

B O(log n)

C O(1)

D O(n^2)

Reversal algorithm runs in linear time O(n) because it reverses parts of the array a fixed number of times.

In right rotation by 1, where does the last element go?

A It stays at the end

B It moves to the front of the array

C It moves to the middle

D It is removed

In right rotation by 1, the last element moves to the front of the array.

If you rotate an array of length n by n positions, what is the result?

A Array is reversed

B Array is empty

C Array is sorted

D Array remains the same

Rotating by n positions (the array length) results in the same array because elements wrap around fully.

Explain how to perform a left rotation of an array by d positions using the reversal algorithm.

Think about reversing parts and then the entire array.

Describe the difference between left and right rotations with examples.

Consider what happens to the first and last elements.

Practice

1. What does rotating an array to the right by 1 position mean?
arr = [1, 2, 3, 4] rotated right by 1 becomes?

easy

A. [4, 1, 2, 3]

B. [2, 3, 4, 1]

C. [1, 2, 3, 4]

D. [3, 4, 1, 2]

Solution

1. Step 1: Understand right rotation by 1

   Right rotation by 1 means the last element moves to the front, and others shift right.

2. Step 2: Apply to given array

   Last element 4 moves to front, rest shift right: [4, 1, 2, 3].

3. Final Answer:

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

4. Quick Check:

   Right rotate by 1 = last element front [OK]

Hint: Last element moves front on right rotation by 1 [OK]

Common Mistakes:

• Confusing left and right rotation
• Shifting elements left instead of right
• Not moving last element to front

2. Which of the following is the correct JavaScript syntax to rotate an array arr to the left by 1 position?

easy

A. arr.unshift(arr.pop())

B. arr.push(arr.shift())

C. arr.pop(arr.unshift())

D. arr.shift(arr.push())

Solution

1. Step 1: Understand left rotation by 1

   Left rotation by 1 means first element moves to the end.

2. Step 2: Match syntax to operation

   arr.shift() removes first element, arr.push() adds it to end. So arr.push(arr.shift()) rotates left by 1.

3. Final Answer:

   arr.push(arr.shift()) -> Option B

4. Quick Check:

   Left rotate = shift then push [OK]

Hint: Left rotate = shift first, then push it back [OK]

Common Mistakes:

• Using pop instead of shift for left rotation
• Using unshift incorrectly
• Mixing push and pop order

3. What is the output of the following code?

const arr = [10, 20, 30, 40, 50];
const k = 2;
const rotated = arr.slice(-k).concat(arr.slice(0, arr.length - k));
console.log(rotated);

medium

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

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

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

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

Solution

1. Step 1: Understand slicing for right rotation by k=2

   arr.slice(-2) gets last 2 elements: [40, 50]. arr.slice(0, 3) gets first 3 elements: [10, 20, 30].

2. Step 2: Concatenate slices

   Concatenate [40, 50] + [10, 20, 30] = [40, 50, 10, 20, 30].

3. Final Answer:

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

4. Quick Check:

   Right rotate by 2 = last 2 front [OK]

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

Common Mistakes:

• Using slice(0, k) instead of slice(-k)
• Concatenating in wrong order
• Confusing left and right rotation

4. Find the error in this code that tries to rotate an array arr left by k positions:

function rotateLeft(arr, k) {
  for(let i = 0; i < k; i++) {
    arr.unshift(arr.shift());
  }
  return arr;
}

medium

A. Using unshift instead of push inside loop

B. Loop should run from i = 1 to k

C. No error, code works correctly

D. shift() removes last element, should use pop()

Solution

1. Step 1: Analyze loop operation

   Inside loop, arr.shift() removes first element correctly for left rotation.

2. Step 2: Check insertion method

   arr.unshift() adds element to front, which reverses the shift effect. It should be arr.push() to add at end.

3. Final Answer:

   No error, code works correctly -> Option C

4. Quick Check:

   Code rotates left by k positions correctly [OK]

Hint: Left rotate = shift then push, not unshift [OK]

Common Mistakes:

• Using unshift instead of push
• Confusing shift and pop
• Incorrect loop range

5. Given an array arr = [1, 2, 3, 4, 5], how can you rotate it left by k = 7 positions efficiently without extra space?

hard

A. Rotate left by k positions using nested loops

B. Rotate left by k positions directly using slice and concat

C. Rotate right by k positions using pop and unshift

D. Rotate left by k % arr.length = 2 positions using reversal algorithm

Solution

1. Step 1: Calculate effective rotation

   Since k=7 and arr.length=5, effective rotation is k % 5 = 2.

2. Step 2: Use reversal algorithm for in-place rotation

   Reverse first 2 elements, reverse last 3 elements, then reverse whole array to rotate left by 2 efficiently without extra space.

3. Final Answer:

   Rotate left by k % arr.length = 2 positions using reversal algorithm -> Option D

4. Quick Check:

   Use k mod length and reversal for efficient rotation [OK]

Hint: Use k mod array length and reversal for efficient rotation [OK]

Common Mistakes:

• Rotating by k without modulo causes extra rotations
• Using slice creates extra space
• Using nested loops is inefficient