Sort Colors Two Pointer Dutch Flag in DSA Javascript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main idea behind the Dutch National Flag problem?

It is to sort an array of three different values (like 0, 1, 2) in one pass using pointers, without extra space.

beginner

In the two-pointer Dutch Flag algorithm, what do the pointers 'low', 'mid', and 'high' represent?

'low' marks the boundary for 0s, 'mid' is the current element under consideration, and 'high' marks the boundary for 2s.

intermediate

Why does the Dutch Flag algorithm swap elements when mid points to 0 or 2?

Because 0s should be at the start and 2s at the end, swapping moves them to their correct partitions while mid moves forward for 0 and stays for 2.

beginner

What is the time complexity of the Dutch National Flag sorting algorithm?

It is O(n) because it makes only one pass through the array.

intermediate

Can the Dutch Flag algorithm be used to sort arrays with more than three distinct values?

No, it is specifically designed for three distinct values. For more values, other sorting methods are needed.

What does the 'mid' pointer do in the Dutch Flag algorithm?

A Marks the end of the array

B Points to the current element being checked

C Points to the first 0 in the array

D Marks the boundary for 2s

'mid' moves through the array checking each element to decide if it should be swapped.

When the element at 'mid' is 0, what action is taken?

A Swap with element at 'high' and decrement 'high'

B Increment 'mid' only

C Swap with element at 'mid' itself

D Swap with element at 'low' and increment both 'low' and 'mid'

0s go to the start, so swap with 'low' and move both pointers forward.

What happens when the element at 'mid' is 2?

A Swap with element at 'low' and increment 'low'

B Swap with element at 'high' and increment 'mid'

C Swap with element at 'high' and decrement 'high' only

D Increment 'mid' only

2s go to the end, so swap with 'high' and move 'high' backward without moving 'mid' yet.

What is the space complexity of the Dutch Flag algorithm?

A O(1)

B O(log n)

C O(n)

D O(n^2)

It sorts the array in place using constant extra space.

Which of these is NOT a pointer used in the Dutch Flag algorithm?

A start

B low

C high

D mid

'start' is not used; the algorithm uses 'low', 'mid', and 'high'.

Explain how the two-pointer Dutch Flag algorithm sorts an array of 0s, 1s, and 2s in one pass.

Think about how you separate colors into three groups by moving pointers and swapping.

Describe the conditions under which the 'mid' pointer moves forward or stays in place during the Dutch Flag sorting.

Consider what happens after swapping with 'high' pointer.

Practice

1. What is the main goal of the Sort Colors Two Pointer Dutch Flag algorithm?

easy

A. To find the maximum value in an array

B. To sort any array of integers in ascending order

C. To reverse the elements of an array

D. To sort an array containing only 0s, 1s, and 2s in a single pass

Solution

1. Step 1: Understand the problem context

   The algorithm is designed specifically for arrays with only three distinct values: 0, 1, and 2.

2. Step 2: Identify the sorting goal

   The goal is to sort these values so that all 0s come first, then all 1s, and finally all 2s, in one pass without extra space.

3. Final Answer:

   To sort an array containing only 0s, 1s, and 2s in a single pass -> Option D

4. Quick Check:

   Sort Colors = Sort 0,1,2 in one pass [OK]

Hint: Remember: Dutch Flag sorts 0,1,2 in one pass [OK]

Common Mistakes:

• Thinking it sorts any integer array
• Confusing it with general sorting algorithms
• Assuming it reverses the array

2. Which of the following is the correct initialization for the two pointers in the Dutch Flag algorithm in JavaScript?

easy

A. let low = 0, mid = 0, high = nums.length - 1;

B. let low = 0, mid = nums.length - 1, high = 0;

C. let low = nums.length - 1, mid = 0, high = 0;

D. let low = nums.length - 1, mid = nums.length - 1, high = 0;

Solution

1. Step 1: Identify pointer roles

   Low and mid start at the beginning (index 0), high starts at the end (last index).

2. Step 2: Match initialization to roles

   Correct initialization is let low = 0, mid = 0, high = nums.length - 1;.

3. Final Answer:

   let low = 0, mid = 0, high = nums.length - 1; -> Option A

4. Quick Check:

   Pointers start low=0, mid=0, high=end [OK]

Hint: Start low and mid at 0, high at array end [OK]

Common Mistakes:

• Swapping high and mid initialization
• Starting pointers at wrong indices
• Using length instead of length - 1 for high

3. What will be the output array after running the Dutch Flag algorithm on nums = [2, 0, 2, 1, 1, 0]?

medium

A. [0, 0, 1, 1, 2, 2]

B. [2, 2, 1, 1, 0, 0]

C. [0, 1, 0, 1, 2, 2]

D. [1, 0, 2, 0, 1, 2]

Solution

1. Step 1: Apply Dutch Flag sorting logic

   Sort 0s to front, 1s in middle, 2s at end in one pass.

2. Step 2: Result after sorting

   The sorted array is [0, 0, 1, 1, 2, 2].

3. Final Answer:

   [0, 0, 1, 1, 2, 2] -> Option A

4. Quick Check:

   Sorted colors = 0s, then 1s, then 2s [OK]

Hint: Sort 0s front, 1s middle, 2s end in one pass [OK]

Common Mistakes:

• Not sorting all 0s to front
• Mixing order of 1s and 2s
• Returning original unsorted array

4. Identify the bug in this snippet of the Dutch Flag algorithm:

let low = 0, mid = 0, high = nums.length - 1;
while (mid <= high) {
  if (nums[mid] === 0) {
    [nums[low], nums[mid]] = [nums[mid], nums[low]];
    low++;
  } else if (nums[mid] === 2) {
    [nums[mid], nums[high]] = [nums[high], nums[mid]];
    high--;
  } else {
    mid++;
  }
}

medium

A. Incorrect comparison operator in while loop

B. Missing increment of mid after swapping 0s

C. Swapping 2s with low instead of high

D. No bug, code is correct

Solution

1. Step 1: Analyze pointer increments after swaps

   When swapping 0s, mid pointer must also move forward to avoid infinite loop.

2. Step 2: Identify missing mid++ after swapping 0s

   The code increments low but forgets to increment mid after swapping 0s.

3. Final Answer:

   Missing increment of mid after swapping 0s -> Option B

4. Quick Check:

   mid++ missing after 0 swap causes infinite loop [OK]

Hint: Increment mid after swapping 0s to avoid infinite loop [OK]

Common Mistakes:

• Forgetting mid++ after swapping 0s
• Swapping 2s with wrong pointer
• Incorrect loop condition

5. Given an array nums with values 0, 1, and 2, how would you modify the Dutch Flag algorithm to count how many swaps are performed during sorting?

hard

A. Use a separate array to track swaps

B. Count the number of 0s, 1s, and 2s before sorting

C. Add a counter variable and increment it each time a swap occurs

D. Increment a counter only when mid pointer moves

Solution

1. Step 1: Understand swap operations in algorithm

   Swaps happen when 0 or 2 is encountered and elements are exchanged.

2. Step 2: Track swaps with a counter

   Introduce a variable initialized to zero and increment it every time a swap line executes.

3. Final Answer:

   Add a counter variable and increment it each time a swap occurs -> Option C

4. Quick Check:

   Count swaps by incrementing counter on each swap [OK]

Hint: Increment counter inside swap blocks to count swaps [OK]

Common Mistakes:

• Counting pointer moves instead of swaps
• Counting elements instead of swaps
• Using extra arrays unnecessarily