Sort Colors Two Pointer Dutch Flag in DSA C# - Build from Scratch

Sort Colors Using Two Pointer Dutch Flag Algorithm

📖 Scenario: You are organizing colored balls in a line. The balls can be red, white, or blue, represented by numbers 0, 1, and 2 respectively. Your task is to sort them so that all reds come first, then whites, and finally blues.

🎯 Goal: Build a program that sorts an array of colors represented by 0s, 1s, and 2s using the two-pointer Dutch Flag algorithm.

📋 What You'll Learn

Create an integer array called colors with the exact values {2, 0, 2, 1, 1, 0}.

Create integer variables low, mid, and high with initial values 0, 0, and colors.Length - 1 respectively.

Use a while loop with the condition mid <= high to sort the array using the Dutch Flag algorithm.

Print the sorted colors array as a sequence of numbers separated by spaces.

💡 Why This Matters

🌍 Real World

Sorting colored items quickly is useful in organizing objects, image processing, and user interface design where grouping similar items improves clarity.

💼 Career

Understanding two-pointer techniques and in-place sorting algorithms is valuable for software developers working on performance-critical applications and coding interviews.

1

Create the colors array

Create an integer array called colors with the exact values {2, 0, 2, 1, 1, 0}.

DSA C#

# Your code here

Hint

Use int[] colors = {2, 0, 2, 1, 1, 0}; to create the array.

2

Initialize pointers for sorting

Create integer variables low, mid, and high with initial values 0, 0, and colors.Length - 1 respectively.

DSA C#

int[] colors = {2, 0, 2, 1, 1, 0};
# Your code here

Hint

Initialize low and mid to 0, and high to colors.Length - 1.

3

Sort the colors array using Dutch Flag algorithm

Use a while loop with the condition mid <= high to sort the colors array using the Dutch Flag algorithm. Inside the loop, use if and else if statements to swap elements and move pointers as follows: if colors[mid] is 0, swap with colors[low] and increment low and mid; if 1, just increment mid; if 2, swap with colors[high] and decrement high.

DSA C#

int[] colors = {2, 0, 2, 1, 1, 0};
int low = 0;
int mid = 0;
int high = colors.Length - 1;
# Your code here

Hint

Use a while loop and swap elements based on the value at colors[mid]. Increment or decrement pointers accordingly.

4

Print the sorted colors array

Print the sorted colors array as a sequence of numbers separated by spaces using Console.WriteLine and string.Join.

DSA C#

int[] colors = {2, 0, 2, 1, 1, 0};
int low = 0;
int mid = 0;
int high = colors.Length - 1;

while (mid <= high)
{
    if (colors[mid] == 0)
    {
        int temp = colors[low];
        colors[low] = colors[mid];
        colors[mid] = temp;
        low++;
        mid++;
    }
    else if (colors[mid] == 1)
    {
        mid++;
    }
    else // colors[mid] == 2
    {
        int temp = colors[mid];
        colors[mid] = colors[high];
        colors[high] = temp;
        high--;
    }
}
# Your code here

Hint

Use Console.WriteLine(string.Join(" ", colors)); to print the sorted array.

Practice

1. What is the main idea behind the Sort Colors Two Pointer Dutch Flag algorithm?

easy

A. Swap elements randomly until sorted

B. Sort the array using built-in sort function

C. Count each color and then overwrite the array

D. Use three pointers to separate 0s, 1s, and 2s in one pass

Solution

1. Step 1: Understand the problem

   The algorithm sorts an array containing only 0s, 1s, and 2s representing colors.

2. Step 2: Use three pointers

   It uses three pointers: low, mid, and high to separate the colors in one pass efficiently.

3. Final Answer:

   Use three pointers to separate 0s, 1s, and 2s in one pass -> Option D

4. Quick Check:

   Three pointers = A [OK]

Hint: Remember three pointers separate colors in one pass [OK]

Common Mistakes:

• Using built-in sort instead of pointers
• Counting colors then rewriting array
• Swapping elements without pointers

2. Which of the following is the correct initialization of pointers in the Dutch Flag algorithm in C#?

easy

A. int low = 0, mid = 0, high = nums.Length - 1;

B. int low = nums.Length - 1, mid = 0, high = 0;

C. int low = 0, mid = nums.Length - 1, high = 0;

D. int low = 0, mid = 1, high = nums.Length;

Solution

1. Step 1: Identify pointer roles

   Low and mid start at 0, high starts at last index (length - 1).

2. Step 2: Check initialization correctness

   int low = 0, mid = 0, high = nums.Length - 1; correctly sets low and mid to 0, high to nums.Length - 1.

3. Final Answer:

   int low = 0, mid = 0, high = nums.Length - 1; -> Option A

4. Quick Check:

   Correct pointer init = C [OK]

Hint: Start low and mid at 0, high at last index [OK]

Common Mistakes:

• Setting high to 0 instead of last index
• Starting mid at length - 1
• Using invalid pointer values

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

medium

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

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

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

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

Solution

1. Step 1: Start with pointers low=0, mid=0, high=5

   Initial array: [2, 0, 2, 1, 1, 0]

2. Step 2: Process elements using Dutch Flag logic

   Swap 2 with 0 at high, move high left; swap 2 with 0 at low; move mid and low accordingly until sorted.

3. Final Answer:

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

4. Quick Check:

   Sorted colors = A [OK]

Hint: Swap 0s left, 2s right, 1s stay middle [OK]

Common Mistakes:

• Not swapping correctly
• Moving pointers incorrectly
• Confusing order of colors

4. Identify the bug in the following C# code snippet for the Dutch Flag algorithm:

int low = 0, mid = 0, high = nums.Length - 1;
while (mid <= high) {
  if (nums[mid] == 0) {
    Swap(nums, low, mid);
    low++;
  } else if (nums[mid] == 1) {
    mid++;
  } else {
    Swap(nums, mid, high);
    high--;
  }
}

medium

A. Swap function parameters are incorrect

B. Missing increment of mid after swapping 0

C. high should be incremented instead of decremented

D. mid should not be incremented when nums[mid] == 1

Solution

1. Step 1: Check pointer increments after swaps

   When nums[mid] == 0, after swapping with low, mid must also increment to avoid infinite loop.

2. Step 2: Identify missing mid++

   The code increments low but misses mid++, causing mid to stay and loop endlessly.

3. Final Answer:

   Missing increment of mid after swapping 0 -> Option B

4. Quick Check:

   Increment mid after 0 swap = D [OK]

Hint: Always increment mid after swapping 0 [OK]

Common Mistakes:

• Forgetting mid++ after swapping 0
• Decrementing high incorrectly
• Incorrect swap parameters

5. Given an array nums containing only 0s, 1s, and 2s, how would you modify the Dutch Flag algorithm to sort an array that also contains 3s, placing all 3s at the end?

hard

A. Add a fourth pointer and extend the logic to handle 3s at the end

B. Use the same three pointers but treat 3s as 2s

C. Sort the array normally using built-in sort for 3s

D. Ignore 3s since they are already at the end

Solution

1. Step 1: Understand limitation of three pointers

   The original algorithm handles only three values (0,1,2). Adding 3 requires extra handling.

2. Step 2: Introduce a fourth pointer

   Use four pointers to separate 0s, 1s, 2s, and 3s, extending the logic to place 3s at the end.

3. Final Answer:

   Add a fourth pointer and extend the logic to handle 3s at the end -> Option A

4. Quick Check:

   Four pointers for four colors = B [OK]

Hint: Add pointer per unique value for correct sorting [OK]

Common Mistakes:

• Treating 3s as 2s causing wrong order
• Using built-in sort instead of pointers
• Ignoring 3s placement