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

Sort Colors Using Two Pointer Dutch Flag Algorithm

📖 Scenario: You are working on a simple image processing tool that needs to sort pixels by their color codes. The colors are represented by numbers 0, 1, and 2, where 0 means red, 1 means white, and 2 means blue.To optimize the sorting, you will use the Dutch National Flag algorithm which sorts the colors in one pass using two pointers.

🎯 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 two integer variables called low and high to track positions

Implement the two-pointer Dutch Flag sorting logic using a while loop and a current index

Print the sorted array elements separated by spaces

💡 Why This Matters

🌍 Real World

Sorting colors efficiently is useful in image processing and graphics where pixels need to be grouped by color quickly.

💼 Career

Understanding two-pointer algorithms and in-place sorting is important for software engineering roles involving performance optimization and data manipulation.

1

Create the colors array

Create an integer array called colors with these exact values: 2, 0, 2, 1, 1, 0.

DSA C

# Your code here

Hint

Use curly braces to initialize the array with the exact numbers.

2

Create pointers for sorting

Create two integer variables called low and high. Set low to 0 and high to 5 (the last index of the array). Also create an integer variable current and set it to 0.

DSA C

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

Hint

Remember array indexes start at 0, so last index is 5 for 6 elements.

3

Implement the Dutch Flag sorting logic

Use a while loop with the condition current <= high. Inside the loop, use if statements to check the value at colors[current]. If it is 0, swap it with colors[low], then increment low and current. If it is 2, swap it with colors[high] and decrement high. If it is 1, just increment current.

DSA C

int colors[] = {2, 0, 2, 1, 1, 0};
int low = 0;
int high = 5;
int current = 0;
// Your code here

Hint

Swap elements when you find 0 or 2, move pointers accordingly, and move current forward for 1.

4

Print the sorted colors array

Use a for loop to print each element of the colors array separated by spaces on a single line.

DSA C

int colors[] = {2, 0, 2, 1, 1, 0};
int low = 0;
int high = 5;
int current = 0;

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

Hint

Use a loop to print all elements with spaces, then print a newline.

Practice

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

easy

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

B. To sort any array of integers in ascending order

C. To find the maximum element in an array

D. To reverse the elements of an array

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 A

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 pointers in the Dutch National Flag algorithm in C?

easy

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

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

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

D. int low = 0, mid = 0, high = 0;

Solution

1. Step 1: Recall pointer roles

   Low starts at 0 to track the boundary of 0s, mid starts at 0 to scan elements, high starts at n-1 to track boundary of 2s.

2. Step 2: Match initialization

   Only int low = 0, mid = 0, high = n - 1; correctly initializes low and mid at 0 and high at n-1.

3. Final Answer:

   int low = 0, mid = 0, high = n - 1; -> Option A

4. Quick Check:

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

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

Common Mistakes:

• Setting high to 0 instead of n-1
• Starting mid at n-1
• Confusing low and high initialization

3. What will be the output array after running the Dutch National Flag algorithm on arr = {2, 0, 2, 1, 1, 0}?

medium

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

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

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

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

Solution

1. Step 1: Trace the algorithm on input

   Initial array: {2, 0, 2, 1, 1, 0}. After sorting: all 0s first, then 1s, then 2s.

2. Step 2: Final sorted array

   Sorted array is [0, 0, 1, 1, 2, 2].

3. Final Answer:

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

4. Quick Check:

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

Hint: Sort 0s, then 1s, then 2s in one pass [OK]

Common Mistakes:

• Not sorting 0s and 2s correctly
• Mixing order of 1s and 0s
• Outputting original array

4. Identify the error in this C code snippet implementing the Dutch National Flag algorithm:

void sortColors(int* arr, int n) {
  int low = 0, mid = 0, high = n - 1;
  while (mid <= high) {
    if (arr[mid] == 0) {
      int temp = arr[low]; arr[low] = arr[mid]; arr[mid] = temp;
      low++;
      mid++;
    } else if (arr[mid] == 1) {
      mid++;
    } else {
      int temp = arr[mid]; arr[mid] = arr[high]; arr[high] = temp;
      high--;
    }
  }
}

medium

A. Missing decrement of high after swapping with low

B. Missing increment of mid after swapping with low

C. Missing increment of mid after swapping with high

D. Incorrect initialization of pointers

Solution

1. Step 1: Analyze pointer increments

   When swapping arr[mid] with arr[low] (for 0), low is incremented but mid is not incremented, causing infinite loop or wrong behavior.

2. Step 2: Correct pointer movement

   After swapping with low, both low and mid should be incremented to move forward.

3. Final Answer:

   Missing increment of mid after swapping with low -> Option B

4. Quick Check:

   Increment mid after swapping with low [OK]

Hint: Increment mid after swapping with low pointer [OK]

Common Mistakes:

• Not incrementing mid after swapping with low
• Incrementing mid after swapping with high
• Incorrect pointer initialization

5. Given an array arr = {1, 2, 0, 1, 2, 0, 1}, how many swaps will the Dutch National Flag algorithm perform to sort it?

hard

A. 3

B. 5

C. 6

D. 4

Solution

1. Step 1: Trace swaps during sorting

   Initial array: {1, 2, 0, 1, 2, 0, 1}
   - Swap 1: mid=1 (2) with high=6 (1) -> [1,1,0,1,2,0,2], high=5
   mid=1 now 1 -> mid=2
   - Swap 2: mid=2 (0) with low=0 (1) -> [0,1,1,1,2,0,2], low=1, mid=3
   mid=3 (1) -> mid=4
   - Swap 3: mid=4 (2) with high=5 (0) -> [0,1,1,1,0,2,2], high=4
   mid=4 now 0 ->
   - Swap 4: mid=4 (0) with low=1 (1) -> [0,0,1,1,1,2,2], low=2, mid=5 (stop)

2. Step 2: Count total swaps

   Total swaps counted are 4.

3. Final Answer:

   4 -> Option D

4. Quick Check:

   Count swaps carefully during pointer moves [OK]

Hint: Count swaps only when actual element exchange happens [OK]

Common Mistakes:

• Counting pointer increments as swaps
• Missing swaps when swapping with high
• Undercounting swaps for consecutive swaps on same mid