Dutch National Flag Three Way Partition in DSA Java - Build from Scratch

Dutch National Flag Three Way Partition

📖 Scenario: You are organizing colored balls in a line. The balls can be red, white, or blue. You want to arrange them so that all red balls come first, then white balls, and then blue balls at the end.

🎯 Goal: Build a program that rearranges an array of integers representing colors (0 for red, 1 for white, 2 for blue) so that all 0s come first, then all 1s, and then all 2s.

📋 What You'll Learn

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

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

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

Print the final state of the colors array as a space-separated string

💡 Why This Matters

🌍 Real World

Sorting colored objects or grouping items by categories quickly without using extra space.

💼 Career

Understanding partitioning algorithms is useful in software development, especially in sorting, searching, and optimizing data processing.

1

Create the initial array

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

DSA Java

# Create the integer array colors with values {2, 0, 2, 1, 1, 0}
// Your code here

Hint

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

2

Initialize pointers for partitioning

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

DSA Java

int[] colors = {2, 0, 2, 1, 1, 0};
// Create int variables low = 0, mid = 0, high = colors.length - 1
// Your code here

Hint

Use int low = 0;, int mid = 0;, and int high = colors.length - 1;.

3

Apply the Dutch National Flag partitioning logic

Use a while loop with the condition mid <= high. Inside the loop, use if statements to check colors[mid]. If it is 0, swap with colors[low] and increment low and mid. If it is 1, just increment mid. If it is 2, swap with colors[high] and decrement high. Use a temporary variable temp for swapping.

DSA Java

int[] colors = {2, 0, 2, 1, 1, 0};
int low = 0;
int mid = 0;
int high = colors.length - 1;
// Use while loop with condition mid <= high
// Inside loop, use if-else to swap and move pointers
// Your code here

Hint

Use the Dutch National Flag algorithm with three pointers and swapping.

4

Print the final array

Print the elements of the colors array separated by spaces on one line using a for loop.

DSA Java

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--;
    }
}
// Print the colors array elements separated by spaces
// Your code here

Hint

Use a for loop and System.out.print to display the array elements separated by spaces.

Practice

1. What is the main goal of the Dutch National Flag Three Way Partition algorithm?

easy

A. To reverse the elements of an array

B. To rearrange an array into three parts based on a pivot value

C. To find the maximum element in an array

D. To sort an array in ascending order

Solution

1. Step 1: Understand the algorithm's purpose

   The Dutch National Flag algorithm divides an array into three parts: elements less than, equal to, and greater than a pivot.

2. Step 2: Compare with other options

   Sorting or finding max are different tasks; reversing is unrelated.

3. Final Answer:

   To rearrange an array into three parts based on a pivot value -> Option B

4. Quick Check:

   Partitioning by pivot = D [OK]

Hint: Remember: It partitions into three groups around a pivot [OK]

Common Mistakes:

• Confusing partitioning with sorting
• Thinking it finds max or min values
• Assuming it reverses the array

2. Which of the following is the correct Java syntax to swap two elements arr[i] and arr[j] in an integer array?

easy

A. int temp = arr[i]; arr[i] = arr[j]; arr[j] = temp;

B. arr[i] = arr[j]; arr[j] = arr[i];

C. swap(arr[i], arr[j]);

D. int temp = arr[i]; arr[i] = arr[j]; arr[j] = arr[i];

Solution

1. Step 1: Understand swapping logic

   Swapping requires a temporary variable to hold one value while assigning the other.

2. Step 2: Check each option

   swap(arr[i], arr[j]); assumes a non-existent swap function; arr[i] = arr[j]; arr[j] = arr[i]; overwrites arr[i] without saving; int temp = arr[i]; arr[i] = arr[j]; arr[j] = arr[i]; loses original arr[i] value by assigning arr[j] = arr[i] after changing arr[i]; int temp = arr[i]; arr[i] = arr[j]; arr[j] = temp; correctly uses temp.

3. Final Answer:

   int temp = arr[i]; arr[i] = arr[j]; arr[j] = temp; -> Option A

4. Quick Check:

   Use temp variable for swap = C [OK]

Hint: Use a temp variable to swap two array elements safely [OK]

Common Mistakes:

• Overwriting one element before saving it
• Using a non-existent swap function
• Swapping without a temporary variable

3. What will be the output array after applying the Dutch National Flag algorithm on arr = [2, 0, 2, 1, 1, 0] with pivot = 1?

medium

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

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

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

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

Solution

1. Step 1: Partition array by pivot 1

   Elements less than 1: 0,0; equal to 1: 1,1; greater than 1: 2,2.

2. Step 2: Arrange in order less, equal, greater

   So the array becomes [0, 0, 1, 1, 2, 2].

3. Final Answer:

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

4. Quick Check:

   Partitioned array = A [OK]

Hint: Group elements less, equal, then greater than pivot [OK]

Common Mistakes:

• Not grouping equal elements in the middle
• Mixing order of groups
• Ignoring pivot value placement

4. Identify the error in this Java code snippet for Dutch National Flag partition:

int low = 0, mid = 0, high = arr.length - 1;
while (mid <= high) {
  if (arr[mid] < pivot) {
    swap(arr[low], arr[mid]);
    low++;
    mid++;
  } else if (arr[mid] == pivot) {
    mid++;
  } else {
    swap(arr[mid], arr[high]);
    high--;
  }
}

medium

A. The pivot comparison should use > instead of <

B. The loop condition should be mid < high

C. swap function is called incorrectly with array elements instead of indices

D. The variables low, mid, high are not initialized properly

Solution

1. Step 1: Check swap function usage

   swap(arr[low], arr[mid]) passes values, not indices; swap needs indices to swap elements in array.

2. Step 2: Verify other parts

   Loop condition and variable initialization are correct; pivot comparisons are standard.

3. Final Answer:

   swap function is called incorrectly with array elements instead of indices -> Option C

4. Quick Check:

   Swap needs indices, not values = A [OK]

Hint: Swap array elements by indices, not by passing values [OK]

Common Mistakes:

• Passing values instead of indices to swap
• Wrong loop boundary condition
• Incorrect pivot comparison operators

5. Given an array arr = [3, 5, 2, 1, 4, 3, 2] and pivot = 3, how many swaps will the Dutch National Flag algorithm perform to partition the array?

hard

A. 5

B. 4

C. 3

D. 6

Solution

1. Step 1: Trace swaps during partition

   Initial: low=0, mid=0, high=6 - mid=0 (3 == pivot): mid++ (0 swaps) - mid=1 (5 > pivot): swap arr[mid] and arr[high] -> swap arr[1] and arr[6] (swap 1), high--=5 - mid=1 (now 2 < pivot): swap arr[low] and arr[mid] -> swap arr[0] and arr[1] (swap 2), low++=1, mid++=2 - mid=2 (2 < pivot): swap arr[low] and arr[mid] -> swap arr[1] and arr[2] (swap 3), low++=2, mid++=3 - mid=3 (1 < pivot): swap arr[low] and arr[mid] -> swap arr[2] and arr[3] (swap 4), low++=3, mid++=4 - mid=4 (4 > pivot): swap arr[mid] and arr[high] -> swap arr[4] and arr[5] (swap 5), high--=4 - mid=4 (now 3 == pivot): mid++=5 Loop ends as mid > high.

2. Step 2: Count total swaps

   Total swaps counted = 5.

3. Final Answer:

   5 -> Option A

4. Quick Check:

   Count swaps carefully during partition = B [OK]

Hint: Count swaps when elements move across low, mid, high pointers [OK]

Common Mistakes:

• Counting swaps incorrectly when pivot equals element
• Ignoring swaps after high pointer moves
• Assuming one swap per iteration