Dutch National Flag Three Way Partition in DSA Java - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the low pointer for the Dutch National Flag algorithm.

DSA Java

int low = [1];

Drag options to blanks, or click blank then click option'

A-1

B1

C0

Darr.length

Attempts:

3 left

💡 Hint

Common Mistakes

Initializing low to 1 instead of 0.

Setting low to -1 which is invalid index.

The low pointer starts at index 0 to begin partitioning from the start of the array.

2fill in blank

medium

Complete the code to swap elements at indices i and low.

DSA Java

int temp = arr[[1]]; arr[[2]] = arr[low]; arr[low] = temp;

Drag options to blanks, or click blank then click option'

Ai

Blow

Chigh

Dpivot

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping with high instead of low.

Using pivot as an index which is incorrect.

We swap the element at index i with the element at index low to move smaller elements to the front.

3fill in blank

hard

Fix the error in the loop condition to correctly iterate over the array.

DSA Java

while (i [1] high) {

Drag options to blanks, or click blank then click option'

A<=

B>

C>=

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Using < may miss processing when i == high and arr[i] > pivot.

Using > or >= reverses the loop logic.

The loop should run while i <= high to properly handle the case when i equals high.

4fill in blank

hard

Fill both blanks to correctly update pointers after swapping with high.

DSA Java

int temp = arr[[1]]; arr[[2]] = arr[high]; arr[high] = temp; high--;

Drag options to blanks, or click blank then click option'

Ai

Blow

Chigh

Dpivot

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping with low instead of high.

Not decrementing high after swap.

Swap element at i with element at high, then decrease high pointer.

5fill in blank

hard

Fill all three blanks to complete the Dutch National Flag partition loop.

DSA Java

while (i [1] high) {
  if (arr[i] [2] pivot) {
    int temp = arr[i]; arr[i] = arr[low]; arr[low] = temp; low++; i++;
  } else if (arr[i] [3] pivot) {
    int temp = arr[i]; arr[i] = arr[high]; arr[high] = temp; high--;
  } else {
    i++;
  }
}

Drag options to blanks, or click blank then click option'

A<=

B<

C>

D==

Attempts:

3 left

💡 Hint

Common Mistakes

Using < in loop condition causing incomplete partitioning.

Mixing up < and > in if conditions.

The loop runs while i <= high. If arr[i] < pivot, swap with low and increment both. If arr[i] > pivot, swap with high and decrement high. Else, just increment i.

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