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

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the low pointer to start the partition.

DSA Javascript

let low = [1];

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

Aarr.length

B1

C-1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Starting low at 1 or -1 causes skipping or invalid index errors.

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 Javascript

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

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

Ahigh

Blow

Ci

Dpivot

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping with high or pivot index causes incorrect partitioning.

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 while loop condition to correctly process the array.

DSA Javascript

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 '<' excludes the last element from processing.

The loop should run while i is less than or equal to high to process all elements.

4fill in blank

hard

Fill both blanks to correctly update pointers after swapping smaller elements.

DSA Javascript

swap(arr, i, low); [1]++; [2]++;

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

Ai

Blow

Chigh

Dpivot

Attempts:

3 left

💡 Hint

Common Mistakes

Incrementing high or pivot instead of low causes incorrect partitioning.

After swapping, both i and low pointers move forward to continue partitioning.

5fill in blank

hard

Fill the blanks to correctly update pointers after swapping larger elements.

DSA Javascript

swap(arr, i, [1]); [2]--; // decrement high pointer
// do not increment i here

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

Ahigh

Blow

Ci

Dpivot

Attempts:

3 left

💡 Hint

Common Mistakes

Incrementing i after swapping with high causes skipping elements.

Swap with high, decrement high pointer, and do not increment i to recheck swapped element.

Practice

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

easy

A. To find the maximum element in an array

B. To sort an array in ascending order using quicksort

C. To reverse the elements of an array

D. To rearrange an array so that all elements less than a pivot come first, then equal elements, then greater elements

Solution

1. Step 1: Understand the partition goal

   The algorithm divides the array into three parts: less than pivot, equal to pivot, and greater than pivot.

2. Step 2: Identify the rearrangement

   It rearranges elements so that all smaller come first, then equal, then larger, without full sorting.

3. Final Answer:

   To rearrange an array so that all elements less than a pivot come first, then equal elements, then greater elements -> Option D

4. Quick Check:

   Partitioning = Rearranging by pivot [OK]

Hint: Remember: three parts - less, equal, greater [OK]

Common Mistakes:

• Confusing partition with full sorting
• Thinking it only finds max or min
• Assuming it reverses the array

2. Which of the following is the correct way to initialize pointers for the Dutch National Flag algorithm in JavaScript?

easy

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

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

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

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

Solution

1. Step 1: Identify pointer roles

   Low and mid start at 0, high at last index to cover full array.

2. Step 2: Match initialization to algorithm

   Correct initialization is low=0, mid=0, high=arr.length-1 to scan and partition properly.

3. Final Answer:

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

4. Quick Check:

   Pointers start at array ends and middle [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 wrong position
• Using array length instead of length - 1

3. What will be the output of the following code snippet?

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

console.log(dutchFlag([2, 5, 1, 2, 3, 2, 4], 2));

medium

A. [1, 2, 2, 2, 5, 3, 4]

B. [2, 2, 2, 1, 3, 4, 5]

C. [1, 2, 2, 2, 3, 4, 5]

D. [1, 2, 2, 2, 4, 3, 5]

Solution

1. Step 1: Trace swaps for elements less than pivot

   Elements less than 2 (which is 1) move to front; 1 swaps to index 0.

2. Step 2: Place all 2s in middle and greater elements at end

   All 2s stay in middle; 3,4,5 move to the right side in any order preserving partition.

3. Final Answer:

   [1, 2, 2, 2, 3, 4, 5] -> Option C

4. Quick Check:

   Partitioned array with less, equal, greater [OK]

Hint: Swap less than pivot left, greater right [OK]

Common Mistakes:

• Not swapping correctly when element equals pivot
• Mixing order of greater elements
• Forgetting to increment mid after swap with low

4. Identify the bug in this Dutch National Flag partition code:

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

medium

A. The pointers low and mid are initialized incorrectly

B. The while loop condition should be mid <= high, not mid < high

C. The swap operation is missing for elements equal to pivot

D. The high pointer should be incremented, not decremented

Solution

1. Step 1: Check loop condition correctness

   The loop must run while mid is less than or equal to high to process all elements.

2. Step 2: Identify impact of incorrect condition

   Using mid < high skips processing when mid equals high, missing last element check.

3. Final Answer:

   The while loop condition should be mid <= high, not mid < high -> Option B

4. Quick Check:

   Loop must cover all elements [OK]

Hint: Use mid <= high to cover all elements [OK]

Common Mistakes:

• Using mid < high causes last element to be skipped
• Incorrect pointer initialization
• Misunderstanding swap necessity for equal elements

5. Given an array [4, 9, 4, 7, 4, 8, 7] and pivot value 7, what will be the final array after applying the Dutch National Flag partition algorithm?

hard

A. [4, 4, 4, 7, 7, 8, 9]

B. [4, 4, 4, 7, 8, 7, 9]

C. [4, 4, 4, 7, 8, 9, 7]

D. [7, 7, 4, 4, 4, 8, 9]

Solution

1. Step 1: Partition elements less than pivot (7)

   All 4s move to the front: [4, 4, 4, ...]

2. Step 2: Place all 7s in the middle and greater elements at the end

   7s stay in the middle; 8 and 9 move to the right side in sorted order.

3. Final Answer:

   [4, 4, 4, 7, 7, 8, 9] -> Option A

4. Quick Check:

   Less, equal, greater partitioned correctly [OK]

Hint: Group less, equal, greater around pivot [OK]

Common Mistakes:

• Mixing order of greater elements
• Placing pivot elements incorrectly
• Not moving all less elements to front