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

Practice - 5 Tasks

1fill in blank

easy

Complete the code to swap two integers using a temporary variable.

DSA C

void swap(int *a, int *b) {
    int temp = *a;
    *a = [1];
    *b = temp;
}

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

A*b

B*a

Ca

Dtemp

Attempts:

3 left

💡 Hint

Common Mistakes

Assigning 'a' instead of '*b'.

Using 'temp' instead of '*b'.

We assign the value pointed by b to the location pointed by a to complete the swap.

2fill in blank

medium

Complete the code to move the 'low' pointer forward when the current element is less than pivot.

DSA C

if (arr[i] < pivot) {
    swap(&arr[i], &arr[[1]]);
    low++;
    i++;
}

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

Apivot

Blow

Ci

Dhigh

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping with 'high' instead of 'low'.

Swapping with 'i' which is the current index.

We swap with the element at 'low' pointer and then increment 'low'.

3fill in blank

hard

Fix the error in the loop condition to correctly process all elements.

DSA C

while ([1] <= high) {
    if (arr[i] < pivot) {
        swap(&arr[i], &arr[low]);
        low++;
        i++;
    } else if (arr[i] > pivot) {
        swap(&arr[i], &arr[high]);
        high--;
    } else {
        i++;
    }
}

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

Ahigh

Blow

Cpivot

Di

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'low' or 'high' as the loop variable incorrectly.

Comparing 'pivot' instead of an index.

The index 'i' should be compared to 'high' to process all elements.

4fill in blank

hard

Fill both blanks to initialize pointers correctly before the partition loop.

DSA C

int low = [1];
int high = [2];

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

A0

B1

Csize - 1

Dsize

Attempts:

3 left

💡 Hint

Common Mistakes

Setting 'low' to 1 instead of 0.

Setting 'high' to size instead of size - 1.

The 'low' pointer starts at 0 and 'high' at the last index (size - 1).

5fill in blank

hard

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

DSA C

void dutch_national_flag(int arr[], int size, int pivot) {
    int low = [1];
    int high = [2];
    int i = [3];

    while (i <= high) {
        if (arr[i] < pivot) {
            swap(&arr[i], &arr[low]);
            low++;
            i++;
        } else if (arr[i] > pivot) {
            swap(&arr[i], &arr[high]);
            high--;
        } else {
            i++;
        }
    }
}

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

A0

Bsize - 1

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Starting 'i' or 'low' at 1 instead of 0.

Setting 'high' to size instead of size - 1.

Initialize 'low' and 'i' to 0, and 'high' to size - 1 to cover the whole array.

Practice

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

easy

A. To sort an array in ascending order using quicksort

B. To rearrange an array into three parts: less than, equal to, and greater than a pivot

C. To find the maximum element in an array

D. To reverse the elements of an array

Solution

1. Step 1: Understand the partitioning goal

   The algorithm divides the array into three parts based on a pivot value: elements less than pivot, equal to pivot, and greater than pivot.

2. Step 2: Compare with other options

   Options A, C, and D describe different operations: sorting, finding max, and reversing, which are not the main goal here.

3. Final Answer:

   To rearrange an array into three parts: less than, equal to, and greater than a pivot -> Option B

4. Quick Check:

   Partitioning = three parts [OK]

Hint: Remember: three parts based on pivot value [OK]

Common Mistakes:

• Confusing with full sorting algorithms
• Thinking it only separates two parts
• Assuming it finds max or min values

2. Which of the following is the correct way to declare the pointers used in the Dutch National Flag algorithm in C?

easy

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

B. int low, mid, high = 0;

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

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

Solution

1. Step 1: Understand pointer initialization

   In the algorithm, low and mid start at 0, and high starts at n-1 (last index).

2. Step 2: Check each option

   int low = 0, mid = 0, high = n - 1; correctly initializes low and mid to 0, high to n-1. Others have incorrect initial values.

3. Final Answer:

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

4. Quick Check:

   Pointers start: low=0, mid=0, high=n-1 [OK]

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

Common Mistakes:

• Setting low or mid to n or n-1 incorrectly
• Not initializing all pointers
• Confusing variable assignments

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, 0, 1, 1, 2, 2]

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

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

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

Solution

1. Step 1: Partition array around 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 A

4. Quick Check:

   Partitioned array = [0,0,1,1,2,2] [OK]

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

Common Mistakes:

• Mixing order of groups
• Not grouping equal elements correctly
• Assuming full sorting instead of partitioning

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

void dnfPartition(int arr[], int n, int pivot) {
  int low = 0, mid = 0, high = n - 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. Pivot comparison should use > instead of <

B. The loop condition should be mid < high

C. Pointers low and mid should start at n-1

D. swap function is not defined for array elements

Solution

1. Step 1: Check swap usage

   The code uses swap(arr[low], arr[mid]) but swap is not a built-in function in C for array elements.

2. Step 2: Verify other parts

   Loop condition and pointer initialization are correct. Pivot comparisons are correct as per algorithm.

3. Final Answer:

   swap function is not defined for array elements -> Option D

4. Quick Check:

   Missing swap definition = error [OK]

Hint: Remember to define or implement swap for array elements [OK]

Common Mistakes:

• Assuming swap is built-in for arrays in C
• Changing loop condition incorrectly
• Wrong pointer initialization

5. Given an array arr = {3, 5, 2, 3, 8, 3, 1, 3} and pivot = 3, how many swaps will the Dutch National Flag algorithm perform to partition the array?

hard

A. 5

B. 3

C. 4

D. 6

Solution

1. Step 1: Trace swaps during partition

   Initial pointers: low=0, mid=0, high=7. - mid=0 (3 == pivot): mid++ (0 swaps) - mid=1 (5 > pivot): swap arr[mid] and arr[high] -> swap(5,3), high=6 (1 swap) - mid=1 (now 3 == pivot): mid++ (1 swap) - mid=2 (2 < pivot): swap arr[low] and arr[mid] -> swap(3,2), low=1, mid=3 (2 swaps) - mid=3 (3 == pivot): mid++ (2 swaps) - mid=4 (8 > pivot): swap arr[mid] and arr[high] -> swap(8,1), high=5 (3 swaps) - mid=4 (now 1 < pivot): swap arr[low] and arr[mid] -> swap(3,1), low=2, mid=5 (4 swaps) - mid=5 (3 == pivot): mid++ (4 swaps) Loop ends as mid=6 > high=5.

2. Step 2: Count total swaps

   Total swaps performed = 4

3. Final Answer:

   4 -> Option C

4. Quick Check:

   Count swaps carefully = 4 [OK]

Hint: Count swaps during each pointer move carefully [OK]

Common Mistakes:

• Counting swaps only when mid moves
• Ignoring swaps after swapping with high
• Miscounting swaps when elements equal pivot