Dutch National Flag Three Way Partition in DSA C# - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main goal of the Dutch National Flag problem?

To rearrange an array so that all elements less than a pivot come first, followed by elements equal to the pivot, and then elements greater than the pivot.

beginner

Which three pointers are commonly used in the Dutch National Flag algorithm?

Low (start of less-than region), Mid (current element), and High (end of greater-than region).

intermediate

In the Dutch National Flag algorithm, what happens when the mid element is less than the pivot?

Swap the mid element with the low element, then increment both low and mid pointers.

intermediate

Why does the Dutch National Flag algorithm run in O(n) time?

Because it processes each element at most once by moving pointers without nested loops.

intermediate

What is the role of the high pointer in the Dutch National Flag algorithm?

It marks the boundary of elements greater than the pivot and moves backward as swaps happen.

What does the 'mid' pointer represent in the Dutch National Flag algorithm?

A The current element being examined

B The start of the less-than region

C The end of the greater-than region

D The pivot element

The mid pointer scans through the array examining each element.

If the element at mid is greater than the pivot, what action is taken?

A Swap with high pointer and decrement high

B Swap with low pointer and increment low and mid

C Increment mid only

D Do nothing and move all pointers

Swap with high pointer and decrement high to move greater elements to the end.

What is the time complexity of the Dutch National Flag algorithm?

A O(n log n)

B O(n)

C O(n^2)

D O(log n)

The algorithm processes each element once, so it runs in linear time O(n).

Which of these is NOT a region maintained by the Dutch National Flag algorithm?

A Less than pivot

B Greater than pivot

C Sorted ascending

D Equal to pivot

The algorithm partitions by pivot but does not sort the array.

When the mid element equals the pivot, what does the algorithm do?

A Swap with low and increment low and mid

B Swap with high and decrement high

C Stop the algorithm

D Increment mid only

When equal, just move mid forward to continue scanning.

Explain the step-by-step process of the Dutch National Flag algorithm using the three pointers.

Think about how each pointer moves and what each swap achieves.

Describe why the Dutch National Flag algorithm is efficient compared to sorting the entire array.

Focus on how many times each element is processed.

Practice

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

easy

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

B. To sort an array 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 algorithm's purpose

   The Dutch National Flag algorithm partitions an array into three parts: 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 A

4. Quick Check:

   Partitioning = Rearranging into three parts [OK]

Hint: Remember: It splits array 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 C# syntax to swap two elements arr[i] and arr[j] in an array?

easy

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

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

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

D. arr.Swap(i, j);

Solution

1. Step 1: Understand swapping in C# arrays

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

2. Step 2: Check each option

   int temp = arr[i]; arr[i] = arr[j]; arr[j] = temp; uses a temp variable correctly; B overwrites values; C and D are invalid syntax in C#.

3. Final Answer:

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

4. Quick Check:

   Swap needs temp variable [OK]

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

Common Mistakes:

• Overwriting values without temp variable
• Using non-existent swap functions
• Confusing syntax from other languages

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

medium

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

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

C. [0, 0, 1, 1, 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

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

3. Final Answer:

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

4. Quick Check:

   Partitioned array = [0,0,1,1,2,2] [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 C# 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. Variables low, mid, high are not declared

B. Loop condition should be mid < high, not mid <= high

C. Pivot value is not initialized

D. Swap method is called incorrectly; should swap array elements by index

Solution

1. Step 1: Check Swap usage

   Swap(arr[low], arr[mid]) passes values, not indices; swapping values won't affect array elements.

2. Step 2: Correct swap call

   Swap should be a method swapping elements by indices or use a temp variable to swap arr[low] and arr[mid].

3. Final Answer:

   Swap method is called incorrectly; should swap array elements by index -> Option D

4. Quick Check:

   Swap must affect array elements, not just values [OK]

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

Common Mistakes:

• Passing values instead of indices to swap
• Incorrect loop boundary conditions
• Forgetting to initialize pivot

5. Given an array arr = [3, 5, 2, 3, 8, 3, 1] and pivot = 3, how would you modify the Dutch National Flag algorithm to partition the array so that all elements less than 3 come first, then all elements equal to 3, and finally all elements greater than 3? What is the final array?

hard

A. [2, 1, 3, 3, 3, 5, 8]

B. [1, 2, 3, 3, 3, 8, 5]

C. [3, 3, 3, 2, 1, 5, 8]

D. [5, 8, 3, 3, 3, 2, 1]

Solution

1. Step 1: Apply Dutch National Flag partition with pivot 3

   Group elements less than 3: 1,2; equal to 3: 3,3,3; greater than 3: 5,8.

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

   Final array is [2, 1, 3, 3, 3, 5, 8].

3. Final Answer:

   [2, 1, 3, 3, 3, 5, 8] -> Option A

4. Quick Check:

   Partitioned array = [2,1,3,3,3,5,8] [OK]

Hint: Place less, equal, then greater elements around pivot [OK]

Common Mistakes:

• Mixing order of groups
• Not grouping all equal elements together
• Ignoring elements equal to pivot