The Dutch National Flag algorithm, also known as three-way partitioning or the three-pointer technique, is a sorting algorithm that divides elements into three different groups.
Understanding and implementing the Dutch National Flag algorithm can significantly enhance efficiency in scenarios where we need to sort or segregate data with a few distinct values. It can be used in the three-way partitioning quicksort for handling arrays with many duplicate values. It can also be used in image processing to segregate pixels of different colors into separate regions.
Note:
Please refer to "The Dutch National Flag Problem" to explore the Dutch National Flag algorithm in more detail.
In this case, the algorithm is modified to sort the array in descending order, prioritizing larger values.
We have a size N array with elements that can only be 0s, 1s, and 2s. The goal is to modify the Dutch National Flag algorithm to sort the array in descending order.
Here are the sample inputs and outputs for the problem:
Input 1: N = 6, arr[] = {2, 1, 0, 1, 2, 0}
Output 1: 2 2 1 1 0 0
Input 2: N = 4, arr[] = {1, 0, 2, 1}
Output 2: 2 1 1 0
Here is the algorithm below:
The algorithm sorts the array using the Dutch National Flag method with modified element-swapping logic to prioritize larger values.
There are three-pointers (low
, middle
, and high
) to classify elements as 0s, 1s, or 2s.
low
and middle
are initialized to the start of the array.
high
is initialized to the end of the array.
The elements of the array are swapped by traversing the array with the mid
pointer.
Depending on the value at mid
:
If it’s 2 (highest value), we swap it with the element at low
and increment both low
and mid
.
If it’s 1 (middle value), we just increment mid
.
If it’s 0 (lowest value), swap it with the element at high
and decrement high
(we do not increment mid
in this case, because the element swapped from high
needs to be examined).
The method continues until the full array has been sorted in descending order. The process continues until mid
exceeds high
. At the end, all 2s will be before low
, all 1s will be between low
and high
, and all 0s will be after high
.
Remember: The Dutch National Flag algorithm efficiently handles edge cases, including arrays with few unique elements or partially sorted arrays. It adjusts its sorting strategy accordingly, ensuring correctness and optimizing performance.
Below is the Kotlin code example demonstrating the implementation of the Dutch National Flag algorithm to sort an array in descending order:
// Function to perform sorting using the Dutch National Flag algorithm in descending orderfun sortDescending012(arr: IntArray, N: Int) {var low = 0var mid = 0var high = N - 1var temp: Intvar temp2: Intwhile (mid <= high) {when (arr[mid]) {// If the current element is 0, swap it with the element at 'high'0 -> {temp2 = arr[mid]arr[mid] = arr[high]arr[high] = temp2high--}// If the current element is 1, leave it in its place and move to the next element1 -> mid++// If the current element is 2, swap it with the element at 'low'2 -> {temp = arr[low]arr[low] = arr[mid]arr[mid] = templow++mid++}}}}// Top-level main functionfun main() {val arr = intArrayOf(2, 1, 0, 1, 2, 0)val size = arr.size// Display the original array before sortingprint("Original Array: ")for (i in 0 until size)print("${arr[i]} ")println()// Sort the array using the Dutch National Flag algorithm in descending ordersortDescending012(arr, size)// Display the sorted arrayprint("Kotlin Sorted Array (Descending): ")for (i in 0 until size)print("${arr[i]} ")println()}
Here’s a breakdown of the provided Kotlin code:
Line 2: This declares the sortDescending012
function that accepts an array of integers arr
and its size N
as parameters.
Lines 3–7: This declares and initializes variables low
, mid
, high
, temp
, and temp2
to maintain pointers for sorting.
Line 9: This iterates through the array with a while
loop until mid
crosses high
.
Lines 10–28: This handles cases according to the current element at arr[mid]
by using a when
statement:
If the element is 0
, it swaps with the element at high
.
If the element is 1
, it remains in place and moves to the next element.
If the element is 2
, it swaps with the element at low
.
Line 33: This initializes an array arr
.
Lines 37–39: This displays the original array before sorting.
Line 43: This calls sortDescending012
to sort the array in descending order.
Lines 45–48: This displays the sorted array after sorting.
Let’s understand the efficiency of the algorithm:
The algorithm traverses the array once and performs constant time operations on each element.
Therefore, the time complexity is
The algorithm uses only a constant amount of extra space for variables (low
, mid
, high
, temp
, and temp2
).
Hence, the space complexity is
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