Solution: The Dutch National Flag Problem
Explore various approaches to solving The Dutch National Flag problem in detail.
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Solution 1: Brute force
using System;class Program{/// <summary>/// This method uses the selection sort approach to solve the Dutch National Flag Problem./// </summary>/// <param name="arr">An array of integers.</param>/// <returns>An array with the Dutch National Flag Problem solved.</returns>public static int[] DutchNationalFlag(int[] arr){int size = arr.Length;int index;for (int i = 0; i < size; i++){index = FindMin(arr, i, size);Swap(arr, i, index);}return arr;}/// <summary>/// Finds the minimum value index in an array within a specific range./// </summary>/// <param name="arr">An array of integers.</param>/// <param name="start">Starting index.</param>/// <param name="end">Ending index.</param>/// <returns>The index of the minimum value within the specified range.</returns>public static int FindMin(int[] arr, int start, int end){int min = arr[start];int index = start;for (int x = start; x < end; x++){if (arr[x] < min){min = arr[x];index = x;}}return index;}// Swaps numbers in an arraypublic static void Swap(int[] arr, int i, int j){int temp = arr[i];arr[i] = arr[j];arr[j] = temp;}// Driver to test above codepublic static void Main(){int[] array = { 2, 0, 0, 1, 2, 1 };int[] result = DutchNationalFlag(array);Console.WriteLine("[" + string.Join(", ", result) + "]");}}
Explanation
We use a simple selection sort to rearrange the array in ascending order. This method is naive and does not cater to the fact that we have just three different digits for this problem.
Time complexity
The time complexity is ...