Dutch National Flag Algorithm Explained — Sort 3 Values in One Pass

package io.thecodeforge.algo;

import java.util.Arrays;

public class DutchNationalFlag {

    /**
     * Sorts an array of three distinct values (0, 1, 2) in-place.
     * O(n) time, O(1) space, single pass.
     */
    public static void sortColors(int[] arr) {
        if (arr == null || arr.length <= 1) return;

        int low = 0;
        int mid = 0;
        int high = arr.length - 1;

        while (mid <= high) {
            switch (arr[mid]) {
                case 0:
                    swap(arr, low, mid);
                    low++;
                    mid++;
                    break;
                case 1:
                    mid++;
                    break;
                case 2:
                    swap(arr, mid, high);
                    high--;
                    // Do NOT increment mid — swapped element is unexamined
                    break;
            }
        }
    }

    private static void swap(int[] arr, int i, int j) {
        int temp = arr[i];
        arr[i] = arr[j];
        arr[j] = temp;
    }

    public static void main(String[] args) {
        int[] arr = {2, 0, 2, 1, 1, 0};
        System.out.println("Before: " + Arrays.toString(arr));
        sortColors(arr);
        System.out.println("After:  " + Arrays.toString(arr));

        // Edge cases
        sortColors(new int[]{2, 2, 2, 2}); // all 2s
        sortColors(new int[]{0, 0, 0, 0}); // all 0s
        sortColors(new int[]{1, 1, 1, 1}); // all 1s
        sortColors(new int[]{2, 0, 1});    // already one of each
        sortColors(new int[]{});            // empty
        sortColors(new int[]{1});           // single element
    }
}

package io.thecodeforge.algo;

/**
 * Dutch National Flag Algorithm Implementation
 * Complexity: Time O(n), Space O(1)
 */
public class SortColors {
    public void sort(int[] nums) {
        if (nums == null || nums.length <= 1) return;

        int low = 0;
        int mid = 0;
        int high = nums.length - 1;

        while (mid <= high) {
            switch (nums[mid]) {
                case 0: // Element belongs in the 'Red' zone
                    swap(nums, low++, mid++);
                    break;
                case 1: // Element belongs in the 'White' (middle) zone
                    mid++;
                    break;
                case 2: // Element belongs in the 'Blue' zone
                    swap(nums, mid, high--);
                    // Note: We do NOT increment mid here because the 
                    // swapped element from 'high' is unexamined.
                    break;
            }
        }
    }

    private void swap(int[] arr, int i, int j) {
        int temp = arr[i];
        arr[i] = arr[j];
        arr[j] = temp;
    }

    public static void main(String[] args) {
        int[] testCase = {2, 0, 2, 1, 1, 0};
        new SortColors().sort(testCase);
        // Result: [0, 0, 1, 1, 2, 2]
    }
}

package io.thecodeforge.algo;

import java.util.Arrays;

public class ThreeWayQuickSort {

    /**
     * 3-way QuickSort using DNF partition.
     * O(n log n) average, O(n) for duplicate-heavy arrays.
     */
    public static void sort(int[] arr) {
        if (arr == null || arr.length <= 1) return;
        quickSort(arr, 0, arr.length - 1);
    }

    private static void quickSort(int[] arr, int lo, int hi) {
        if (lo >= hi) return;

        // DNF partition around arr[lo] as pivot
        int lt = lo;     // arr[lo..lt-1] < pivot
        int gt = hi;     // arr[gt+1..hi] > pivot
        int mid = lo;    // arr[lt..mid-1] == pivot
        int pivot = arr[lo];

        while (mid <= gt) {
            if (arr[mid] < pivot) {
                swap(arr, lt++, mid++);
            } else if (arr[mid] > pivot) {
                swap(arr, mid, gt--);
            } else {
                mid++;
            }
        }

        // Recurse only on < and > zones. The == zone is done.
        quickSort(arr, lo, lt - 1);
        quickSort(arr, gt + 1, hi);
    }

    private static void swap(int[] arr, int i, int j) {
        int temp = arr[i];
        arr[i] = arr[j];
        arr[j] = temp;
    }

    public static void main(String[] args) {
        // Duplicate-heavy array: 90% identical elements
        int[] arr = {5, 5, 5, 5, 5, 3, 3, 3, 7, 7, 7, 7, 5, 5, 5};
        System.out.println("Before: " + Arrays.toString(arr));
        sort(arr);
        System.out.println("After:  " + Arrays.toString(arr));

        // All identical: O(n) with 3-way, O(n^2) with standard QuickSort
        int[] allSame = {4, 4, 4, 4, 4, 4, 4, 4};
        sort(allSame);
        System.out.println("All same: " + Arrays.toString(allSame));
    }
}

package io.thecodeforge.algo;

import java.util.Arrays;

public class CountingSortKValues {

    /**
     * Sorts an array of k distinct values using counting sort.
     * O(n + k) time, O(k) space.
     * Use when k is small (k <= 10) and you need a simple solution.
     */
    public static void sort(int[] arr, int k) {
        if (arr == null || arr.length <= 1) return;

        int[] count = new int[k];
        for (int val : arr) {
            count[val]++;
        }

        int idx = 0;
        for (int val = 0; val < k; val++) {
            for (int j = 0; j < count[val]; j++) {
                arr[idx++] = val;
            }
        }
    }

    public static void main(String[] args) {
        // Sort 5 values (0-4)
        int[] arr = {3, 0, 4, 1, 2, 3, 0, 1, 4, 2};
        System.out.println("Before: " + Arrays.toString(arr));
        sort(arr, 5);
        System.out.println("After:  " + Arrays.toString(arr));
    }
}