Sorting Algorithms

// Quick Sort - O(n log n) average, O(n²) worst case
public void quickSort(int[] arr, int low, int high) {
    if (low < high) {
        int pi = partition(arr, low, high);
        quickSort(arr, low, pi - 1);
        quickSort(arr, pi + 1, high);
    }
}

private int partition(int[] arr, int low, int high) {
    int pivot = arr[high];
    int i = low - 1;
    
    for (int j = low; j < high; j++) {
        if (arr[j] <= pivot) {
            i++;
            swap(arr, i, j);
        }
    }
    
    swap(arr, i + 1, high);
    return i + 1;
}

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

// Merge Sort - O(n log n) time, O(n) space
public void mergeSort(int[] arr, int left, int right) {
    if (left < right) {
        int mid = left + (right - left) / 2;
        mergeSort(arr, left, mid);
        mergeSort(arr, mid + 1, right);
        merge(arr, left, mid, right);
    }
}

private void merge(int[] arr, int left, int mid, int right) {
    int n1 = mid - left + 1;
    int n2 = right - mid;
    
    int[] leftArr = new int[n1];
    int[] rightArr = new int[n2];
    
    for (int i = 0; i < n1; i++) {
        leftArr[i] = arr[left + i];
    }
    for (int j = 0; j < n2; j++) {
        rightArr[j] = arr[mid + 1 + j];
    }
    
    int i = 0, j = 0, k = left;
    while (i < n1 && j < n2) {
        if (leftArr[i] <= rightArr[j]) {
            arr[k] = leftArr[i];
            i++;
        } else {
            arr[k] = rightArr[j];
            j++;
        }
        k++;
    }
    
    while (i < n1) {
        arr[k] = leftArr[i];
        i++;
        k++;
    }
    
    while (j < n2) {
        arr[k] = rightArr[j];
        j++;
        k++;
    }
}

// Heap Sort - O(n log n) time, O(1) space
public void heapSort(int[] arr) {
    int n = arr.length;
    
    // Build max heap
    for (int i = n / 2 - 1; i >= 0; i--) {
        heapify(arr, n, i);
    }
    
    // Extract elements from heap one by one
    for (int i = n - 1; i > 0; i--) {
        swap(arr, 0, i);
        heapify(arr, i, 0);
    }
}

private void heapify(int[] arr, int n, int i) {
    int largest = i;
    int left = 2 * i + 1;
    int right = 2 * i + 2;
    
    if (left < n && arr[left] > arr[largest]) {
        largest = left;
    }
    
    if (right < n && arr[right] > arr[largest]) {
        largest = right;
    }
    
    if (largest != i) {
        swap(arr, i, largest);
        heapify(arr, n, largest);
    }
}