Quick Sort: Algorithm & Implementation

1️⃣ What is Quick Sort?

🔹 Quick Sort is a divide-and-conquer sorting algorithm.
🔹 It selects a pivot element and partitions the array so that:

• Elements smaller than pivot go to the left.
• Elements greater than pivot go to the right.
  🔹 The process repeats recursively until the array is sorted.

✅ Time Complexity

Case	Complexity
Best Case (Balanced Partitioning)	O(n log n)
Average Case	O(n log n)
Worst Case (Already Sorted, Unbalanced Partitioning)	O(n²)

✅ Space Complexity

• O(log n) (for recursive stack calls)

✅ Is it Stable?

❌ No (Relative order of equal elements may change)

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2️⃣ How Quick Sort Works

🔹 Select a pivot element.
🔹 Partition the array so that:

• Left part contains elements < pivot
• Right part contains elements > pivot
  🔹 Recursively sort left and right partitions.

Step-by-Step Example

📝 Input: [10, 80, 30, 90, 40, 50, 70]
Pivot = 70 (can be any element, commonly last, first, or random)

Step	Array State	Partitioning Around Pivot
1	[10, 30, 40, 50, 70, 90, 80]	Pivot 70 placed correctly
2	`[10, 30, 40, 50]	70
3	`[10, 30]	40

🔹 Final Sorted Array: [10, 30, 40, 50, 70, 80, 90]

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3️⃣ Quick Sort Algorithm

🔹 Pseudocode

QuickSort(arr, low, high):
    if low < high:
        pivotIndex = Partition(arr, low, high)
        QuickSort(arr, low, pivotIndex - 1)
        QuickSort(arr, pivotIndex + 1, high)

Partition(arr, low, high):
    pivot = arr[high]
    i = low - 1
    for j = low to high - 1:
        if arr[j] < pivot:
            i++
            Swap arr[i] and arr[j]
    Swap arr[i+1] and arr[high]
    return i+1

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4️⃣ Quick Sort Implementation in C

#include <stdio.h>

// Function to swap two elements
void swap(int *a, int *b) {
    int temp = *a;
    *a = *b;
    *b = temp;
}

// Partition function to place pivot in correct position
int partition(int arr[], int low, int high) {
    int pivot = arr[high]; // Choosing last element as pivot
    int i = low - 1;

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

// QuickSort function
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);
    }
}

// Function to print an array
void printArray(int arr[], int n) {
    for (int i = 0; i < n; i++)
        printf("%d ", arr[i]);
    printf("\n");
}

// Main function
int main() {
    int arr[] = {10, 80, 30, 90, 40, 50, 70};
    int n = sizeof(arr) / sizeof(arr[0]);

    printf("Original array: ");
    printArray(arr, n);

    quickSort(arr, 0, n - 1);

    printf("Sorted array: ");
    printArray(arr, n);

    return 0;
}

🔹 Output

Original array: 10 80 30 90 40 50 70
Sorted array: 10 30 40 50 70 80 90

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5️⃣ Advantages & Disadvantages

✅ Advantages

✔ Faster than other O(n²) algorithms like Selection and Insertion Sort.
✔ Efficient for large datasets (O(n log n) in average case).
✔ In-place sorting (O(log n) extra space for recursion).

❌ Disadvantages

❌ Worst case O(n²) if pivot selection is poor (already sorted or reversed).
❌ Not stable (relative order of equal elements may change).
❌ Uses recursion, which may cause stack overflow for large arrays.

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6️⃣ When to Use Quick Sort?

🔹 Best for large datasets (better than Bubble, Insertion, or Selection Sort).
🔹 Useful when in-place sorting is required (O(1) extra space).
🔹 Not ideal if stable sorting is required (use Merge Sort instead).

💡 For best performance, use a randomized or median pivot selection! 🚀