Sorting in Data Structures

1️⃣ What is Sorting?

Sorting is the process of arranging elements in a particular order (ascending or descending). It helps in efficient searching, data retrieval, and processing.

2️⃣ Types of Sorting Algorithms

Sorting algorithms are mainly categorized into:

• Comparison-based Sorting (Bubble Sort, Selection Sort, Quick Sort, Merge Sort, etc.)
• Non-comparison Sorting (Counting Sort, Radix Sort, Bucket Sort, etc.)

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3️⃣ Common Sorting Algorithms

Algorithm	Best Case	Worst Case	Average Case	Space Complexity	Stable?
Bubble Sort	O(n)	O(n²)	O(n²)	O(1)	✅ Yes
Selection Sort	O(n²)	O(n²)	O(n²)	O(1)	❌ No
Insertion Sort	O(n)	O(n²)	O(n²)	O(1)	✅ Yes
Merge Sort	O(n log n)	O(n log n)	O(n log n)	O(n)	✅ Yes
Quick Sort	O(n log n)	O(n²)	O(n log n)	O(log n)	❌ No
Heap Sort	O(n log n)	O(n log n)	O(n log n)	O(1)	❌ No
Counting Sort	O(n + k)	O(n + k)	O(n + k)	O(n + k)	✅ Yes
Radix Sort	O(nk)	O(nk)	O(nk)	O(n + k)	✅ Yes

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4️⃣ Sorting Algorithm Implementations in C

✅ 1. Bubble Sort (Simple but Inefficient)

Bubble Sort repeatedly swaps adjacent elements if they are in the wrong order.

#include <stdio.h>

void bubbleSort(int arr[], int n) {
    for (int i = 0; i < n - 1; i++) {
        for (int j = 0; j < n - i - 1; j++) {
            if (arr[j] > arr[j + 1]) {
                // Swap
                int temp = arr[j];
                arr[j] = arr[j + 1];
                arr[j + 1] = temp;
            }
        }
    }
}

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

int main() {
    int arr[] = {5, 3, 8, 4, 2};
    int n = sizeof(arr) / sizeof(arr[0]);
    
    bubbleSort(arr, n);
    printf("Sorted array: ");
    printArray(arr, n);
    
    return 0;
}

✅ Simple but slow (O(n²))
❌ Not suitable for large datasets

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✅ 2. Insertion Sort (Efficient for Small Datasets)

Insertion Sort builds a sorted array one item at a time.

#include <stdio.h>

void insertionSort(int arr[], int n) {
    for (int i = 1; i < n; i++) {
        int key = arr[i];
        int j = i - 1;

        while (j >= 0 && arr[j] > key) {
            arr[j + 1] = arr[j];
            j--;
        }
        arr[j + 1] = key;
    }
}

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

int main() {
    int arr[] = {9, 7, 5, 3, 1};
    int n = sizeof(arr) / sizeof(arr[0]);
    
    insertionSort(arr, n);
    printf("Sorted array: ");
    printArray(arr, n);
    
    return 0;
}

✅ Good for small datasets (O(n²))
✅ Performs well when data is nearly sorted

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✅ 3. Merge Sort (Efficient, Uses Divide & Conquer)

Merge Sort divides the array into two halves, sorts them, and merges them.

#include <stdio.h>

void merge(int arr[], int left, int mid, int right) {
    int n1 = mid - left + 1;
    int n2 = right - mid;
    int L[n1], R[n2];

    for (int i = 0; i < n1; i++) L[i] = arr[left + i];
    for (int j = 0; j < n2; j++) R[j] = arr[mid + 1 + j];

    int i = 0, j = 0, k = left;
    while (i < n1 && j < n2) {
        if (L[i] <= R[j]) arr[k++] = L[i++];
        else arr[k++] = R[j++];
    }
    
    while (i < n1) arr[k++] = L[i++];
    while (j < n2) arr[k++] = R[j++];
}

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);
    }
}

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

int main() {
    int arr[] = {12, 11, 13, 5, 6, 7};
    int n = sizeof(arr) / sizeof(arr[0]);

    mergeSort(arr, 0, n - 1);
    printf("Sorted array: ");
    printArray(arr, n);

    return 0;
}

✅ Efficient (O(n log n))
❌ Uses extra memory (O(n))

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✅ 4. Quick Sort (Best for Large Datasets)

Quick Sort picks a pivot, partitions the array, and recursively sorts both halves.

#include <stdio.h>

void swap(int* a, int* b) {
    int temp = *a;
    *a = *b;
    *b = temp;
}

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], &arr[j]);
        }
    }
    swap(&arr[i + 1], &arr[high]);
    return (i + 1);
}

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);
    }
}

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

int main() {
    int arr[] = {10, 7, 8, 9, 1, 5};
    int n = sizeof(arr) / sizeof(arr[0]);

    quickSort(arr, 0, n - 1);
    printf("Sorted array: ");
    printArray(arr, n);

    return 0;
}

✅ Fastest in practice (O(n log n) average case)
❌ Worst-case O(n²) if poorly implemented