Merge pull request #1595 from Subashree-selvaraj/librarysort

Added library sort

Sorting Algorithms/Library Sort/Program.c

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+#include <stdio.h>
+#include <stdlib.h>
+
+// Function to insert an element into the sorted array with gaps
+void insert(int arr[], int *size, int element) {
+    int i = *size - 1;
+    while (i >= 0 && arr[i] > element) {
+        arr[i + 1] = arr[i];
+        i--;
+    }
+    arr[i + 1] = element;
+    (*size)++;
+}
+
+// Function to perform library sort
+void library_sort(int arr[], int n) {
+    int *sorted = (int *)malloc(2 * n * sizeof(int));
+    int size = 0;
+
+    for (int i = 0; i < n; i++) {
+        insert(sorted, &size, arr[i]);
+    }
+
+    for (int i = 0; i < n; i++) {
+        arr[i] = sorted[i];
+    }
+
+    free(sorted);
+}
+
+// Function to print array
+void print_array(int arr[], int n) {
+    for (int i = 0; i < n; i++) {
+        printf("%d ", arr[i]);
+    }
+    printf("\n");
+}
+
+int main() {
+    int arr[] = {78, 650, 100, 21, 23, 12, 90, 0};
+    int n = sizeof(arr) / sizeof(arr[0]);
+
+    printf("Original array:\n");
+    print_array(arr, n);
+
+    library_sort(arr, n);
+
+    printf("Sorted array:\n");
+    print_array(arr, n);
+
+    return 0;
+}

Sorting Algorithms/Library Sort/README.md

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+# Library Sort
+
+## Description
+
+Library Sort is a sorting algorithm that is a variant of insertion sort. It maintains a sorted array with gaps to allow for efficient insertion of new elements. This algorithm is also known as gapped insertion sort.
+
+## Problem Definition
+
+Given:
+- An array `arr` of `n` elements.
+
+Objectives:
+- Sort an array in ascending order using library sort.
+
+## Algorithm Overview
+
+1. **Initialize**: Start with an empty sorted array with gaps.
+2. **Insert**: For each element in the input array, find the correct position in the sorted array and insert it, shifting elements as necessary.
+3. **Rebalance**: Periodically rebalance the array to maintain gaps for efficient insertion.
+
+## Time Complexity
+
+The time complexity of Library Sort is `O(n log n)` on average, but it can degrade to `O(n^2)` in the worst case if the gaps are not managed properly. It is efficient for datasets where insertions are frequent and the array needs to remain sorted.