Searching_and_Sorting_Algorithms_in_C.pptx

Searching_and_Sorting_Algorithms_in_C.pptx

• 1.
  Searching and SortingAlgorithms in C Linear Search, Binary Search, Insertion Sort, and Bubble Sort For B.Tech Students, IIT (BHU)
• 2.
  Linear Search -Introduction • Linear search scans each element in a list sequentially until the target element is found. • Works on both sorted and unsorted lists. • Simple but inefficient for large datasets.
• 3.
  Linear Search -Flowchart • Start → Input array & key → For each element → If element == key → Print Found → Stop → Else continue → End
• 4.
  Linear Search -C Program • #include <stdio.h> • int main() { • int arr[5] = {10, 20, 30, 40, 50}; • int key = 30, i, found = 0; • for(i=0; i<5; i++) { • if(arr[i] == key) { • printf("Element found at index %d", i); • found = 1; • break; • } • } • if(!found) printf("Element not found"); • return 0; • }
• 5.
  Linear Search -Complexity • Best Case: O(1) • Worst Case: O(n) • Average Case: O(n) • Space Complexity: O(1)
• 6.
  Binary Search -Introduction • Works on sorted arrays only. • Repeatedly divides the search interval in half. • More efficient than linear search.
• 7.
  Binary Search -Flowchart • Start → Set low=0, high=n-1 → while(low<=high): mid=(low+high)/2 → If arr[mid]==key → Found → Else adjust low/high → End
• 8.
  Binary Search -C Program • #include <stdio.h> • int main() { • int arr[] = {10, 20, 30, 40, 50}; • int low = 0, high = 4, key = 30, mid; • while(low <= high) { • mid = (low + high) / 2; • if(arr[mid] == key) { • printf("Element found at index %d", mid); • return 0; • } else if(arr[mid] < key) • low = mid + 1; • else • high = mid - 1; • } • printf("Element not found"); • return 0;
• 9.
  Binary Search -Complexity • Best Case: O(1) • Worst Case: O(log n) • Average Case: O(log n) • Space Complexity: O(1)
• 10.
  Insertion Sort -Introduction • Builds the sorted array one item at a time. • Good for small datasets. • Works similar to sorting playing cards in hand.
• 11.
  Insertion Sort -Flowchart • Start → Loop from 1 to n → Pick key = arr[i] → Compare with left side → Shift elements → Insert key → Repeat → End
• 12.
  Insertion Sort -C Program • #include <stdio.h> • int main() { • int arr[] = {5, 2, 4, 6, 1, 3}; • int n = 6, i, j, key; • for(i = 1; i < n; i++) { • key = arr[i]; • j = i - 1; • while(j >= 0 && arr[j] > key) { • arr[j + 1] = arr[j]; • j = j - 1; • } • arr[j + 1] = key; • } • for(i = 0; i < n; i++) printf("%d ", arr[i]); • return 0; • }
• 13.
  Insertion Sort -Complexity • Best Case: O(n) • Worst Case: O(n²) • Average Case: O(n²) • Space Complexity: O(1)
• 14.
  Bubble Sort -Introduction • • Repeatedly swaps adjacent elements if they are in wrong order. • • Largest element bubbles to the end after each pass.
• 15.
  Bubble Sort -Flowchart • Start → Outer loop i=0 to n-1 → Inner loop j=0 to n-i-1 → If arr[j]>arr[j+1] swap → Repeat → End
• 16.
  Bubble Sort -C Program • #include <stdio.h> • int main() { • int arr[] = {64, 34, 25, 12, 22, 11, 90}; • int n = 7, i, j, temp; • for(i = 0; i < n-1; i++) { • for(j = 0; j < n-i-1; j++) { • if(arr[j] > arr[j+1]) { • temp = arr[j]; • arr[j] = arr[j+1]; • arr[j+1] = temp; • } • } • } • for(i = 0; i < n; i++) printf("%d ", arr[i]); • return 0; • }
• 17.
  Bubble Sort -Complexity • Best Case: O(n) • Worst Case: O(n²) • Average Case: O(n²) • Space Complexity: O(1)
• 18.
  Comparison of Algorithms •Linear Search: O(n) • Binary Search: O(log n) • Insertion Sort: O(n²) • Bubble Sort: O(n²) • Binary Search is faster for large sorted data. • Insertion Sort often outperforms Bubble Sort for small datasets.
• 19.
  Summary • Searching andsorting are core algorithmic operations. • Linear and Binary Search differ in efficiency and precondition (sorted data). • Insertion and Bubble Sort are simple but not efficient for large datasets. • Useful for understanding basic algorithm design and complexity.