Adding Sublinear Search Algorithm

searching/sublinear_search.c

@@ -0,0 +1,115 @@
+/**
+ * @file
+ * @brief Program to perform a "sublinear search" of a target
+ * value in a given *sorted* array by skipping elements.
+ * @authors [Your Name] - iterative and recursive algorithms
+ */
+
+#include <assert.h>
+#include <stdio.h>
+#include <math.h>
+
+/** Recursive implementation
+ * \param[in] arr array to search
+ * \param[in] l left index of search range
+ * \param[in] r right index of search range
+ * \param[in] x target value to search for
+ * \param[in] step_size the size of steps to skip in each search iteration
+ * \returns location of x assuming array arr[l..r] is present
+ * \returns -1 otherwise
+ */
+int sublinear_search_recursive(const int *arr, int l, int r, int x, int step_size)
+{
+    if (l > r) {
+        return -1; // Element is not present in array
+    }
+
+    int mid = l + step_size;
+
+    // Check if we've found the element
+    if (mid > r) {
+        return -1; // Exceeded range without finding the element
+    } else if (arr[mid] == x) {
+        return mid; // Element found
+    } else if (arr[mid] > x) {
+        // If element at mid is greater than x, search the remaining part from l to mid - 1
+        return sublinear_search_recursive(arr, l, mid - 1, x, 1);
+    } else {
+        // Else continue with a larger step from mid + step_size to r
+        return sublinear_search_recursive(arr, mid + 1, r, x, step_size);
+    }
+}
+
+/** Iterative implementation
+ * \param[in] arr array to search
+ * \param[in] n length of the array
+ * \param[in] x target value to search for
+ * \param[in] step_size the size of steps to skip in each search iteration
+ * \returns location of x assuming array arr is present
+ * \returns -1 otherwise
+ */
+int sublinear_search_iterative(const int *arr, int n, int x, int step_size)
+{
+    int i = 0;
+
+    // Traverse the array in steps of step_size
+    while (i < n) {
+        // Check if element is found at current position
+        if (arr[i] == x) {
+            return i;
+        }
+        // If the current element is greater than x, do a linear search backwards
+        if (arr[i] > x) {
+            for (int j = i - step_size + 1; j < i; j++) {
+                if (j >= 0 && arr[j] == x) {
+                    return j;
+                }
+            }
+            return -1; // Element not found
+        }
+        // Move to the next step
+        i += step_size;
+    }
+
+    // Check the last block linearly
+    for (int j = i - step_size + 1; j < n; j++) {
+        if (arr[j] == x) {
+            return j;
+        }
+    }
+
+    return -1; // Element is not present in array
+}
+
+/** Test implementations */
+void test()
+{
+    int arr[] = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19};
+    int n = sizeof(arr) / sizeof(arr[0]);
+    int step_size = sqrt(n); // Choosing a step size based on array size
+
+    printf("Test 1.... ");
+    int x = 7;
+    int result = sublinear_search_recursive(arr, 0, n - 1, x, step_size);
+    assert(result == 3);
+    printf("passed recursive... ");
+    result = sublinear_search_iterative(arr, n, x, step_size);
+    assert(result == 3);
+    printf("passed iterative...\n");
+
+    printf("Test 2.... ");
+    x = 8; // Element not in array
+    result = sublinear_search_recursive(arr, 0, n - 1, x, step_size);
+    assert(result == -1);
+    printf("passed recursive... ");
+    result = sublinear_search_iterative(arr, n, x, step_size);
+    assert(result == -1);
+    printf("passed iterative...\n");
+}
+
+/** Main function */
+int main(void)
+{
+    test();
+    return 0;
+}