From 5d962a6f5402b34b83c36d4a6121c130a64654d3 Mon Sep 17 00:00:00 2001
From: Luiz Felipe Schulz Coria <luizschulz2004@gmail.com>
Date: Wed, 13 Nov 2024 21:22:08 -0300
Subject: [PATCH] Create quadratic_search.c

---
 searching/quadratic_search.c | 102 +++++++++++++++++++++++++++++++++++
 1 file changed, 102 insertions(+)
 create mode 100644 searching/quadratic_search.c

diff --git a/searching/quadratic_search.c b/searching/quadratic_search.c
new file mode 100644
index 00000000..954a98cd
--- /dev/null
+++ b/searching/quadratic_search.c
@@ -0,0 +1,102 @@
+/**
+ * @file
+ * @brief Program to perform a "quadratic search" of a target
+ * value in a given *sorted* array.
+ * @authors [Your Name] - recursive and iterative algorithms
+ */
+
+#include <assert.h>
+#include <stdio.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
+ * \returns location of x assuming array arr[l..r] is present
+ * \returns -1 otherwise
+ */
+int quadratic_search_recursive(const int *arr, int l, int r, int x)
+{
+    if (r >= l)
+    {
+        // Calculate "midpoint" using a quadratic function
+        int mid = l + ((r - l) * (r - l)) / ((r - l + 1) * (r - l + 1));
+
+        // Check if element is present at the midpoint
+        if (arr[mid] == x)
+            return mid;
+
+        // If the element is smaller than arr[mid], search in the left subarray
+        if (arr[mid] > x)
+            return quadratic_search_recursive(arr, l, mid - 1, x);
+
+        // Otherwise, search in the right subarray
+        return quadratic_search_recursive(arr, mid + 1, r, x);
+    }
+
+    // Element is not present in the array
+    return -1;
+}
+
+/** Iterative 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
+ * \returns location of x assuming array arr[l..r] is present
+ * \returns -1 otherwise
+ */
+int quadratic_search_iterative(const int *arr, int l, int r, int x)
+{
+    while (l <= r)
+    {
+        // Calculate "midpoint" using a quadratic function
+        int mid = l + ((r - l) * (r - l)) / ((r - l + 1) * (r - l + 1));
+
+        // Check if element is present at the midpoint
+        if (arr[mid] == x)
+            return mid;
+
+        // If the element is smaller than arr[mid], search in the left subarray
+        if (arr[mid] > x)
+            r = mid - 1;
+        else // Otherwise, search in the right subarray
+            l = mid + 1;
+    }
+
+    // Element is not present in the array
+    return -1;
+}
+
+/** Test implementations */
+void test()
+{
+    int arr[] = {2, 3, 4, 10, 40};
+    int n = sizeof(arr) / sizeof(arr[0]);
+
+    printf("Test 1.... ");
+    int x = 10;
+    int result = quadratic_search_recursive(arr, 0, n - 1, x);
+    assert(result == 3);
+    printf("passed recursive... ");
+    result = quadratic_search_iterative(arr, 0, n - 1, x);
+    assert(result == 3);
+    printf("passed iterative...\n");
+
+    printf("Test 2.... ");
+    x = 5;
+    result = quadratic_search_recursive(arr, 0, n - 1, x);
+    assert(result == -1);
+    printf("passed recursive... ");
+    result = quadratic_search_iterative(arr, 0, n - 1, x);
+    assert(result == -1);
+    printf("passed iterative...\n");
+}
+
+/** Main function */
+int main(void)
+{
+    test();
+    return 0;
+}