feat: Add floyd cycle-detection-algorithm to find duplicate number (#844)

* floyd algorithm application

* Update searching/floyd_cycle_detection_algorithm.c

Co-authored-by: David Leal <halfpacho@gmail.com>

* updating DIRECTORY.md

* Update searching/floyd_cycle_detection_algorithm.c

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update searching/floyd_cycle_detection_algorithm.c

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update searching/floyd_cycle_detection_algorithm.c

Co-authored-by: David Leal <halfpacho@gmail.com>

* minor correction

* Update searching/floyd_cycle_detection_algorithm.c

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update searching/floyd_cycle_detection_algorithm.c

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update searching/floyd_cycle_detection_algorithm.c

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update searching/floyd_cycle_detection_algorithm.c

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update searching/floyd_cycle_detection_algorithm.c

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update searching/floyd_cycle_detection_algorithm.c

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update floyd_cycle_detection_algorithm.c

* Update searching/floyd_cycle_detection_algorithm.c

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update searching/floyd_cycle_detection_algorithm.c

Co-authored-by: Abhinn Mishra <49574460+mishraabhinn@users.noreply.github.com>

Co-authored-by: David Leal <halfpacho@gmail.com>
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Abhinn Mishra <49574460+mishraabhinn@users.noreply.github.com>

DIRECTORY.md

@@ -355,6 +355,7 @@
   * [Binary Search](https://github.com/TheAlgorithms/C/blob/master/searching/binary_search.c)
   * [Exponential Search](https://github.com/TheAlgorithms/C/blob/master/searching/exponential_search.c)
   * [Fibonacci Search](https://github.com/TheAlgorithms/C/blob/master/searching/fibonacci_search.c)
+  * [Floyd Cycle Detection Algorithm](https://github.com/TheAlgorithms/C/blob/master/searching/floyd_cycle_detection_algorithm.c)
   * [Interpolation Search](https://github.com/TheAlgorithms/C/blob/master/searching/interpolation_search.c)
   * [Jump Search](https://github.com/TheAlgorithms/C/blob/master/searching/jump_search.c)
   * [Linear Search](https://github.com/TheAlgorithms/C/blob/master/searching/linear_search.c)

searching/floyd_cycle_detection_algorithm.c

@@ -0,0 +1,68 @@
+/**
+ * @file
+ * @brief Implementation of [Floyd's Cycle
+ * Detection](https://en.wikipedia.org/wiki/Cycle_detection) algorithm
+ * @details
+ * Given an array of integers containing `n + 1` integers, where each
+ * integer is in the range [1, n] inclusive. If there is only one duplicate
+ * number in the input array, this algorithm returns the duplicate number in
+ * O(1) space and the time complexity is less than O(n^2) without modifying the
+ * original array, otherwise, it returns -1.
+ * @author [Swastika Gupta](https://github.com/Swastyy)
+ */
+ 
+#include <assert.h>   /// for assert
+#include <inttypes.h> /// for uint32_t
+#include <stdio.h>    /// for IO operations
+
+/**
+ * @brief The main function implements the search algorithm
+ * @tparam T type of array
+ * @param in_arr the input array
+ * @param n size of the array
+ * @returns the duplicate number
+ */
+uint32_t duplicateNumber(const uint32_t *in_arr, size_t n)
+{
+    if (n <= 1) {  // to find duplicate in an array its size should be atleast 2
+        return -1;
+    }
+    uint32_t tortoise = in_arr[0];  ///< variable tortoise is used for the longer
+                                    ///< jumps in the array
+    uint32_t hare = in_arr[0];  ///< variable hare is used for shorter jumps in the array
+    do {                                   // loop to enter the cycle
+        tortoise = in_arr[tortoise];       // tortoise is moving by one step
+        hare = in_arr[in_arr[hare]];       // hare is moving by two steps
+    } while (tortoise != hare);
+    tortoise = in_arr[0];
+    while (tortoise != hare) {             // loop to find the entry point of cycle
+        tortoise = in_arr[tortoise];
+        hare = in_arr[hare];
+    }
+    return tortoise;
+}
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void test()
+{
+    uint32_t arr[] = {1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610}; // input array
+    size_t n = sizeof(arr) / sizeof(int);
+
+    printf("1st test... ");
+    uint32_t index = duplicateNumber(arr, n); // calling the duplicateNumber function to check which number occurs twice in the array
+    assert(index == 1); // the number which occurs twice is 1 or not
+    printf("passed\n");
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main()
+{
+    test();  // run self-test implementations
+    return 0;
+}