🚀[Feat]: Adding Fibonacci Search in C++ (HarshCasper#2265)

* 🚀[Feat]:Added Fibonacci Search in C++ * 🚀[Feat]:Adding Fibonacci Search in C++ * ♻️[Refactor]: Formatted the Code * ♻️[Refactor]: Requested Chamges Updated
JanhaviSoni · Mar 8, 2021 · 9a5fc1d · 9a5fc1d
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diff --git a/C-Plus-Plus/README.md b/C-Plus-Plus/README.md
@@ -122,6 +122,7 @@
 - [Randomized Select Search](search/Randomized_Select.cpp)
 - [Staircase Search](search/Staircase_Search.cpp)
 - [Tenary Search](search/TernarySearch.cpp)
+- [Fibonacci Search](search/fibonacci_search.cpp)
 
 ## Sorting
 

diff --git a/C-Plus-Plus/search/fibonacci_search.cpp b/C-Plus-Plus/search/fibonacci_search.cpp
@@ -0,0 +1,114 @@
+/*
+                                              Fibonacci Search
+Search for an element in a Sorted Array
+
+fibonacci series generalisation:
+F(0) = 0
+F(1) = 1
+F(2) = F(1) + F(0) = 0+1 = 1 
+F(n) = F(n-1)+F(n-2) for n>=2
+*/
+
+#include<bits/stdc++.h>
+using namespace std;
+
+int fibonacciSearch(int arr[], int n, int element) {
+   // Initializing fibonacci no 
+   int fibM2 = 0; //(m-2)th fibonacci no.
+   int fibM1 = 1; //(m-1)th fibonacci no. 
+   int fibM = fibM1 + fibM2; //mth fibonacci no.
+
+   /*finding smallest fibonacci no. greater than or equal to 
+     n in Fibonacci sereies and storing it in fibM */
+
+   while (fibM < n) {
+      fibM2 = fibM1;
+      fibM1 = fibM;
+      fibM = fibM1 + fibM2;
+   }
+
+   // to mark range elminated from front 
+   int offset = -1;
+
+   /* until there are elements to be inspected 
+      we compare arr[fibM2] with element when fibM becomes 1 
+      then fibM1 becomes 1 and fibM2 becomes 0 */
+
+   while (fibM > 1) {
+
+      // Check if fibM2 is valid location
+      int i = min(offset + fibM2, n - 1);
+
+      /*
+        when element is greater than value at index fibM2 ,
+        we move 3 fibonacci variable ,1 fibonacci down reset offset to i.
+        we drop approx front 1/3 of remaining array 
+      */
+      if (arr[i] < element) {
+         fibM = fibM1;
+         fibM1 = fibM2;
+         fibM2 = fibM - fibM1;
+         offset = i;
+      }
+      /*
+        when element is less than value at index fibM2 ,
+        we move 3 fibonacci variable ,2 fibonacci down
+        we drop approx rear 2/3 of remaining array 
+      */
+      else if (arr[i] > element) {
+         fibM = fibM2;
+         fibM1 = fibM1 - fibM2;
+         fibM2 = fibM - fibM1;
+      }
+      // if found return index 
+      else return i;
+   }
+   // check for last array element 
+   if (fibM1 && arr[offset + 1] == element)
+      return offset + 1;
+
+   // element not found return -1
+   return -1;
+}
+
+int main() {
+   int n; 
+   cout << "Enter Size Of Arrary:" << "\n";
+   cin >> n;
+
+   int arr[n]; 
+   cout << "Enter Elements In Array" << "\n";
+
+   for (int i = 0; i < n; i++) {
+      cin >> arr[i];
+   }
+
+   int element; 
+   cout << "Enter The Element To Be Searched" << "\n";
+   cin >> element;
+   // Call fibonacci search function 
+   int index = fibonacciSearch(arr, n, element); 
+
+   if (index == -1)
+      cout << "Element Not Found" << "\n"; 
+   else
+      cout << "Element Found At Array Index : " << index; 
+
+   return 0;
+}
+
+/*
+Sample I/O:
+Enter Size Of Arrary:
+5
+Enter Elements In Array
+1 6 10 11 78   
+Enter The Element To Be Searched
+78
+Element Found At Array Index : 4
+
+Algorithm Analysis:
+Time Complexity : O(log(n))
+Auxiliary Space : O(1) 
+
+*/