Merge pull request #364 from ShubhankarKG/branchSkg

Added Fibonacci Search

Author: probot-auto-merge[bot]

Searching and Sorting/Fibonacci Search/fibonacciSearch.c

@@ -0,0 +1,89 @@
+#include <stdio.h>
+
+
+/*
+    Fibonacci Search
+    Coded by ShubhankarKG
+
+    Properties :
+    1. Works with sorted arrays
+    2. A Divide and Conquer ALgorithm
+    3. Has Log n time complexity
+
+*/
+
+// Utility function that returns the minimum of two numbers
+int min(int a, int b){
+    if (a <= b) return a;
+    else return b;
+}
+
+
+/*
+    Main function :
+    parameters :
+    1. Integer Array where element is to be searched
+    2. Integer Element that is to be searched.
+    3. Length of Array (n)
+    
+    Find the fibonacci number just greater than n.
+    Find the two preceding Fibonacci numbers.
+    Scan all the elements in array as follows :
+        a. Compare element with last element of range covered by fib2
+        b. if x matches, return index.
+        c. Else if x is less than the element, move the three Fibonacci variables two Fibonacci down, indicating elimination of
+         approximately rear two-third of the remaining array.
+        d. Else x is greater than the element, move the three Fibonacci variables one Fibonacci down. Reset offset to index. 
+         Together these indicate elimination of approximately front one-third of the remaining array.
+
+    Since there might be a single element remaining for comparison, check if fibMm1 is 1. If Yes, compare x with that remaining element. If match, return index.
+
+*/
+int fibonacciSearch(int arr[], int x, int n){
+    int fib2 = 0;
+    int fib1 = 1;
+    int fibM = fib1 + fib2;
+
+    while(fibM<n){
+        fib2 = fib1;
+        fib1 = fibM;
+        fibM = fib1 + fib2;
+    }
+
+    int offset = -1;
+
+    while(fibM > 1){
+        int i = min(offset + fib2 , n-1);
+
+        if (arr[i]<x){
+            fibM = fib1;
+            fib1 = fib2;
+            fib2 = fibM - fib1;
+            offset = i;
+        }
+
+        else if (arr[i]>x){
+            fibM = fib2;
+            fib1 = fib1 - fib2;
+            fib2 = fibM - fib1;
+        }
+
+        else return i;
+    }
+
+    if (fib1 && arr[offset+1] == x) return (offset+1);
+
+    return -1;
+}
+
+/* Driver code to check search
+
+int main(){
+    int arr[] = {1,2,3,4,5,6,7,8,9,11, 12,13};
+    int n = sizeof(arr)/sizeof(arr[1]);
+    int x = 6;
+    printf("Element found at index %d", fibonacciSearch(arr,x,n));
+    return 0;
+}
+
+*/