Create fibonacci_search.py

Searching Algorithms/fibonacci_search.py

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+'''
+Fibonacci Search is a comparison-based technique 
+that uses Fibonacci numbers to search an element in a sorted array.
+'''
+def fibonacci_search(arr, val):
+    # Initialize fibonacci numbers  
+    fib_N_2 = 0 # (m-2)'th Fibonacci No
+    fib_N_1 = 1 # (m-1)'th Fibonacci No.
+    fibNext = fib_N_1 + fib_N_2 # m'th Fibonacci 
+
+    length = len(arr)
+    if length == 0:
+        return 0
+
+    # fibNext is going to store the smallest  
+    # Fibonacci Number greater than or equal to array's length  
+    while fibNext < len(arr):
+        fib_N_2 = fib_N_1
+        fib_N_1 = fibNext
+        fibNext = fib_N_1 + fib_N_2
+
+    # Marks the eliminated range from front
+    index = -1
+
+    # while there are elements to be inspected. 
+    # Note that we compare arr[fib_N_2] with x. 
+    # When fibNext becomes 1, fib_N_2 becomes 0 
+    while fibNext > 1:
+
+        # Check if fib_N_2 is a valid location 
+        i = min(index + fib_N_2, (length - 1))
+
+        if arr[i] < val:
+            fibNext = fib_N_1
+            fib_N_1 = fib_N_2
+            fib_N_2 = fibNext - fib_N_1
+            index = i
+        elif arr[i] > val:
+            fibNext = fib_N_2
+            fib_N_1 = fib_N_1 - fib_N_2
+            fib_N_2 = fibNext - fib_N_1
+        else:
+            return i
+
+    # comparing the last element with x */        
+    if (fib_N_1 and index < length - 1) and (arr[index + 1] == val):
+        return index + 1
+
+    # element not found. return -1
+    return -1