Merge pull request himanshu-03#43 from Avdhesh-Varshney/fiboSearch

Fibonacci Searching Algorithm

Author: himanshu-03

Searching Techniques/Fibonacci_Searching.py

@@ -0,0 +1,72 @@
+# Fibonacci searching algorithm only works on the sorted array with time complexity O(log(n)).
+
+# Function to find minimum out of two element
+def min(x, y):
+    return x if x <= y else y
+
+# Returns the index of x if present, else returns -1
+def fibonacciSearch(array, target, n):
+    # If target is greater than last element of the array or smaller than first element of the array
+    if target > array[n-1] or target < array[0]:
+        return -1
+    
+    # Initialize Fibonacci numbers
+    fiboMMm2 = 0  # (m-2)'th Fibonacci No.
+    fiboMMm1 = 1  # (m-1)'th Fibonacci No.
+    fiboM = fiboMMm2 + fiboMMm1  # m'th Fibonacci
+
+    # fiboM is going to store the smallest Fibonacci Number greater than or equal to n
+    while fiboM < n:
+        fiboMMm2, fiboMMm1 = fiboMMm1, fiboM
+        fiboM = fiboMMm2 + fiboMMm1
+
+    # Marks the eliminated range from the front
+    offset = -1
+
+    # While there are elements to be inspected.
+    # Note that we compare array[fiboMm2] with target.
+    # When fiboM becomes 1, fiboMm2 becomes 0
+    while fiboM > 1:
+        # Check if fiboMm2 is a valid location
+        i = min(offset + fiboMMm2, n - 1)
+
+        # If target is greater than the value at index fiboMm2, cut the subarray array from offset to i
+        if array[i] < target:
+            fiboM, fiboMMm1, fiboMMm2 = fiboMMm1, fiboMMm2, fiboM - fiboMMm1
+            offset = i
+
+        # If target is greater than the value at index fiboMm2, cut the subarray after i+1
+        elif array[i] > target:
+            fiboM, fiboMMm1, fiboMMm2 = fiboMMm2, fiboMMm1 - fiboMMm2, fiboM - fiboMMm1
+
+        # Element found, return index
+        else:
+            return i
+
+    # Comparing the last element with target
+    if fiboMMm1 and array[offset + 1] == target:
+        return offset + 1
+
+    # Element not found, return -1
+    return -1
+
+if __name__ == "__main__":
+    n = int(input("\nEnter number of elements in the array: "))
+    array = []
+    print('\n')
+    for i in range(n):
+        array.append(int(input(f"Enter element {i+1}: ")))
+    array.sort()
+    target = int(input("\nEnter target element: "))
+
+    index = fibonacciSearch(array, target, n)
+
+    print('\nEntered elements are: ', end='')
+    for i in range(n):
+        print(array[i], end=' ')
+    print('\n')
+
+    if index != -1:
+        print(f"\n{target} is present at index: {index}\n")
+    else:
+        print(f"\n{target} isn't present in the array.\n")