add Meta binary search (aka one.sided search

meta_binary.py

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+# Python implementation of Meta binary search algorithm.
+# Meta binary search is a modified form of binary search
+# that incrementally constructs the index of the target value
+# in the array. Like normal binary search, meta binary search
+# takes O(log n) time. This algorithm is designed to reduce
+# the number of comparisons needed to search the list for
+# a given element. The basic idea behind Meta binary search is
+# to start with an initial interval of size n that included the
+# entire array. The algorithm then computes a middle element and
+# compares it to the target element. If the target is found, the
+# search terminates. If the middle element is greater than the
+#target element, the algorithm sets the new interval to the left
+# half of the previous interval, and if the middle element is less
+#than the target element, the new interval is set to the right half
+# of the previous interval. However, unlike binary search, Meta
+# binary search does not perform a comparison for each iteration
+# of the loop.
+#
+# Instead the algorithm uses a heuristic to determine the size of
+# the next interval. it computes the difference between the value of 
+# the middle element and the value of the target element, and divides
+# the difference by a predetermined constant, usually 2. The result is
+# then used as the size of the new interval.
+# See <https://www.quora.com/What-is-meta-binary-search> for more
+# detail with examples. 
+
+# Function to show the working
+# of Meta binary search
+import math
+def bsearch(A, key_to_search):
+
+	n = len(A)
+	# Set number of bits to represent
+	lg = int(math.log2(n-1)) + 1;
+
+	# largest array index
+	#while ((1 << lg) < n - 1):
+		#lg += 1
+
+	pos = 0
+	for i in range(lg - 1, -1, -1) :
+		if (A[pos] == key_to_search):
+			return pos
+
+		# Incrementally construct the
+		# index of the target value
+		new_pos = pos | (1 << i)
+
+		# find the element in one
+		# direction and update position
+		if ((new_pos < n) and
+			(A[new_pos] <= key_to_search)):
+			pos = new_pos
+
+	# if element found return
+	# pos otherwise -1
+	return (pos if(A[pos] == key_to_search) else -1)
+
+# Driver code
+if __name__ == "__main__":
+
+	A = [ -2, 10, 100, 250, 32315 ]
+	print( bsearch(A, 10))
+
+