Added Binary Search algorithm

SearchingAlgorithms/binary_search.py

@@ -0,0 +1,51 @@
+'''
+Python 3
+
+Binary search is a really effective search algorithm that requires the searched array to be sorted.
+The basic idea is that we all the time split our array in half, and determine which half our wanted item
+is located. This way, we continuously cut the area we search in half, and in the end, we will have found our
+item.
+'''
+
+def binary_search(needle, haystack, low = 0, high = None):
+    '''
+    Searches for the needle using the binary search algorithm.
+    This is a recursive implementation.
+    :param needle: The item we want to locate
+    :param haystack: The array in which we want to search for the needle
+    :param low: The lower limit of where in the haystack we want to search.
+    :param high: The upper limit of where in the haystack we want to search.
+    :return: The index of the needle in the haystack, or -1 if it is not present
+    '''
+
+    # If no value for high is specified, we should search until the end of the array
+    if high == None:
+        high = len(haystack)
+
+    # If the high limit is lower than the low, the haystack does not contain the needle
+    if high < low:
+        return -1
+
+    # We calculate the mid point of our array (rounding it to closest integer)
+    mid = int((low + high) / 2)
+
+    if haystack[mid] > needle:
+        # If the middle element is higher than the needle, we need to search the lower half of the haystack
+        return binary_search(needle, haystack, low, mid - 1)
+    elif haystack[mid] < needle:
+        # If the middle element is lower than the needle, we need to search the upper half of the haystack
+        return binary_search(needle, haystack, mid + 1, high)
+    else:
+        # If the middle element is neither lower or higher than the needle, the needle is located in the mid position
+        return mid
+
+if __name__ == '__main__':
+    needle = 3
+    haystack = [0, 1, 2, 3, 4, 5, 6, 7]
+    index = binary_search(needle, haystack)
+    print('The result for needle', needle, 'in haystack', haystack, 'is', index)
+
+    needle = 0
+    haystack = [1, 2, 3, 4, 5, 6, 7]
+    index = binary_search(needle, haystack)
+    print('The result for needle', needle, 'in haystack', haystack, 'is', index)