added median of medians algorithms for searching

Author: coderbeta1

Diff for: searches/median_of_medians.py

@@ -0,0 +1,78 @@
+"""
+A Python implementation of the Median of Medians algorithm to select pivots for QuickSelect,
+which is efficient for calculating the value that would appear in the index of a list if it
+would be sorted, even if it is not already sorted. Search in time complexity O(n) at any rank
+deterministically
+https://en.wikipedia.org/wiki/Median_of_medians
+"""
+
+def MedianofFive(arr:list) -> int:
+    """
+    Return the median of the input list
+    :param arr: Array to find median of
+    :return: median of arr
+    """
+    arr=sorted(arr)
+    return arr[len(arr)//2]
+
+def MedianofMedians(arr:list) -> int:
+    """
+    Return a pivot to partition data on by calculating
+    Median of medians of input data
+    :param arr: The data to be sorted (a list)
+    :param k: The rank to be searched
+    :return: element at rank k
+    """
+    if len(arr) <= 5:        return MedianofFive(arr)
+    medians = []
+    i=0
+    while i<len(arr):
+        if (i + 4) <= len(arr):            medians.append(MedianofFive(arr[i:].copy()))
+        else:                              medians.append(MedianofFive(arr[i:i+5].copy()))
+        i+=5
+    return MedianofMedians(medians)
+
+def QuickSelect(arr:list, k:int) -> int:
+    """
+    >>> QuickSelect([2, 4, 5, 7, 899, 54, 32], 5)
+    32
+    >>> QuickSelect([2, 4, 5, 7, 899, 54, 32], 1)
+    2
+    >>> QuickSelect([5, 4, 3, 2], 2)
+    3
+    >>> QuickSelect([3, 5, 7, 10, 2, 12], 3)
+    5
+    """
+
+    """
+    Two way partition the data into smaller and greater lists,
+    in relationship to the pivot
+    :param arr: The data to be sorted (a list)
+    :param k: The rank to be searched
+    :return: element at rank k
+    """
+
+    # Invalid Input
+    if k>len(arr):
+        return None
+
+    # x is the estimated pivot by median of medians algorithm
+    x = MedianofMedians(arr)
+    left = []
+    right = []
+    check = False
+    smaller = 0
+    for i in range(len(arr)):
+        if arr[i] < x:
+            left.append(arr[i])
+        elif arr[i] > x:
+            right.append(arr[i])
+        elif arr[i] == x and not check:
+            check = True
+        else:
+            right.append(arr[i])
+    rankX = len(left) + 1
+    if(rankX==k):        answer = x
+    elif rankX>k:        answer = QuickSelect(left,k)
+    elif rankX<k:        answer = QuickSelect(right,k-rankX)
+    return answer;