Added Optimal Merge Pattern Algorithm (#5274)

* Minor changes due to precommit

* Update optimal_merge_pattern.py

Co-authored-by: Christian Clauss <cclauss@me.com>

greedy_methods/optimal_merge_pattern.py

@@ -0,0 +1,56 @@
+"""
+This is a pure Python implementation of the greedy-merge-sort algorithm
+reference: https://www.geeksforgeeks.org/optimal-file-merge-patterns/
+
+For doctests run following command:
+python3 -m doctest -v greedy_merge_sort.py
+
+Objective
+Merge a set of sorted files of different length into a single sorted file.
+We need to find an optimal solution, where the resultant file
+will be generated in minimum time.
+
+Approach
+If the number of sorted files are given, there are many ways
+to merge them into a single sorted file.
+This merge can be performed pair wise.
+To merge a m-record file and a n-record file requires possibly m+n record moves
+the optimal choice being,
+merge the two smallest files together at each step (greedy approach).
+"""
+
+
+def optimal_merge_pattern(files: list) -> float:
+    """Function to merge all the files with optimum cost
+
+    Args:
+        files [list]: A list of sizes of different files to be merged
+
+    Returns:
+        optimal_merge_cost [int]: Optimal cost to merge all those files
+
+    Examples:
+    >>> optimal_merge_pattern([2, 3, 4])
+    14
+    >>> optimal_merge_pattern([5, 10, 20, 30, 30])
+    205
+    >>> optimal_merge_pattern([8, 8, 8, 8, 8])
+    96
+    """
+    optimal_merge_cost = 0
+    while len(files) > 1:
+        temp = 0
+        # Consider two files with minimum cost to be merged
+        for i in range(2):
+            min_index = files.index(min(files))
+            temp += files[min_index]
+            files.pop(min_index)
+        files.append(temp)
+        optimal_merge_cost += temp
+    return optimal_merge_cost
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()