Added minimum cost path algorithm (TheAlgorithms#2135)

* Added maximum path sum for matrix (top left to bottom right)

* Changed maximum cost path to minimum cost path + added video explaination

Author: ruppysuppy

dynamic_programming/minimum_cost_path.py

@@ -0,0 +1,37 @@
+# Youtube Explaination: https://www.youtube.com/watch?v=lBRtnuxg-gU
+
+from typing import List
+
+
+def minimum_cost_path(matrix: List[List[int]]) -> int:
+    '''
+    Find the minimum cost traced by all possible paths from top left to bottom right in
+    a given matrix
+
+    >>> minimum_cost_path([[2, 1], [3, 1], [4, 2]])
+    6
+
+    >>> minimum_cost_path([[2, 1, 4], [2, 1, 3], [3, 2, 1]])
+    7
+    '''
+
+    # preprocessing the first row
+    for i in range(1, len(matrix[0])):
+        matrix[0][i] += matrix[0][i - 1]
+
+    # preprocessing the first column
+    for i in range(1, len(matrix)):
+        matrix[i][0] += matrix[i - 1][0]
+
+    # updating the path cost for current position
+    for i in range(1, len(matrix)):
+        for j in range(1, len(matrix[0])):
+            matrix[i][j] += min(matrix[i - 1][j], matrix[i][j - 1])
+
+    return matrix[-1][-1]
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()