From 73ebec674a7cbfb5aab145074ea41a724a1e3010 Mon Sep 17 00:00:00 2001
From: Sakshi Sharma <45708920+sakshi1717@users.noreply.github.com>
Date: Sat, 2 Oct 2021 07:15:24 -0700
Subject: [PATCH] Create MinimumPathSum.py

Fixes#4796
SA-Matrix-Python- Minimum Path sum #4796

This code implements a dynamic program to find the minimum cost to reach the bottom rightmost corner of the grid.
It has been implemented with the best time & space complexity
---
 data_structures/MinimumPathSum.py | 47 +++++++++++++++++++++++++++++++
 1 file changed, 47 insertions(+)
 create mode 100644 data_structures/MinimumPathSum.py

diff --git a/data_structures/MinimumPathSum.py b/data_structures/MinimumPathSum.py
new file mode 100644
index 000000000000..e31455e1ad9f
--- /dev/null
+++ b/data_structures/MinimumPathSum.py
@@ -0,0 +1,47 @@
+def findPath( arr , rows, cols):
+    #iterating the whole grid
+
+    """
+    since only two movements are allowed right and down. To arrive at a particular cell
+    we can either comes from left cell(by taking right step) or
+    from top cell (by taking  down step)
+    """
+    for r in range(rows):
+        for c in range(cols):
+            option1, option2 =None, None
+
+            #option1 is when minimum path sum to arr[r][c] comes from left
+            if(c-1>=0):
+                option1= arr[r][c-1]
+            #option2 is when minimum path sum to arr[r][c] comes from top
+            if(r-1>=0):
+                option2= arr[r-1][c]
+
+            if(option1==None and option1==None):
+                continue
+            if(option1!=None and option2!=None):
+                arr[r][c]= min(option1, option2) +arr[r][c]
+            elif(option1!= None):
+                arr[r][c]= option1+ arr[r][c]
+            else:
+                arr[r][c]= option2+ arr[r][c]
+
+    return(arr[rows-1][cols-1])
+
+#defining the grid matrix
+grid= [[1,3,1],[1,5,1],[4,2,1]]
+#number of rows
+rows=len(grid)
+#number of columns
+cols=len(grid[0])
+
+if(rows==0 or cols==0):
+  print("please give a valid input")
+else:
+  print( findPath( grid, rows, cols));
+
+
+"""
+Time complexity for this algorithm is O(n^2) , since we are traversing the grid.
+Space complexity is O(1), since we are not using any extra space.
+"""