day_18.py

'''
Problem Statement:
Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.

Note: You can only move either down or right at any point in time.

Example:

Input:
[
  [1,3,1],
  [1,5,1],
  [4,2,1]
]
Output: 7
Explanation: Because the path 1→3→1→1→1 minimizes the sum.
'''

#Solution:

class Solution:
    def minPathSum(self, grid: List[List[int]]) -> int:
        if len(grid) <= 0 or grid is None:
            return 0
        rows = len(grid)
        cols = len(grid[0])
        
        for r in range(rows):
            for c in range(cols):
                if r==0 and c==0: # We just want to skip the top-left corner of the grid
                    continue
                if r-1<0: # Cases for elements in top row
                    grid[r][c] = grid[r][c] + grid[r][c-1]  
                elif c-1<0: # Cases for elements in leftmost column
                    grid[r][c] = grid[r][c] + grid[r-1][c]  
                else: # Normal cell
                    grid[r][c] = grid[r][c] + min(grid[r-1][c], grid[r][c-1])               
        
        return grid[rows-1][cols-1] # We have got the minimum path accumaled at the bottom-right corner, just return this