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 1:
Input: grid = [[1,3,1],[1,5,1],[4,2,1]]
Output: 7
Explanation: Because the path 1 → 3 → 1 → 1 → 1 minimizes the sum.
Example 2:
Input: grid = [[1,2,3],[4,5,6]]
Output: 12
Constraints:
-
m == grid.length -
n == grid[i].length -
1 <= m, n <= 200 -
0 <= grid[i][j] <= 100
SOLUTION:
class Solution:
def calcMin(self, grid, x, y, m, n):
if (x, y) in self.cache:
return self.cache[(x, y)]
if (x, y) == (m - 1, n - 1):
self.cache[(x, y)] = grid[m - 1][n - 1]
return self.cache[(x, y)]
right = float('inf')
bottom = float('inf')
if y < n - 1:
right = self.calcMin(grid, x, y + 1, m, n)
if x < m - 1:
bottom = self.calcMin(grid, x + 1, y, m, n)
currMin = min(right, bottom)
self.cache[(x, y)] = grid[x][y] + currMin
return self.cache[(x, y)]
def minPathSum(self, grid: List[List[int]]) -> int:
self.cache = {}
return self.calcMin(grid, 0, 0, len(grid), len(grid[0]))
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