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.
- code better dp
class Solution:
def minPathSum(self, grid):
m = len(grid)
n = len(grid[0])
for i in range(1, n):
grid[0][i] += grid[0][i-1]
for i in range(1, m):
grid[i][0] += grid[i-1][0]
for i in range(1, m):
for j in range(1, n):
grid[i][j] += min(grid[i-1][j], grid[i][j-1])
return grid[-1][-1]
- code naive dp
class Solution:
def minPathSum(self, grid: List[List[int]]) -> int:
m, n = len(grid), len(grid[0])
path = {(0,0):grid[0][0]}
for x in range(m):
for y in range(n):
if x == 0 and y == 0: continue
if x == 0:
path[(x, y)] = path[(x, y-1)] + grid[x][y]
elif y == 0:
path[(x, y)] = path[(x-1, y)] + grid[x][y]
else:
path[(x, y)] = min(path[(x, y-1)], path[(x-1, y)]) + grid[x][y]
return path[(m-1, n-1)]