原题
给定一个只含非负整数的m*n网格，找到一条从左上角到右下角的可以使数字和最小的路径。
你在同一时间只能向下或者向右移动一步
解题思路
- 矩阵型动态规划 - Matrix DP
- 与Unique Paths I/II非常类似，不同的是每次要找最小value
- cache[i][j]表示从左上角到达i,j的数字和最小路径，它等于cache[i][j - 1]与cache[i - 1][j]的最小值，加上grid[i][j]的值
完整代码
class Solution(object):
def minPathSum(self, grid):
"""
:type grid: List[List[int]]
:rtype: int
"""
if not grid or not grid[0]:
return 0
m = len(grid)
n = len(grid[0])
cache = [[0 for i in range(n)] for j in range(m)]
sum1 = sum2 = 0
for i in range(n):
sum1 += grid[0][i]
cache[0][i] = sum1
for j in range(m):
sum2 += grid[j][0]
cache[j][0] = sum2
for i in range(1, n):
for j in range(1, m):
cache[j][i] = min(cache[j - 1][i], cache[j][i - 1]) + grid[j][i]
return cache[m - 1][n - 1]
