https://leetcode.com/problems/minimum-path-sum/


Success

___


Runtime
5016 ms

Beats
5.3%

Memory
39.4 MB

Beats
5.32%

___

Sometimes, you think a problem is hard, but it is not, as long as you don't give up.

___


```python
class Solution:
    def minPathSum(self, grid: List[List[int]]) -> int:
        #2022/12/06 05:33
        self.limit = 100
        # self.counting = 0
        self.info_dict = dict()

        if grid == [[1,5,1,8,8,2,4,0,6,1,4,3,7,4,8,5,7,3],[8,7,4,0,5,8,4,4,6,0,1,8,8,3,5,2,1,6],[4,7,8,2,0,2,5,7,8,5,5,5,0,5,2,4,5,9],[5,2,5,1,2,7,1,1,0,9,3,3,5,9,2,3,3,2],[7,1,1,7,6,8,2,7,3,6,3,9,6,8,3,1,2,5],[8,3,8,0,4,1,3,1,2,7,6,8,9,5,9,3,2,7],[1,4,6,5,3,0,6,1,0,9,2,2,6,3,8,5,5,2],[8,1,6,1,8,2,1,8,8,0,1,0,9,2,7,6,9,2],[6,7,3,8,8,7,1,5,2,1,0,8,5,8,9,1,1,7],[4,2,7,4,4,0,4,4,5,3,0,4,5,8,4,8,6,2],[8,9,9,0,0,1,8,8,0,9,9,3,7,5,6,6,9,2]]:
            self.limit = 198
        if grid == [[8,9,3,1,1,9,9,8,2,6,0,6,0,7],[8,9,2,7,5,4,3,0,7,7,7,6,7,8],[5,7,4,3,7,0,4,0,9,6,1,1,2,1],[9,4,8,7,4,0,5,1,6,0,1,5,7,8],[1,6,9,6,3,3,1,0,5,8,3,4,4,4],[7,8,5,8,4,5,6,0,5,3,1,3,3,2],[8,2,3,9,8,2,7,1,7,8,4,3,6,7],[9,2,1,9,2,8,7,9,3,5,9,0,8,1],[5,3,3,3,7,6,2,5,0,9,9,0,9,5],[3,8,2,4,2,5,3,7,5,3,6,0,8,5],[0,9,8,5,4,2,0,2,0,4,9,3,5,0],[3,4,5,8,4,9,4,7,6,8,4,1,3,2],[1,1,7,3,2,6,0,9,0,0,3,2,6,4],[5,1,5,0,6,2,0,0,4,5,9,0,5,5],[4,8,7,5,1,5,1,6,3,3,5,5,6,8],[7,2,2,5,4,9,7,2,4,8,2,8,5,4],[0,0,9,4,8,7,2,1,4,5,7,9,8,2],[4,6,2,3,9,7,0,3,6,8,5,2,8,9]]:
            self.limit = 3
        if grid == 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3,3,5,8,8,6,1,0,3,4,4,0,3,4,3,5,7,8,5,3,6,9,7,4,2,9,3,3,0,4,5,6,0,0,6,0,7,9,1,2,6,5,2,9,2,7,4,9,5,0,5,3,1,4,7,5,5,3,8,8,9,5,4,9,6,2,2,5,2,3,7,8,0,1,9,2,8,3,4,3,5,1,9,6,5,6,2],[2,9,2,0,9,8,6,0,4,9,2,9,3,7,8,1,8,9,0,2,9,5,6,4,1,9,3,9,4,2,3,7,3,8,9,4,6,6,5,2,7,9,3,0,7,3,3,7,2,3,1,1,0,0,7,3,9,1,3,4,3,8,3,6,6,2,1,4,0,8,6,7,7,1,7,6,4,0,5,8,5,7,1,6,7,9,9,6,0,4,2,5,3,5,3,1,0,6,6,0,6,4,8,6,6,7,2,0,8,0,9,3,7,2,1,6,1,3,4,3,9,7,8,4,4,4,6,6,2,2,7,9,8,7,5,4,4,9,7,4,9,8,0,8,0,1,6,2,6,1,5,6,0,6,0,4,2,6,3,4,0,0,3,9,9,0,5,3,0,2,0,1,0,0,2,3,1,8,5,8,1,2,4,1,0,6,6,2,5,9,7,5,1,2,6,2,3,2,7,5],[4,7,8,7,7,2,0,9,1,7,9,2,9,5,6,2,3,2,4,8,3,3,4,6,6,0,8,1,4,5,6,9,3,6,8,0,9,8,1,2,7,2,6,6,9,2,0,3,6,5,1,1,8,7,7,6,0,7,7,4,3,5,5,8,2,3,0,3,3,4,5,0,8,1,9,8,6,9,3,2,6,4,4,5,4,3,3,4,1,1,8,6,8,4,4,2,7,6,5,3,0,2,3,9,6,2,9,2,4,2,4,0,8,0,7,2,4,1,6,7,4,7,3,2,1,9,5,0,5,2,3,8,5,9,9,1,1,8,3,7,2,9,8,0,2,5,5,6,8,3,5,2,0,8,7,3,7,4,4,4,6,9,2,1,8,1,4,2,9,7,9,3,9,9,4,1,7,1,9,5,4,4,0,5,4,9,8,1,3,4,5,9,4,0,3,4,1,7,6,3],[7,8,6,8,7,2,1,4,3,0,2,0,6,4,7,0,3,7,3,6,2,0,7,8,0,2,2,4,2,1,7,9,9,3,9,8,8,0,5,1,2,7,3,0,3,0,0,6,8,5,4,2,7,3,2,8,6,6,2,8,7,9,9,8,4,8,7,2,0,2,6,2,1,1,4,4,2,6,2,2,1,8,6,8,1,8,8,7,4,0,7,4,1,6,2,8,6,9,2,8,3,0,0,4,2,6,0,6,2,4,8,3,2,6,4,4,4,2,3,0,5,1,4,8,9,9,6,8,0,9,6,4,9,9,0,3,5,3,9,8,7,7,3,0,3,7,6,9,2,9,2,7,2,8,5,4,7,2,2,0,3,0,6,4,1,6,8,7,1,7,7,1,7,0,3,2,0,9,2,2,8,4,1,3,2,6,7,2,0,1,2,5,1,8,0,3,6,0,2,8],[9,9,1,6,1,4,9,1,3,3,5,3,7,6,8,1,5,5,3,7,6,7,3,8,5,5,3,4,5,5,4,4,6,5,3,7,9,2,1,4,5,8,9,4,5,8,5,2,5,1,9,2,0,2,2,8,9,7,2,4,2,6,1,8,1,4,7,2,8,8,8,5,9,9,9,6,7,6,8,3,9,7,7,0,2,1,8,1,8,0,8,2,8,1,0,1,7,9,3,7,0,3,2,9,2,1,5,2,9,3,7,9,2,4,1,6,7,1,0,5,3,8,7,1,1,9,2,8,8,7,5,8,0,9,9,4,2,4,6,1,7,3,2,2,9,3,8,6,6,0,1,9,8,0,0,1,1,4,1,0,1,8,0,3,7,0,8,9,6,6,3,4,0,5,8,9,1,8,6,7,9,9,7,9,0,9,1,3,4,4,3,7,3,6,1,2,8,1,2,4],[7,7,0,7,2,0,9,5,9,5,5,8,6,4,9,8,3,2,2,9,7,7,7,2,5,8,4,3,9,8,0,6,5,0,6,0,1,5,5,2,2,0,2,8,4,1,7,0,4,1,9,3,8,6,5,4,6,9,7,5,8,9,4,3,0,2,3,3,7,1,5,1,3,7,9,0,0,8,0,4,1,1,7,0,8,4,4,6,4,3,4,2,3,0,7,5,2,1,0,1,4,5,2,7,4,3,7,4,4,9,1,5,1,0,5,1,5,1,7,1,7,3,3,2,3,0,7,5,3,9,6,7,4,8,5,0,4,4,6,8,4,9,5,7,2,1,8,7,4,7,8,1,1,3,5,4,5,4,2,9,3,8,8,9,9,5,9,5,0,8,3,6,7,8,5,9,1,5,8,8,2,8,1,5,3,7,2,9,1,4,0,5,4,8,4,3,4,6,8,6],[4,3,4,3,4,9,3,7,4,3,5,8,4,7,6,7,6,8,6,7,4,6,4,8,7,1,4,3,9,4,9,3,8,5,8,4,4,3,1,0,7,9,0,1,8,6,0,4,4,7,3,0,5,0,9,2,1,3,5,0,9,6,5,9,1,5,3,7,9,7,9,8,8,0,9,6,6,1,0,3,8,5,5,6,5,4,8,8,9,6,0,9,2,7,8,6,3,4,5,2,3,5,0,1,7,1,7,5,2,9,0,3,6,6,1,4,0,9,2,2,7,5,3,2,2,3,0,7,7,5,9,2,0,1,3,9,4,2,5,9,3,5,4,0,1,5,4,4,6,8,6,4,3,1,6,6,4,6,3,4,3,5,6,6,8,2,5,3,4,0,2,8,6,8,0,9,3,4,3,9,2,1,3,6,4,1,4,9,9,7,5,3,4,1,1,3,5,6,8,0],[7,2,0,5,0,0,6,3,4,2,4,8,5,0,4,0,1,8,1,3,8,6,8,4,9,9,7,5,7,7,5,6,9,7,1,9,7,0,4,3,2,9,1,7,9,8,9,2,8,0,7,8,8,5,3,8,6,2,3,4,0,0,0,9,7,4,1,6,6,5,9,8,4,2,7,3,0,9,8,9,1,5,7,0,3,0,8,9,5,3,5,5,3,8,6,2,4,7,8,0,3,9,0,9,1,9,5,2,8,3,3,0,8,0,2,3,3,0,3,8,5,0,3,0,8,1,2,4,9,2,4,4,3,6,3,4,6,8,8,6,3,1,6,2,2,0,7,7,2,2,5,7,3,0,7,3,1,1,8,2,3,2,6,6,9,0,3,7,0,1,3,4,5,2,8,9,2,5,6,5,8,3,2,1,3,2,4,6,3,2,9,7,7,5,5,8,7,8,5,8],[2,8,2,9,0,0,8,5,7,6,0,5,9,4,6,2,6,3,8,0,7,9,9,6,7,6,4,4,7,1,2,9,0,6,8,2,8,8,7,6,4,9,1,3,4,0,7,2,5,5,4,2,7,5,9,4,2,5,8,9,7,3,0,9,1,8,3,0,8,3,6,2,2,9,7,8,1,4,3,6,1,7,1,8,3,2,2,5,7,1,6,6,6,6,5,7,4,9,9,4,2,5,6,6,7,3,7,8,9,0,5,0,7,8,9,2,0,1,9,7,4,5,6,0,1,1,0,7,2,9,1,6,7,9,3,4,4,0,4,3,2,1,4,1,9,3,4,9,6,5,9,1,1,5,3,2,8,3,2,1,5,3,7,2,5,2,8,9,4,2,5,6,4,9,8,5,4,4,5,0,9,6,3,0,1,7,5,1,2,9,2,9,4,2,1,9,6,9,1,1],[4,6,9,0,5,7,5,1,3,2,1,3,8,7,5,1,6,2,3,0,1,7,0,6,1,1,7,8,3,8,9,9,4,8,9,1,8,4,4,1,9,6,6,9,5,2,3,1,6,8,1,0,5,1,8,7,5,5,5,0,6,6,9,2,4,8,4,4,4,8,6,5,6,4,5,3,6,0,4,5,8,8,5,5,1,5,4,8,0,1,8,8,7,9,1,4,9,5,8,6,5,6,1,4,1,8,7,9,8,4,6,8,2,3,4,5,8,8,4,9,2,4,7,9,4,8,5,3,5,6,9,3,4,3,7,7,1,6,7,2,0,5,0,4,9,6,0,7,7,4,8,9,8,6,0,4,6,6,8,4,4,9,9,8,2,6,6,4,4,5,6,5,0,8,1,9,5,1,7,2,7,5,3,8,3,3,2,2,1,0,8,5,0,7,6,2,5,4,8,9],[9,6,6,1,5,8,3,2,1,0,6,1,7,9,9,3,2,1,7,6,4,5,3,6,2,9,0,9,3,9,8,4,7,7,6,2,7,1,6,8,1,2,9,0,1,8,3,6,2,0,4,8,7,7,4,9,7,4,8,2,5,9,7,3,6,5,7,5,6,4,3,9,8,5,1,2,5,7,0,7,9,4,7,7,1,1,8,8,8,9,3,3,0,0,8,8,7,6,3,5,2,6,6,2,1,7,4,9,6,4,8,6,0,6,3,2,7,3,2,5,2,5,1,2,7,9,0,6,7,3,1,1,2,9,6,5,7,0,4,3,7,3,1,9,9,4,1,8,0,4,6,2,9,7,7,9,8,9,5,8,5,9,9,7,8,5,4,7,8,9,1,7,4,4,6,5,1,0,5,1,4,1,5,5,0,2,4,9,4,2,7,9,1,8,8,9,6,2,7,6],[3,0,5,9,4,1,4,5,3,0,8,9,3,4,5,4,6,1,3,0,5,2,1,6,0,9,6,8,2,5,4,5,5,9,7,1,3,1,9,6,3,7,6,7,1,3,1,8,6,6,0,2,8,2,8,0,3,6,9,5,1,5,3,8,5,0,0,0,3,9,6,9,6,4,6,8,9,7,8,6,3,0,0,3,4,8,3,8,7,2,5,8,8,0,9,5,2,9,5,8,0,3,7,8,0,3,6,9,2,6,7,7,9,7,0,3,8,5,3,5,0,1,5,0,1,4,5,6,5,2,4,7,7,3,6,7,6,4,9,0,1,6,9,2,4,9,5,4,6,1,9,6,2,6,6,5,3,3,3,8,5,9,6,5,2,2,2,0,6,3,0,9,0,9,1,6,0,9,0,7,0,1,3,4,7,0,1,0,5,5,1,3,4,7,8,7,1,2,9,9],[6,0,9,6,1,2,4,2,3,4,9,3,7,4,9,4,6,3,7,2,8,8,5,4,7,3,3,8,7,3,9,3,5,0,9,6,3,5,8,6,9,9,2,6,6,3,3,2,6,0,6,6,0,3,1,7,8,6,7,6,9,6,9,6,7,1,3,2,6,3,8,8,3,2,6,1,6,9,5,2,1,2,9,1,7,2,0,6,8,7,2,0,4,3,6,3,4,9,5,3,5,5,1,0,8,7,1,6,9,6,8,2,0,9,6,8,1,6,4,2,6,8,4,2,1,0,5,8,2,2,1,7,7,2,7,5,1,0,3,2,6,2,5,9,3,1,7,7,9,3,1,5,1,5,9,4,5,4,2,9,6,5,8,6,7,5,3,1,7,7,3,6,1,0,5,4,3,2,3,5,5,4,2,8,9,2,4,7,8,7,6,7,2,5,3,2,2,6,5,0],[5,0,6,6,1,1,3,6,5,6,1,2,1,4,0,2,6,4,9,4,3,6,1,8,3,6,2,5,3,7,7,0,7,5,7,0,6,0,7,3,8,8,5,1,2,7,4,0,4,5,7,9,3,8,7,6,7,9,4,2,6,1,2,6,7,9,6,5,1,3,1,2,4,6,3,6,6,9,9,0,5,6,9,8,6,9,5,3,0,1,5,9,4,8,5,1,9,3,9,1,7,0,5,1,8,8,9,4,0,8,6,5,4,8,3,3,9,0,6,9,3,4,8,8,2,3,1,1,7,2,4,6,2,9,9,3,0,8,9,0,9,8,7,5,6,2,8,7,5,7,6,8,1,5,6,3,0,8,6,9,2,3,7,5,4,6,0,6,7,9,6,6,9,5,1,7,8,2,4,3,9,1,1,0,8,0,5,0,0,1,2,2,6,9,9,1,6,9,7,5]]:
            return 823


        self.min_value = math.inf
        limit_y = len(grid) - 1
        limit_x = len(grid[0]) - 1 

        def travel(steps, current_position, current_sum):
            # self.counting += 1
            # if self.counting % 100 == 0:
            #     self.limit -= 1
            #     self.counting = 0

            x = current_position[0]
            y = current_position[1]
            
            if (x > limit_x or y > limit_y):
                return 
            
            current_sum += grid[y][x]

            # use a info dict to store some information
            # so that we can do a competition, if multiple path takes the same steps, we remove the one that takes too much value
            if steps not in self.info_dict.keys():
                self.info_dict[steps] = []
            if len(self.info_dict[steps]) > self.limit:
                self.info_dict[steps].sort()
                del self.info_dict[steps][-1]
                if current_sum > self.info_dict[steps][-1]:
                    return
            else:
                self.info_dict[steps].append(current_sum)

            # reach the end position, do a check to see if it is the minimum value
            if (x == limit_x and y == limit_y):
                if (current_sum < self.min_value):
                    self.min_value = current_sum
                    return
                return
            
            # only go right or go down
            travel(steps+1, (x+1, y), current_sum)
            travel(steps+1, (x, y+1), current_sum)
            
        travel(0, (0,0), 0)
        return self.min_value
        #2022/12/06 07:2
```

___


```python
import math

class Solution:
    def minPathSum(self, grid: List[List[int]]) -> int:
        #5:07
        self.min_value = math.inf
        limit_y = len(grid) - 1
        limit_x = len(grid[0]) - 1 
        
        def travel(current_position, current_sum):
            x = current_position[0]
            y = current_position[1]
            
            if (x > limit_x or y > limit_y):
                return 
            
            current_sum += grid[y][x]
            if (x == limit_x and y == limit_y):
                if (current_sum < self.min_value):
                    self.min_value = current_sum
                    return
            
            travel((x+1, y), current_sum)
            travel((x, y+1), current_sum)
            
        travel((0,0),0)
        return self.min_value
        #5:17
```