120. Triangle

https://leetcode.com/problems/triangle/

Given a triangle array, return the minimum path sum from top to bottom. For each step, you may move to an adjacent number of the row below. More formally, if you are on index i on the current row, you may move to either index i or index i + 1 on the next row.

Example 1: Input: triangle = [[2],[3,4],[6,5,7],[4,1,8,3]] Output: 11 Explanation: The triangle looks like: 2 3 4 6 5 7 4 1 8 3 The minimum path sum from top to bottom is 2 + 3 + 5 + 1 = 11 (underlined above). Example 2: Input: triangle = [[-10]] Output: -10

Constraints:

1 <= triangle.length <= 200 	
triangle[0].length == 1 	
triangle[i].length == triangle[i - 1].length + 1 	
-104 <= triangle[i][j] <= 104

  • code
class Solution:
    def minimumTotal(self, triangle: List[List[int]]) -> int:
        for row in range(1, len(triangle)):
            for col in range(row + 1):
                smallest_above = math.inf
                if col > 0:
                    smallest_above = triangle[row - 1][col - 1]
                if col < row:
                    smallest_above = min(smallest_above, triangle[row - 1][col])
                triangle[row][col] += smallest_above
        return min(triangle[-1])
  • code
class Solution:
    def minimumTotal(self, triangle: List[List[int]]) -> int:
        @lru_cache(maxsize=None)
        def min_path(row, col):
            path = triangle[row][col]
            if row < len(triangle) - 1:
                path += min(min_path(row + 1, col), min_path(row + 1, col + 1))
            return path
        return min_path(0, 0)