120. Triangle[M]

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

Description

Given a triangle, find the minimum path sum from top to bottom. Each step you may move to adjacent numbers on the row below.

For example, given the following triangle

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[
     [2],
    [3,4],
   [6,5,7],
  [4,1,8,3]
]

The minimum path sum from top to bottom is 11 (i.e., 2 + 3 + 5 + 1 = 11).

Note:

Bonus point if you are able to do this using only O(n) extra space, where n is the total number of rows in the triangle.

Solution

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class Solution:
    def minimumTotal(self, triangle: List[List[int]]) -> int:
        if triangle is None or len(triangle) == 0:
            return 0
        ls = len(triangle)
        dp = [0] * ls
        dp[0] = triangle[0][0]
        for i in range(1, ls):
            # note that dp should be updated in reversed order
            dp[i] = dp[i - 1] + triangle[i][i]
            for j in reversed(range(1, i)):
                dp[j] = min(dp[j - 1] + triangle[i][j], dp[j] + triangle[i][j])
            dp[0] = dp[0] + triangle[i][0]
        return min(dp)