120. Triangle

Medium

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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

Follow up: Could you do this using only O(n) extra space, where n is the total number of rows in the triangle?

class Solution:
    def minimumTotal(self, triangle: List[List[int]]) -> int:
        # Move from Bottom to UP
        # For Second row from bottom update minimum in that row using its below row
        # Same goes for its upper rows
        for i in range(len(triangle)-2, -1, -1):
            for j in range(len(triangle[i])):
                # For Row 2 Column 0 <--- Min(Row 3 Column 0, Row 3 Column 1)
                # In Same way do for other columns in same row, then ,move to upper row
                triangle[i][j] += min(triangle[i+1][j], triangle[i+1][j+1])
        return triangle[0][0]