# Question

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

```
[
[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

```
class Solution(object):
def minimumTotal(self, triangle):
"""
:type triangle: List[List[int]]
:rtype: int
"""
if len(triangle) == 0 or len(triangle[0]) == 0:
return 0
numRows = len(triangle)
prev_row = triangle[0]
for i in range(1, numRows):
row = triangle[i]
for j in range(0, len(row)):
if j == 0:
row[j] += prev_row[j]
elif j == len(row) - 1:
row[j] += prev_row[j - 1]
else:
row[j] += min(prev_row[j], prev_row[j - 1])
prev_row = row
return min(prev_row)
```