动态规划，Python 3 实现：
源代码已上传 Github，持续更新。
"""
120. Triangle
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.
"""
class Solution:
def minimumTotal(self, triangle):
"""
:type triangle: List[List[int]]
:rtype: int
"""
# 增加行列各增加一行，便于边界处理
height = len(triangle) + 1
width = len(triangle[-1]) + 1
optimal_matrix = [[0 for x in range(width)] for y in range(height)]
width_range = width - 1
for h in range(height - 2, -1, -1):
for w in range(width_range):
# 状态转移方程
optimal_matrix[h][w] = min(optimal_matrix[h + 1][w], optimal_matrix[h + 1][w + 1]) + triangle[h][w]
width_range -= 1
return optimal_matrix[0][0]
if __name__ == '__main__':
triangle = [
[2],
[3,4],
[6,5,7],
[4,1,8,3]
]
solution = Solution()
print(solution.minimumTotal(triangle))
源代码已上传至 Github，持续更新中。
