- Triangle Medium
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Share 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.
Accepted
思路：动态规划
1.问题拆解： 经过[i][j]的路径肯定会经过[i-1][j]或者[i-1][j-1]
2.状态定义： 从上到下，从下到上，从下到上，状态定义变为最后一行元素到当前元素最小路径和
3.递推方程推导
倒推 dp[i][j]=min(dp[i+1][j],dp[i+1][j+1])+triangle[i][j]
4.实现
代码：python3
class Solution:
def minimumTotal(self, triangle: List[List[int]]) -> int:
for i in range(len(triangle)-2,-1,-1):
for j in range(len(triangle[i])):
triangle[i][j]=triangle[i][j]+min(triangle[i+1][j],triangle[i+1][j+1])
return triangle[0][0]
if __name__ == '__main__':
print(Solution().minimumTotal([
[2],
[3,4],
[6,5,7],
[4,1,8,3]
]))
参考：mp.weixin.qq.com/s?__biz=MzU…
时间复杂度:O(n^2)
空间复杂度:O(1)
