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.
分析
找出一個三角形從頂?shù)降鬃疃搪窂角痴蕖：芎唵蔚膭討B(tài)規(guī)劃問題，從上到下汇跨，依次計算到當前行左邊路線和右邊路線哪個是最短距離诽嘉。不過需要兩端的點只有一條路，需要另處理圈浇。
當然也可以從下到上袍榆，更方面了沦泌。
int minimumTotal(int** triangle, int triangleRowSize, int *triangleColSizes) {
int ans=0;
for(int i=1;i<triangleRowSize;i++)
{
triangle[i][0]=triangle[i-1][0]+triangle[i][0];
for(int j=1;j<triangleColSizes[i]-1;j++)
{
int left=triangle[i-1][j-1]+triangle[i][j];
int right=triangle[i-1][j]+triangle[i][j];
if(left<right)
triangle[i][j]=left;
else
triangle[i][j]=right;
}
triangle[i][ triangleColSizes[i]-1 ]=triangle[i-1][ triangleColSizes[i]-2 ]+triangle[i][ triangleColSizes[i]-1 ];
}
ans=triangle[triangleRowSize-1][0];
for(int j=1;j<triangleColSizes[triangleRowSize-1];j++)
if(triangle[triangleRowSize-1][j]<ans)
ans=triangle[triangleRowSize-1][j];
return ans;
}
