题目: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).
思路:
典型的动态规划,从上到下,或者采用递推的方法。具体的公式就是 num[i][j] = max(num[i-1][j+1],num[i-1][j])+nums[i][j];
意思就是:当前的数值,等于其下方和下面右边一个的最大值加上当前数字数值。
采用一个循环即可达到目的。
代码:
class Solution { public: int minimumTotal(vector<vector<int>>& triangle) { int m=triangle.size(); int dp[m][m]; for(int i=0;i<m;i++){ dp[m-1][i]=triangle[m-1][i]; } for(int i=m-2;i>=0;i--){ for(int j=0;j<=i;j++){ dp[i][j]=min(dp[i+1][j],dp[i+1][j+1])+triangle[i][j]; } } return dp[0][0]; } };