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.
Answer
class Solution { public: int minimumTotal(vector<vector<int>>& triangle) { if (triangle.size() == 0) return 0; vector<int> dp(triangle.size()); dp[0] = triangle[0][0]; for (int i = 1; i < triangle.size(); i++) { int pre = dp[0]; dp[0] += triangle[i][0]; for (int j = 1; j < triangle[i].size()-1; j++) { int mid = dp[j]; dp[j] = min(mid, pre) + triangle[i][j]; pre = mid; } dp[triangle[i].size()-1] = pre + triangle[i][triangle[i].size()-1]; } int minVal = dp[0]; for (int i = 1; i < triangle.size(); i++) if (minVal > dp[i]) minVal = dp[i]; return minVal; } int min(int a, int b) { if (a > b) return b; return a; } };
动态规划问题。