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.
一,动态规划解法:
class Solution{ public: int minimumTotal(vector<vector<int>>& triangle){ int n = triangle.size(); vector<vector<int>> memo(n,vector<int>(n,-1)); for(int j = 0; j < n; j++){ memo[n-1][j] = triangle[n-1][j]; } for(int i = n - 2; i >= 0; i--){ for(int j = 0; j <= i; j++){ memo[i][j] = min(memo[i+1][j], memo[i+1][j+1]) + triangle[i][j]; } } return memo[0][0]; } }; class Solution{ public: int minimumTotal(vector<vector<int> > &triangle){ int n = triangle.size(); vector<int> memo(n,-1); for(int j = 0; j < n; j++){ memo[j] = triangle[n-1][j]; } for(int i = n - 2; i >= 0; i--){ for(int j = 0; j <= i; j++){ memo[j] = min(memo[j],memo[j+1]) + triangle[i][j]; } } return memo[0]; } };
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怕什么真理无穷,进一寸有一寸的欢喜。---胡适