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  • DP-Triangle

    题目描述:

    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.

    思路:

    记f(i, j)为以(x, j)为根的最短路径和。

    状态转移方程:f(i, j) = min{f(i+1, j), f(i+1, j+1)} + (i, j)。

    实现:

    class Solution {
    public:
        int minimumTotal(vector<vector<int>>& triangle) {
            for (int i = triangle.size() - 2; i >= 0; i--)
            {
                for (int j = 0; j != (triangle[i].size()); j++)
                    triangle[i][j] += min(triangle[i+1][j], triangle[i+1][j+1]);
            }
            
            return triangle[0][0];
        }
    };
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  • 原文地址:https://www.cnblogs.com/gatsbydhn/p/4970328.html
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