Triangle ---DP

最新推荐文章于 2021-12-25 16:45:17 发布

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本文介绍了一种求解三角形结构中从顶点到底边的最小路径和的方法。通过动态规划的方式，自底向上计算每一步到达各节点所需的最小路径和，最终返回从顶部开始的最小路径总和。

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Given a triangle, find the minimum path sum from top to bottom. Each step you may move to adjacent numbers on the row below.

Have you met this question in a real interview? Yes
Example
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

public class Solution {
    public int minimumTotal(int [][] triangle){
        if(triangle == null || triangle.length ==0)
            return -1;
        if(triangle[0]==null || triangle[0].length==0)
            return -1;

        int n = triangle.length;
        int [][] f = new int [n][n];


        for(int i =0; i<n; i++)
            f[n-1][i]=triangle[n-1][i];


        for(int i=n-2;i>=0;i--){
            for(int j =0;j<=i;j++){
                f[i][j]=Math.min(f[i+1][j],f[i+1][j+1]) +triangle[i][j];
            }
        }
        return f[0][0];
    }
}