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.

class Solution {
    public int minimumTotal(List<List<Integer>> triangle) {
        int n = triangle.size();
        int[] dp = new int[n];
        for(int i = 0; i < n; i++) dp[i] = triangle.get(n - 1).get(i);
        
        for(int i = n - 2; i >= 0; i--) {
            for(int j = 0; j <= i; j++) {
                dp[j] = Math.min(dp[j], dp[j + 1]) + triangle.get(i).get(j);
            }
        }
        return dp[0];
    }
}

class Solution {
    public int minimumTotal(List<List<Integer>> triangle) {
        int n = triangle.size();
        int[][] dp = new int[n][n];
        for(int i = 0; i < n; i++) dp[n - 1][i] = triangle.get(n - 1).get(i);
        
        for(int i = n - 2; i >= 0; i--) {
            for(int j = 0; j <= i; j++) {
                dp[i][j] = Math.min(dp[i + 1][j], dp[i + 1][j + 1]) + triangle.get(i).get(j);
            }
        }
        return dp[0][0];
    }
}

 

自底向上的DP算法

f(i,j)=min{f(i,j),f(i,j+1)}+(i,j)

https://www.cnblogs.com/mozi-song/p/9615167.html