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.

public class Solution {
    public int minimumTotal(List> triangle) {
        int n = triangle.size();
        if(n==1)
          return triangle.get(n-1).get(n-1);
        int[][] f = new int[n][n];
        for(int i=0;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.get(i).get(j);   // f(i,j) = min{f(i+1,j),f(i+1,j+1)} + triangle(i,j);
          }
        return f[0][0];
        
    }
}

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