120 Title: triangles, and minimum path

One. Problem Description

Given a triangle, find the minimum and the top-down path. Each step can move to the next line adjacent nodes.

For example, given triangle:

[

     [2],

    [3,4],

   [6,5,7],

  [4,1,8,3]

]

Top-down and minimum path 11 (i.e., 2 + 3 + 5 + 1 = 11).

Description:

If you can use only O (n) extra space (n number of rows as a triangle) to solve this problem, then your algorithm will be a plus.

two. Problem-solving ideas

Body of ideas: the use of bottom-up dynamic programming algorithm to solve it. Find the state transition function. N is the n-th row to the last row of the maximum value, i is a i-th row.

f (n) (i) = f (n) (i) + min (f (n + 1) (i), f (n + 1) (i + 1))

Step a: The state transition equation, we can be counted from the last line, all the values ​​obtained on each line, and instead of the line.

Step Two: Repeat steps until the first line is replaced with the new values, the new output value is the value of the request.

three. Results of the

When execution: 7 ms, beat the 27.06% of all users in java submission

Memory consumption: 37.2 MB, defeated 77.58% of all users in java submission

four. Java code

class Solution {
    public int minimumTotal(List<List<Integer>> triangle) {
        if(triangle.size()==0) {
            return 0;
        }
        for(int i=triangle.size()-2;i>=0;i--) {
            List<Integer> list=new ArrayList<Integer>(triangle.get(i));
            for(int j=0;j<list.size();j++) {
                int temp=list.get(j)+Math.min(triangle.get(i+1).get(j), triangle.get(i+1).get(j+1));
                list.set(j, temp);
            }
            triangle.set(i, list);
        }
        return triangle.get(0).get(0);
    }
}