Lee他Code 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.

题意：数塔求最小的路径和是多少。

思路：数塔的DP思想，为了不妨碍后面的计算，我们每行计算从后面开始。

public class Solution {
    public int minimumTotal(List<List<Integer>> triangle) {
        int n = triangle.size();
    	if (n == 0) return 0;

    	int f[] = new int[triangle.size()];
    	f[0]=  triangle.get(0).get(0);
    	for (int i = 1; i < triangle.size(); i++)
    		for (int j = triangle.get(i).size()-1; j >= 0; j--) {
    			if (j == 0)
    				f[j] = f[j] + triangle.get(i).get(j);
    			else if (j == triangle.get(i).size() - 1)
    				f[j] = f[j-1] + triangle.get(i).get(j);
    			else f[j] = Math.min(f[j-1], f[j]) + triangle.get(i).get(j);
    		}

    	int ans = Integer.MAX_VALUE;
    	for (int i = 0; i < f.length; i++)
    		ans = Math.min(ans, f[i]);

    	return ans;
    }
}

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