LeetCode 120. Triangle（三角形）

原题网址：https://leetcode.com/problems/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.

方法一：递归+记忆化搜索。

public class Solution {
    private boolean[][] visit;
    private int[][] min;
    public int dp(List> triangle, int i, int j) {
        if (i == triangle.size()-1) return triangle.get(i).get(j);
        if (visit[i][j]) return min[i][j];
        int m = Math.min(dp(triangle, i+1, j), dp(triangle, i+1, j+1)) + triangle.get(i).get(j);
        min[i][j] = m;
        visit[i][j] = true;
        return m;
    }
    public int minimumTotal(List> triangle) {
        visit = new boolean[triangle.size()][triangle.size()];
        min = new int[triangle.size()][triangle.size()];
        return dp(triangle, 0, 0);
    }    
}

方法二：递推+动态规划。

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