leetcode 120. Triangle

给一个三角形，寻找一个从顶到底的最小的路径和，只能是临近的数字的和

[
     [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).

解题思路

动态规划

每一层都依赖于上一层

按照从上到下，从右到左的顺序，一层一层的求

开一个int[] f = new int[triangle.size()];这么大的空间重复利用就可以了

class Solution {
    public int minimumTotal(List> triangle) {
        if(triangle == null || triangle.size() == 0) return 0;
        int[] f = new int[triangle.size()];                                 
        f[0] = triangle.get(0).get(0);                                      
        for (int i = 1; i < triangle.size(); i++) {                         
            List innerTriangle = triangle.get(i);                  
            for (int j = innerTriangle.size() - 1; j >= 0; j--) {           
                if (j == 0) {                                               
                    f[j] = f[j] + innerTriangle.get(j);                     
                } else if (j == innerTriangle.size() - 1) {                 
                    f[j] = f[j-1] + innerTriangle.get(j);                   
                } else {                                                    
                    f[j] = innerTriangle.get(j) + Math.min(f[j], f[j - 1]); 
                }                                                           
            }                                                               
        }                                                                   
        int min = f[0];                                                     
        for (int i = 1; i < f.length; i++) {                                
            if (min > f[i]) {                                               
                min = f[i];                                                 
            }                                                               
        }                                                                   
        return min;                                                                                                                             
       
    }
}