120. Triangle

 1 class Solution {
 2     public int minimumTotal(List<List<Integer>> triangle) {
 3         if(triangle == null) return 0;
 4         Integer[][] cache = new Integer[triangle.size()][triangle.size()];
 5         return backtrack(triangle, 0, 0, cache);
 6         
 7     }
 8     
 9     public int backtrack(List<List<Integer>> triangle, int level, int index, Integer[][] cache) {
10         if(level+1 >= triangle.size()) {
11             return triangle.get(level).get(index);    
12         }    
13         if( cache[level][index] != null) return cache[level][index];
14         return cache[level][index] = triangle.get(level).get(index) + Math.min(backtrack(triangle, level+1, index, cache), backtrack(triangle, level+1, index+1, cache));    
15   
16         
17         
18     }
19 }