Medium
Given a nested list of integers, return the sum of all integers in the list weighted by their depth.
Each element is either an integer, or a list — whose elements may also be integers or other lists.
Different from the previous question where weight is increasing from root to leaf, now the weight is defined from bottom up. i.e., the leaf level integers have weight 1, and the root level integers have the largest weight.

Example 1:Given the list [[1,1],2,[1,1]], return 8. (four 1’s at depth 1, one 2 at depth 2)

Example 2:Given the list [1,[4,[6]]], return 17. (one 1 at depth 3, one 4 at depth 2, and one 6 at depth 1; 13 + 42 + 6*1 = 17)

这道题看的答案，用的是DFS.比较难的地方是一开始不知道总的层数，所以不能直接累加。解决方法也比较巧妙，一直更新一个maxDepth, 到最后遍历完所有的List就可以得到总层数。遍历的时候以（val, depth) pair进行储蓄，最后累加的时候就可以用 val * (maxDepth – depth)。

/**
 * // This is the interface that allows for creating nested lists.
 * // You should not implement it, or speculate about its implementation
 * public interface NestedInteger {
 *     // Constructor initializes an empty nested list.
 *     public NestedInteger();
 *
 *     // Constructor initializes a single integer.
 *     public NestedInteger(int value);
 *
 *     // @return true if this NestedInteger holds a single integer, rather than a nested list.
 *     public boolean isInteger();
 *
 *     // @return the single integer that this NestedInteger holds, if it holds a single integer
 *     // Return null if this NestedInteger holds a nested list
 *     public Integer getInteger();
 *
 *     // Set this NestedInteger to hold a single integer.
 *     public void setInteger(int value);
 *
 *     // Set this NestedInteger to hold a nested list and adds a nested integer to it.
 *     public void add(NestedInteger ni);
 *
 *     // @return the nested list that this NestedInteger holds, if it holds a nested list
 *     // Return null if this NestedInteger holds a single integer
 *     public List<NestedInteger> getList();
 * }
 */

class Solution {
    class ResultType{
        public int val;
        public int depth;
        public ResultType(int val, int depth){
            this.val = val;
            this.depth = depth;
        }
    }
    public List<ResultType> resList;
    public int maxDepth = 1;
    public int res;
    
    public int depthSumInverse(List<NestedInteger> nestedList) {
        if (nestedList == null || nestedList.size() == 0){
            return 0;
        } 
        res = 0;
        int depth = 1;
        resList = new ArrayList<>();
        for (NestedInteger ni : nestedList){
            if (!ni.isInteger()){
                DFS(ni.getList(), depth + 1);
            } else {
                resList.add(new ResultType(ni.getInteger(), depth));
            }
        }
        for (ResultType pair : resList){
            res += pair.val * (maxDepth - pair.depth + 1);
        }
        return res;
    }
    
    private void DFS(List<NestedInteger> niList, int depth){
        maxDepth = Math.max(maxDepth, depth);
        for (NestedInteger ni : niList){
            if (ni.isInteger()){
                resList.add(new ResultType(ni.getInteger(), depth));
            } else {
                DFS(ni.getList(), depth + 1);
            }         
        }                    
    }
}