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.

Example 1:

Input: [[1,1],2,[1,1]]
Output: 10 
Explanation: Four 1's at depth 2, one 2 at depth 1.

这道题算是LinkedIn的电话面试万年不变的一道题了，可以算是DFS，也可以算是BFS。思路差不多，对每一层的数字求和，按照深度加权，遇到list的时候把权重加一。

答出来之后一般会有个follow up，就是Nested List Weight Sum II

/**
 * // 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 {
    public int depthSum(List<NestedInteger> nestedList) {
        if(nestedList == null || nestedList.size() == 0)
            return 0;

        return depthSum(nestedList, 1);
    }

    public int depthSum(List<NestedInteger> nestedList, int factor) {
        int res = 0;
        for(NestedInteger n: nestedList) {
            if(n.isInteger()) {
                res += n.getInteger() * factor;
            } else {
                res += depthSum(n.getList(), factor + 1);
            }
        }

        return res;
    }
}