# 339 Nested List Weight Sum

## 1. Question

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: Given the list`[[1,1],2,[1,1]]`, return 10. (four 1's at depth 2, one 2 at depth 1)
Example 2: Given the list`[1,[4,[6]]]`, return27. (one 1 at depth 1, one 4 at depth 2, and one 6 at depth 3; 1 + 4*2 + 6*3 = 27)

## 2. Implementation

(1) DFS
/**
* // 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.
*
* // @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 getDepthSum(nestedList, 1);
}
public int getDepthSum(List<NestedInteger> nestedList, int depth) {
int res = 0;
for (NestedInteger ni : nestedList) {
res += ni.isInteger() ? ni.getInteger() * depth : getDepthSum(ni.getList(), depth + 1);
}
return res;
}
}

## 3. Time & Space Complexity

DFS: 时间复杂度O(n), n为nestedList的所有数的个数， 空间复杂度O(k), k为nestedList中的深度