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# 339 Nested List Weight Sum

## 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]]]`, return**27**. (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**

```java
/**
 * // 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 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