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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)

b'

\n\n## Summary

\n## Solution

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\n#### Depth-first Traversal [Accepted]

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'
This is a very simple recursion problem and is a nice introduction to Depth-first Search (DFS).

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**Algorithm**

Because the input is nested, it is natural to think about the problem in a recursive way. We go through the list of nested integers one by one, keeping track of the current depth . If a nested integer is an integer , we calculate its sum as . If the nested integer is a list, we calculate the sum of this list recursively using the same process but with depth .

\n**Java**

/**\n * // This is the interface that allows for creating nested lists.\n * // You should not implement it, or speculate about its implementation\n * public interface NestedInteger {\n *\n * // @return true if this NestedInteger holds a single integer,\n * // rather than a nested list.\n * public boolean isInteger();\n *\n * // @return the single integer that this NestedInteger holds,\n * // if it holds a single integer\n * // Return null if this NestedInteger holds a nested list\n * public Integer getInteger();\n *\n * // @return the nested list that this NestedInteger holds,\n * // if it holds a nested list\n * // Return null if this NestedInteger holds a single integer\n * public List<NestedInteger> getList();\n * }\n */\npublic int depthSum(List<NestedInteger> nestedList) {\n return depthSum(nestedList, 1);\n}\n\npublic int depthSum(List<NestedInteger> list, int depth) {\n int sum = 0;\n for (NestedInteger n : list) {\n if (n.isInteger()) {\n sum += n.getInteger() * depth;\n } else {\n sum += depthSum(n.getList(), depth + 1);\n }\n }\n return sum;\n}\n

**Complexity Analysis**

The algorithm takes time, where is the total number of nested elements in the input list. For example, the list `[ [[[[1]]]], 2 ]`

contains nested lists and nested integers ( and ), so .

In terms of space, at most recursive calls are placed on the stack, where is the maximum level of nesting in the input. For example, for the input `[[1,1],2,[1,1]]`

, and for the input `[1,[4,[6]]]`

.

Analysis written by: @noran

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