## 339. Nested List Weight Sum

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,]], return 27. (one 1 at depth 1, one 4 at depth 2, and one 6 at depth 3; 1 + 4*2 + 6*3 = 27)

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## Summary

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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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## Solution

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#### Depth-first Traversal [Accepted]

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Algorithm

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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 .

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Java

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/**\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
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Complexity Analysis

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The algorithm takes time, where is the total number of nested elements in the input list. For example, the list [ [[[]]], 2 ] contains nested lists and nested integers ( and ), so .

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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,]].

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Analysis written by: @noran

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