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,[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)


Summary

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

Solution

Depth-first Traversal [Accepted]

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 .

Java

/**
 * // This is the interface that allows for creating nested lists.
 * // You should not implement it, or speculate about its implementation
 * public interface NestedInteger {
 *
 *     // @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();
 *
 *     // @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();
 * }
 */
public int depthSum(List<NestedInteger> nestedList) {
    return depthSum(nestedList, 1);
}

public int depthSum(List<NestedInteger> list, int depth) {
    int sum = 0;
    for (NestedInteger n : list) {
        if (n.isInteger()) {
            sum += n.getInteger() * depth;
        } else {
            sum += depthSum(n.getList(), depth + 1);
        }
    }
    return sum;
}

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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