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364. Nested List Weight Sum II πŸ”’

Description

You are given a nested list of integers nestedList. Each element is either an integer or a list whose elements may also be integers or other lists.

The depth of an integer is the number of lists that it is inside of. For example, the nested list [1,[2,2],[[3],2],1] has each integer's value set to its depth. Let maxDepth be the maximum depth of any integer.

The weight of an integer is maxDepth - (the depth of the integer) + 1.

Return the sum of each integer in nestedList multiplied by its weight.

 

Example 1:

Input: nestedList = [[1,1],2,[1,1]]
Output: 8
Explanation: Four 1's with a weight of 1, one 2 with a weight of 2.
1*1 + 1*1 + 2*2 + 1*1 + 1*1 = 8

Example 2:

Input: nestedList = [1,[4,[6]]]
Output: 17
Explanation: One 1 at depth 3, one 4 at depth 2, and one 6 at depth 1.
1*3 + 4*2 + 6*1 = 17

 

Constraints:

  • 1 <= nestedList.length <= 50
  • The values of the integers in the nested list is in the range [-100, 100].
  • The maximum depth of any integer is less than or equal to 50.
  • There are no empty lists.

Solutions

Solution 1: DFS

Let's assume the integers are $a_1, a_2, \cdots, a_n$, their depths are $d_1, d_2, \cdots, d_n$, the maximum depth is $\textit{maxDepth}$, then the answer is:

$$ a_1 \times \textit{maxDepth} - a_1 \times d_1 + a_1 + a_2 \times \textit{maxDepth} - a_2 \times d_2 + a_2 + \cdots + a_n \times \textit{maxDepth} - a_n \times d_n + a_n $$

which is:

$$ (\textit{maxDepth} + 1) \times (a_1 + a_2 + \cdots + a_n) - (a_1 \times d_1 + a_2 \times d_2 + \cdots + a_n \times d_n) $$

If we denote the sum of all integers as $s$, and the sum of each integer multiplied by its depth as $ws$, then the answer is:

$$ (\textit{maxDepth} + 1) \times s - ws $$

Therefore, we design a function $dfs(x, d)$, which starts searching from $x$ with depth $d$. The execution process of $dfs(x, d)$ is as follows:

  • We first update $\textit{maxDepth} = \max(\textit{maxDepth}, d)$;
  • If $x$ is an integer, then we update $s = s + x$, $ws = ws + x \times d$;
  • Otherwise, we recursively traverse each element $y$ of $x$, and call $dfs(y, d + 1)$.

We traverse the entire list, for each element $x$, we call $dfs(x, 1)$, and finally return $(\textit{maxDepth} + 1) \times s - ws$.

The time complexity is $O(n)$, and the space complexity is $O(n)$. Where $n$ is the number of integers.

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# """
# This is the interface that allows for creating nested lists.
# You should not implement it, or speculate about its implementation
# """
# class NestedInteger:
#    def __init__(self, value=None):
#        """
#        If value is not specified, initializes an empty list.
#        Otherwise initializes a single integer equal to value.
#        """
#
#    def isInteger(self):
#        """
#        @return True if this NestedInteger holds a single integer, rather than a nested list.
#        :rtype bool
#        """
#
#    def add(self, elem):
#        """
#        Set this NestedInteger to hold a nested list and adds a nested integer elem to it.
#        :rtype void
#        """
#
#    def setInteger(self, value):
#        """
#        Set this NestedInteger to hold a single integer equal to value.
#        :rtype void
#        """
#
#    def getInteger(self):
#        """
#        @return the single integer that this NestedInteger holds, if it holds a single integer
#        Return None if this NestedInteger holds a nested list
#        :rtype int
#        """
#
#    def getList(self):
#        """
#        @return the nested list that this NestedInteger holds, if it holds a nested list
#        Return None if this NestedInteger holds a single integer
#        :rtype List[NestedInteger]
#        """
class Solution:
    def depthSumInverse(self, nestedList: List[NestedInteger]) -> int:
        def dfs(x, d):
            nonlocal maxDepth, s, ws
            maxDepth = max(maxDepth, d)
            if x.isInteger():
                s += x.getInteger()
                ws += x.getInteger() * d
            else:
                for y in x.getList():
                    dfs(y, d + 1)

        maxDepth = s = ws = 0
        for x in nestedList:
            dfs(x, 1)
        return (maxDepth + 1) * s - ws

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/**
 * // 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 empty list if this NestedInteger holds a single integer
 *     public List<NestedInteger> getList();
 * }
 */
class Solution {
    private int maxDepth;
    private int ws;
    private int s;

    public int depthSumInverse(List<NestedInteger> nestedList) {
        for (NestedInteger x : nestedList) {
            dfs(x, 1);
        }
        return (maxDepth + 1) * s - ws;
    }

    private void dfs(NestedInteger x, int d) {
        maxDepth = Math.max(maxDepth, d);
        if (x.isInteger()) {
            ws += x.getInteger() * d;
            s += x.getInteger();
        } else {
            for (NestedInteger y : x.getList()) {
                dfs(y, d + 1);
            }
        }
    }
}

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/**
 * // This is the interface that allows for creating nested lists.
 * // You should not implement it, or speculate about its implementation
 * class NestedInteger {
 *   public:
 *     // Constructor initializes an empty nested list.
 *     NestedInteger();
 *
 *     // Constructor initializes a single integer.
 *     NestedInteger(int value);
 *
 *     // Return true if this NestedInteger holds a single integer, rather than a nested list.
 *     bool isInteger() const;
 *
 *     // Return the single integer that this NestedInteger holds, if it holds a single integer
 *     // The result is undefined if this NestedInteger holds a nested list
 *     int getInteger() const;
 *
 *     // Set this NestedInteger to hold a single integer.
 *     void setInteger(int value);
 *
 *     // Set this NestedInteger to hold a nested list and adds a nested integer to it.
 *     void add(const NestedInteger &ni);
 *
 *     // Return the nested list that this NestedInteger holds, if it holds a nested list
 *     // The result is undefined if this NestedInteger holds a single integer
 *     const vector<NestedInteger> &getList() const;
 * };
 */
class Solution {
public:
    int depthSumInverse(vector<NestedInteger>& nestedList) {
        int maxDepth = 0, ws = 0, s = 0;
        function<void(NestedInteger&, int)> dfs = [&](NestedInteger& x,