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algorithm notes: leetcode#339 nested list weight sum

admin 11月 12, 2020 0

Problem

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:

Input: [[1,1],2,[1,1]]
Output: 10
Explanation: Four 1’s at depth 2, one 2 at depth 1.

Example 2:

Input: [1,[4,[6]]]
Output: 27
Explanation: One 1 at depth 1, one 4 at depth 2, and one 6 at depth 3; 1 + 4*2 + 6*3 = 27.

Solution

Basic idea

Use depth first search. Elements of the given nested list are integers or nested lists, which means the total depth sum we care about consists of depth sum of integers and that of child nested lists. Depth sum of integers equals to sum of integers times its depth. Similarly, to compute depth sum of a child nested list, we can iterate each element, get the weight sum of integers and its child nested list and add them up. And, the depth of child nested list is the depth of parent nested list plus 1.

Python implementation

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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 :
    def depthSum(self, nestedList):
        """
        :type nestedList: List[NestedInteger]
        :rtype: int
        """
        
        def getDepthSum(nestedList, curDepth):
            return sum(ni.getInteger() * curDepth if ni.isInteger() 
                       else getDepthSum(ni.getList(), curDepth+1)
                       for ni in nestedList)
        
        return getDepthSum(nestedList, 1)

Java implementation

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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 null if this NestedInteger holds a single integer
 *     public List<NestedInteger> getList();
 * }
 */
class  {
    public int depthSum(List<NestedInteger> nestedList) {
        return getDepthSum(nestedList, 1);
    }
    
    private int getDepthSum(List<NestedInteger> nestedList, int curDepth){
        int sum = 0;
        for(NestedInteger ni : nestedList){
            if(ni.isInteger()){
                sum += ni.getInteger() * curDepth;
            }else {
                sum += getDepthSum(ni.getList(), curDepth+1);
            }
        }
        return sum;
    }
}

Time complexity analysis

O(N). N is the total number of nested elements, which is the number of items the algotrithm has to iterate in total.

Space complexity analysis

O(D). D is maximum depth, which is times we call the getDepthSum() function.

339. Nested List Weight Sum
(中文版) 算法笔记: Leetcode#339 Nested List Weight Sum

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