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.
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:
# """# 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]# """classSolution:defdepthSumInverse(self,nestedList:List[NestedInteger])->int:defdfs(x,d):nonlocalmaxDepth,s,wsmaxDepth=max(maxDepth,d)ifx.isInteger():s+=x.getInteger()ws+=x.getInteger()*delse:foryinx.getList():dfs(y,d+1)maxDepth=s=ws=0forxinnestedList:dfs(x,1)return(maxDepth+1)*s-ws
/** * // 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(); * } */classSolution{privateintmaxDepth;privateintws;privateints;publicintdepthSumInverse(List<NestedInteger>nestedList){for(NestedIntegerx:nestedList){dfs(x,1);}return(maxDepth+1)*s-ws;}privatevoiddfs(NestedIntegerx,intd){maxDepth=Math.max(maxDepth,d);if(x.isInteger()){ws+=x.getInteger()*d;s+=x.getInteger();}else{for(NestedIntegery:x.getList()){dfs(y,d+1);}}}}
/** * // 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; * }; */classSolution{public:intdepthSumInverse(vector<NestedInteger>&nestedList){intmaxDepth=0,ws=0,s=0;function<void(NestedInteger&,int)>dfs=[&](NestedInteger&x,intd){maxDepth=max(maxDepth,d);if(x.isInteger()){ws+=x.getInteger()*d;s+=x.getInteger();}else{for(auto&y:x.getList()){dfs(y,d+1);}}};for(auto&x:nestedList){dfs(x,1);}return(maxDepth+1)*s-ws;}};
/** * // This is the interface that allows for creating nested lists. * // You should not implement it, or speculate about its implementation * type NestedInteger struct { * } * * // Return true if this NestedInteger holds a single integer, rather than a nested list. * func (n NestedInteger) IsInteger() bool {} * * // 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 * // So before calling this method, you should have a check * func (n NestedInteger) GetInteger() int {} * * // Set this NestedInteger to hold a single integer. * func (n *NestedInteger) SetInteger(value int) {} * * // Set this NestedInteger to hold a nested list and adds a nested integer to it. * func (n *NestedInteger) Add(elem NestedInteger) {} * * // Return the nested list that this NestedInteger holds, if it holds a nested list * // The list length is zero if this NestedInteger holds a single integer * // You can access NestedInteger's List element directly if you want to modify it * func (n NestedInteger) GetList() []*NestedInteger {} */funcdepthSumInverse(nestedList[]*NestedInteger)int{varmaxDepth,ws,sintvardfsfunc(*NestedInteger,int)dfs=func(x*NestedInteger,dint){maxDepth=max(maxDepth,d)ifx.IsInteger(){ws+=x.GetInteger()*ds+=x.GetInteger()}else{for_,y:=rangex.GetList(){dfs(y,d+1)}}}for_,x:=rangenestedList{dfs(x,1)}return(maxDepth+1)*s-ws}
/** * // This is the interface that allows for creating nested lists. * // You should not implement it, or speculate about its implementation * class NestedInteger { * If value is provided, then it holds a single integer * Otherwise it holds an empty nested list * constructor(value?: number) { * ... * }; * * Return true if this NestedInteger holds a single integer, rather than a nested list. * isInteger(): boolean { * ... * }; * * Return the single integer that this NestedInteger holds, if it holds a single integer * Return null if this NestedInteger holds a nested list * getInteger(): number | null { * ... * }; * * Set this NestedInteger to hold a single integer equal to value. * setInteger(value: number) { * ... * }; * * Set this NestedInteger to hold a nested list and adds a nested integer elem to it. * add(elem: NestedInteger) { * ... * }; * * Return the nested list that this NestedInteger holds, * or an empty list if this NestedInteger holds a single integer * getList(): NestedInteger[] { * ... * }; * }; */functiondepthSumInverse(nestedList:NestedInteger[]):number{let[maxDepth,ws,s]=[0,0,0];constdfs=(x:NestedInteger,d:number)=>{maxDepth=Math.max(maxDepth,d);if(x.isInteger()){ws+=x.getInteger()*d;s+=x.getInteger();}else{for(constyofx.getList()){dfs(y,d+1);}}};for(constxofnestedList){dfs(x,1);}return(maxDepth+1)*s-ws;}
/** * // This is the interface that allows for creating nested lists. * // You should not implement it, or speculate about its implementation * function NestedInteger() { * * Return true if this NestedInteger holds a single integer, rather than a nested list. * @return {boolean} * this.isInteger = function() { * ... * }; * * Return the single integer that this NestedInteger holds, if it holds a single integer * Return null if this NestedInteger holds a nested list * @return {integer} * this.getInteger = function() { * ... * }; * * Set this NestedInteger to hold a single integer equal to value. * @return {void} * this.setInteger = function(value) { * ... * }; * * Set this NestedInteger to hold a nested list and adds a nested integer elem to it. * @return {void} * this.add = function(elem) { * ... * }; * * Return the nested list that this NestedInteger holds, if it holds a nested list * Return null if this NestedInteger holds a single integer * @return {NestedInteger[]} * this.getList = function() { * ... * }; * }; *//** * @param {NestedInteger[]} nestedList * @return {number} */vardepthSumInverse=function(nestedList){let[maxDepth,ws,s]=[0,0,0];constdfs=(x,d)=>{maxDepth=Math.max(maxDepth,d);if(x.isInteger()){ws+=x.getInteger()*d;s+=x.getInteger();}else{for(constyofx.getList()){dfs(y,d+1);}}};for(constxofnestedList){dfs(x,1);}return(maxDepth+1)*s-ws;};