You are given a 0-indexed array of positive integers w where w[i] describes the weight of the ith index.
You need to implement the function pickIndex(), which randomly picks an index in the range [0, w.length - 1] (inclusive) and returns it. The probability of picking an index i is w[i] / sum(w).
For example, if w = [1, 3], the probability of picking index 0 is 1 / (1 + 3) = 0.25 (i.e., 25%), and the probability of picking index 1 is 3 / (1 + 3) = 0.75 (i.e., 75%).
Example 1:
Input
["Solution","pickIndex"]
[[[1]],[]]
Output
[null,0]
Explanation
Solution solution = new Solution([1]);
solution.pickIndex(); // return 0. The only option is to return 0 since there is only one element in w.
Example 2:
Input
["Solution","pickIndex","pickIndex","pickIndex","pickIndex","pickIndex"]
[[[1,3]],[],[],[],[],[]]
Output
[null,1,1,1,1,0]
Explanation
Solution solution = new Solution([1, 3]);
solution.pickIndex(); // return 1. It is returning the second element (index = 1) that has a probability of 3/4.
solution.pickIndex(); // return 1
solution.pickIndex(); // return 1
solution.pickIndex(); // return 1
solution.pickIndex(); // return 0. It is returning the first element (index = 0) that has a probability of 1/4.
Since this is a randomization problem, multiple answers are allowed.
All of the following outputs can be considered correct:
[null,1,1,1,1,0]
[null,1,1,1,1,1]
[null,1,1,1,0,0]
[null,1,1,1,0,1]
[null,1,0,1,0,0]
......
and so on.
Constraints:
1 <= w.length <= 104
1 <= w[i] <= 105
pickIndex will be called at most 104 times.
Solutions
Solution 1
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classSolution:def__init__(self,w:List[int]):self.s=[0]forcinw:self.s.append(self.s[-1]+c)defpickIndex(self)->int:x=random.randint(1,self.s[-1])left,right=1,len(self.s)-1whileleft<right:mid=(left+right)>>1ifself.s[mid]>=x:right=midelse:left=mid+1returnleft-1# Your Solution object will be instantiated and called as such:# obj = Solution(w)# param_1 = obj.pickIndex()
classSolution{privateint[]s;privateRandomrandom=newRandom();publicSolution(int[]w){intn=w.length;s=newint[n+1];for(inti=0;i<n;++i){s[i+1]=s[i]+w[i];}}publicintpickIndex(){intx=1+random.nextInt(s[s.length-1]);intleft=1,right=s.length-1;while(left<right){intmid=(left+right)>>1;if(s[mid]>=x){right=mid;}else{left=mid+1;}}returnleft-1;}}/** * Your Solution object will be instantiated and called as such: * Solution obj = new Solution(w); * int param_1 = obj.pickIndex(); */
classSolution{public:vector<int>s;Solution(vector<int>&w){intn=w.size();s.resize(n+1);for(inti=0;i<n;++i)s[i+1]=s[i]+w[i];}intpickIndex(){intn=s.size();intx=1+rand()%s[n-1];intleft=1,right=n-1;while(left<right){intmid=left+right>>1;if(s[mid]>=x)right=mid;elseleft=mid+1;}returnleft-1;}};/** * Your Solution object will be instantiated and called as such: * Solution* obj = new Solution(w); * int param_1 = obj->pickIndex(); */
typeSolutionstruct{s[]int}funcConstructor(w[]int)Solution{n:=len(w)s:=make([]int,n+1)fori:=0;i<n;i++{s[i+1]=s[i]+w[i]}returnSolution{s}}func(this*Solution)PickIndex()int{n:=len(this.s)x:=1+rand.Intn(this.s[n-1])left,right:=1,n-1forleft<right{mid:=(left+right)>>1ifthis.s[mid]>=x{right=mid}else{left=mid+1}}returnleft-1}/** * Your Solution object will be instantiated and called as such: * obj := Constructor(w); * param_1 := obj.PickIndex(); */
userand::{thread_rng,Rng};structSolution{sum:Vec<i32>,}/** * `&self` means the method takes an immutable reference. * If you need a mutable reference, change it to `&mut self` instead. */implSolution{fnnew(w:Vec<i32>)->Self{letn=w.len();letmutsum=vec![0;n+1];foriin1..=n{sum[i]=sum[i-1]+w[i-1];}Self{sum}}fnpick_index(&self)->i32{letx=thread_rng().gen_range(1,self.sum.last().unwrap()+1);let(mutleft,mutright)=(1,self.sum.len()-1);whileleft<right{letmid=(left+right)>>1;ifself.sum[mid]<x{left=mid+1;}else{right=mid;}}(left-1)asi32}}
/** * @param {number[]} w */varSolution=function(w){constn=w.length;this.s=newArray(n+1).fill(0);for(leti=0;i<n;++i){this.s[i+1]=this.s[i]+w[i];}};/** * @return {number} */Solution.prototype.pickIndex=function(){constn=this.s.length;constx=1+Math.floor(Math.random()*this.s[n-1]);letleft=1,right=n-1;while(left<right){constmid=(left+right)>>1;if(this.s[mid]>=x){right=mid;}else{left=mid+1;}}returnleft-1;};/** * Your Solution object will be instantiated and called as such: * var obj = new Solution(w) * var param_1 = obj.pickIndex() */