Random Pick with Weight in C++

Suppose we have an array w of positive integers, were w[i] describes the weight of index i, we have to define a function pickIndex() which randomly picks an index in proportion to its weight.

So if the input is like [1,3], call pickIndex() five times, then the answer may come as − 0, 1, 1, 1, 0.

To solve this, we will follow these steps −

• Define an array v,
• Through the initializer, initialize as
• n := w[0]
• for i in range 1 to size of w
  • w[i] := w[i] + w[i – 1]
  • n := w[i]
• v = w
• The pickIndex() will work as follows −
• Take a random number r, perform r mod last element of v
• take the smallest number, not smaller than r from v, then subtract first number of v from the element and return.

Let us see the following implementation to get better understanding −

Example

 Live Demo

#include <bits/stdc++.h>
using namespace std;
class Solution {
   public:
   int n;
   vector <int> v;
   Solution(vector<int>& w) {
      srand(time(NULL));
      n = w[0];
      for(int i = 1; i < w.size(); i++){
         w[i] += w[i - 1];
         n = w[i];
      }
      v = w;
   }
   int pickIndex() {
      return upper_bound(v.begin(), v.end(), rand() % v.back()) - v.begin();
   }
};
main(){
   vector<int> v = {1,3};
   Solution ob(v);
   cout << (ob.pickIndex()) << endl;
   cout << (ob.pickIndex()) << endl;
   cout << (ob.pickIndex()) << endl;
   cout << (ob.pickIndex()) << endl;
   cout << (ob.pickIndex()) << endl;
}

Input

Initialize with [1, 3] and call pickIndex five times.

Output

1
1
1
1
0