Question

528. Random Pick with Weight

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Description

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

class Solution:
  def __init__(self, w: List[int]):
    self.s = [0]
    for c in w:
      self.s.append(self.s[-1] + c)

  def pickIndex(self) -> int:
    x = random.randint(1, self.s[-1])
    left, right = 1, len(self.s) - 1
    while left < right:
      mid = (left + right) >> 1
      if self.s[mid] >= x:
        right = mid
      else:
        left = mid + 1
    return left - 1


# Your Solution object will be instantiated and called as such:
# obj = Solution(w)
# param_1 = obj.pickIndex()

class Solution {
  private int[] s;
  private Random random = new Random();

  public Solution(int[] w) {
    int n = w.length;
    s = new int[n + 1];
    for (int i = 0; i < n; ++i) {
      s[i + 1] = s[i] + w[i];
    }
  }

  public int pickIndex() {
    int x = 1 + random.nextInt(s[s.length - 1]);
    int left = 1, right = s.length - 1;
    while (left < right) {
      int mid = (left + right) >> 1;
      if (s[mid] >= x) {
        right = mid;
      } else {
        left = mid + 1;
      }
    }
    return left - 1;
  }
}

/**
 * Your Solution object will be instantiated and called as such:
 * Solution obj = new Solution(w);
 * int param_1 = obj.pickIndex();
 */

class Solution {
public:
  vector<int> s;

  Solution(vector<int>& w) {
    int n = w.size();
    s.resize(n + 1);
    for (int i = 0; i < n; ++i) s[i + 1] = s[i] + w[i];
  }

  int pickIndex() {
    int n = s.size();
    int x = 1 + rand() % s[n - 1];
    int left = 1, right = n - 1;
    while (left < right) {
      int mid = left + right >> 1;
      if (s[mid] >= x)
        right = mid;
      else
        left = mid + 1;
    }
    return left - 1;
  }
};

/**
 * Your Solution object will be instantiated and called as such:
 * Solution* obj = new Solution(w);
 * int param_1 = obj->pickIndex();
 */

type Solution struct {
  s []int
}

func Constructor(w []int) Solution {
  n := len(w)
  s := make([]int, n+1)
  for i := 0; i < n; i++ {
    s[i+1] = s[i] + w[i]
  }
  return Solution{s}
}

func (this *Solution) PickIndex() int {
  n := len(this.s)
  x := 1 + rand.Intn(this.s[n-1])
  left, right := 1, n-1
  for left < right {
    mid := (left + right) >> 1
    if this.s[mid] >= x {
      right = mid
    } else {
      left = mid + 1
    }
  }
  return left - 1
}

/**
 * Your Solution object will be instantiated and called as such:
 * obj := Constructor(w);
 * param_1 := obj.PickIndex();
 */

use rand::{ thread_rng, Rng };

struct Solution {
  sum: Vec<i32>,
}

/**
 * `&self` means the method takes an immutable reference.
 * If you need a mutable reference, change it to `&mut self` instead.
 */
impl Solution {
  fn new(w: Vec<i32>) -> Self {
    let n = w.len();
    let mut sum = vec![0; n + 1];
    for i in 1..=n {
      sum[i] = sum[i - 1] + w[i - 1];
    }
    Self { sum }
  }

  fn pick_index(&self) -> i32 {
    let x = thread_rng().gen_range(1, self.sum.last().unwrap() + 1);
    let (mut left, mut right) = (1, self.sum.len() - 1);
    while left < right {
      let mid = (left + right) >> 1;
      if self.sum[mid] < x {
        left = mid + 1;
      } else {
        right = mid;
      }
    }
    (left - 1) as i32
  }
}/**
 * Your Solution object will be instantiated and called as such:
 * let obj = Solution::new(w);
 * let ret_1: i32 = obj.pick_index();
 */

/**
 * @param {number[]} w
 */
var Solution = function (w) {
  const n = w.length;
  this.s = new Array(n + 1).fill(0);
  for (let i = 0; i < n; ++i) {
    this.s[i + 1] = this.s[i] + w[i];
  }
};

/**
 * @return {number}
 */
Solution.prototype.pickIndex = function () {
  const n = this.s.length;
  const x = 1 + Math.floor(Math.random() * this.s[n - 1]);
  let left = 1,
    right = n - 1;
  while (left < right) {
    const mid = (left + right) >> 1;
    if (this.s[mid] >= x) {
      right = mid;
    } else {
      left = mid + 1;
    }
  }
  return left - 1;
};

/**
 * Your Solution object will be instantiated and called as such:
 * var obj = new Solution(w)
 * var param_1 = obj.pickIndex()
 */