528. Random Pick with Weight

528. Random Pick with Weight

Given an array w of positive integers, where w[i] describes the weight of index i, write a function pickIndex which randomly picks an index in proportion to its weight.

Note:

1. 1 <= w.length <= 10000
2. 1 <= w[i] <= 10^5
3. pickIndex will be called at most 10000 times.

Example 1:

Input: 
["Solution","pickIndex"]
[[[1]],[]]
Output: [null,0]

Example 2:

Input: 
["Solution","pickIndex","pickIndex","pickIndex","pickIndex","pickIndex"]
[[[1,3]],[],[],[],[],[]]
Output: [null,0,1,1,1,0]

Explanation of Input Syntax:

The input is two lists: the subroutines called and their arguments. Solution's constructor has one argument, the array w. pickIndex has no arguments. Arguments are always wrapped with a list, even if there aren't any.

---------------------------
Solution #1
pickIndex O(n) time

class Solution {

    private double calls;
    private int[] count;
    private double totalWeight;
    private Random rand;
    private int[] w;
    
    public Solution(int[] w) {
        count = new int[w.length];
        calls = 0;
        rand = new Random();
        this.w = w;
        for (int i : w) totalWeight += (double)i;
    }
    
    public int pickIndex() {
        calls++;
        int next = rand.nextInt(w.length);
        
        while (count[next] / calls > w[next] / totalWeight) {
            next = rand.nextInt(w.length);
        }
        
        count[next]++;
        return next;
    }
}

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

Solution #2
与Solution #1用array的大小当做random范围不同，这里我们用整个array的totalWeight当做random的范围，然后用accumulative sum来划分原来的weight array。然后用二分法找到落入该区间的所属的index
O(lgN)

class Solution {
    
    private int[] sums;
    private Random rand = new Random();
    private int range;
    private int n;
    
    public Solution(int[] w) {
        
        n = w.length;
        sums = new int[n];
        sums[0] = w[0] - 1;
        
        for (int i = 1; i < n; i++) {
            sums[i] = sums[i - 1] + w[i];
        }
        
        range = sums[n - 1];
    }
    
    public int pickIndex() {
        int target = rand.nextInt(range + 1);
        int left = 0, right = n - 1;
        
        while (left < right) {
            int mid = (left + right) / 2;
            if (sums[mid] == target) {
                return mid;
            }else if (sums[mid] > target) {
                right = mid;
            }else {
                left = mid + 1;
            }
        }
        
        return left;
    }
}

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