[LeetCode] 528. Random Pick with Weight

Problem

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 <= w.length <= 10000
1 <= w[i] <= 10^5
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. create an array sum, to save sum of weights
2. create a Random random to create random in a range
3. the range should be [1, maxValue] as [1, sum[len-1]]
4. use Random.nextInt(maxValue) + 1 to get a random num of the range
5. use binary search to find the index of random in sum array

class Solution {
    int[] sums;
    int max;
    Random random;
    public Solution(int[] w) {
        sums = new int[w.length];
        sums[0] = w[0];
        for (int i = 1; i < sums.length; i++) {
            sums[i] = sums[i-1]+w[i];
        }
        max = sums[sums.length-1];
        random = new Random();
    }
    
    public int pickIndex() {
        int rand = random.nextInt(max)+1;
        int index = findIndex(sums, rand);
        return index;
    }
    
    private int findIndex(int[] nums, int k) {
        int start = 0, end = nums.length-1;
        while (start+1 < end) {
            int mid = start+(end-start)/2;
            if (nums[mid] == k) return mid;
            else if (nums[mid] < k) start = mid+1;
            else end = mid-1;
        }
        if (k > nums[end]) return end+1;
        else if (k > nums[start]) return start+1;
        else return start;
    }
}