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## Problem

You are given a 0-indexed array of positive integers w where w[i] describes the weight of the i^th 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 <= 10^4
• 1 <= w[i] <= 10^5
• pickIndex will be called at most 10^4 times.

## Code

class Solution {
int[] sum;

public Solution(int[] w) {
sum = new int[w.length];

sum[0] = w[0];
for(int i = 1; i < w.length; i++) {
sum[i] = sum[i - 1] + w[i];
}
}

public int pickIndex() {
double target = Math.random() * sum[sum.length - 1];

int left = 0;
int right = sum.length - 1;

while(left + 1 < right) {
int mid = (left + right) / 2;

if(sum[mid] == target) return mid;

if(sum[mid] > target) {
right = mid;
} else {
left = mid;
}
}

if(sum[left] >= target) {
return left;
} else {
return right;
}
}
}

class Solution {
int sum;
TreeMap<Double, Integer> map;

public Solution(int[] w) {
map = new TreeMap<>();
sum = 0;

for(int i = 0; i < w.length; i++) {
sum += w[i];
map.put((double)sum, i);
}
}

public int pickIndex() {
double target = Math.random() * sum;
return map.get(map.ceilingKey(target));
}
}