# 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

**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.

## Note

Use accumulated freq array to get idx.\
w\[] = {2,5,3,4} => wsum\[] = {2,7,10,14}\
then get random val`random.nextInt(14)+1`, idx is in range`[1,14]`

```
idx in [1,2] return 0
idx in [3,7] return 1
idx in [8,10] return 2
idx in [11,14] return 3
```

then become LeetCode 35. Search Insert Position\
Time:`O(n)`to init,`O(logn)`for one pick\
Space:`O(n)`

## Code

```java
class Solution {
    Random random;
    int[] presum;
    int[] nums;
    public Solution(int[] w) {
        int len = w.length;
        nums = w;
        random = new Random();
        presum = new int[len + 1];
        for (int i = 0; i < len; i++) {
            presum[i + 1] = presum[i] + w[i];
        }
    }

    public int pickIndex() {
        int len = presum.length;
        int target = random.nextInt(presum[len - 1]) + 1; // closed range: [1, presum[len - 1]]
        int index = binarySearch(target);

        return index - 1;
    }

    private int binarySearch(int target) {
        int start = 0, end = presum.length - 1;
        while (start + 1 < end) {
            int mid = (end - start) / 2 + start;
            if (presum[mid] < target) {
                start = mid;
            } else if (presum[mid] > target) {
                end = mid;
            } else {
                return mid;
            }
        }

        if (presum[start] >= target) {
            return start;
        }
        if (presum[end] >= target) {
            return end;
        }

        return end + 1;
    }
}

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


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://luj.gitbook.io/code/advanced-data-structures/random/random-pick-with-weight.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.