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# 528     Random Pick with Weight

## 528. [Random Pick with Weight](https://leetcode.com/problems/random-pick-with-weight/)

## 1. Question

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]
```

## 2. Implementation

**(1) TreeMap**

```java
class Solution {
    TreeMap<Integer, Integer> map;
    Random rand;
    int totalWeight;
    int[] weight;

    public Solution(int[] w) {
        this.weight = w;
        map = new TreeMap();
        totalWeight = 0;
        rand = new Random();

        for (int i = 0; i < weight.length; i++) {
            totalWeight += weight[i];
            map.put(totalWeight, i);
        }
    }

    public int pickIndex() {
        int randWeight = rand.nextInt(totalWeight) + 1;
        int key = map.ceilingKey(randWeight);
        return map.get(key);
    }
}

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

**(2) Binary Search**

```java
class Solution {
    Random rand;
    int[] weight;
    int totalWeight;

    public Solution(int[] w) {
        rand = new Random();
        this.weight = w;
        totalWeight = weight[0];

        for (int i = 1; i < weight.length; i++) {
            totalWeight += weight[i];
            weight[i] += weight[i - 1];
        }
    }

    public int pickIndex() {
        int target = rand.nextInt(totalWeight) + 1;

        int left = 0, right = weight.length - 1;

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

            if (weight[mid] < target) {
                left = mid + 1;
            }
            else {
                right = mid;
            }
        }
        return weight[left] >= target ? left : right;
    }
}

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

## 3. Time & Space Complexity

**(1) TreeMap: Time**: constructor: O(n), pickIndex: O(logn), **Space**: O(n)

**(2) Binary Tree: Time**: constructor: O(n), pickIndex: O(logn), **Space**: O(n)


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