Random Pick with Weight
<p>You are given a <strong>0-indexed</strong> array of positive integers <code>w</code> where <code>w[i]</code> describes the <strong>weight</strong> of the <code>i<sup>th</sup></code> index.</p>

<p>You need to implement the function <code>pickIndex()</code>, which <strong>randomly</strong> picks an index in the range <code>[0, w.length - 1]</code> (<strong>inclusive</strong>) and returns it. The <strong>probability</strong> of picking an index <code>i</code> is <code>w[i] / sum(w)</code>.</p>

<ul>
	<li>For example, if <code>w = [1, 3]</code>, the probability of picking index <code>0</code> is <code>1 / (1 + 3) = 0.25</code> (i.e., <code>25%</code>), and the probability of picking index <code>1</code> is <code>3 / (1 + 3) = 0.75</code> (i.e., <code>75%</code>).</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input</strong>
[&quot;Solution&quot;,&quot;pickIndex&quot;]
[[[1]],[]]
<strong>Output</strong>
[null,0]

<strong>Explanation</strong>
Solution solution = new Solution([1]);
solution.pickIndex(); // return 0. The only option is to return 0 since there is only one element in w.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input</strong>
[&quot;Solution&quot;,&quot;pickIndex&quot;,&quot;pickIndex&quot;,&quot;pickIndex&quot;,&quot;pickIndex&quot;,&quot;pickIndex&quot;]
[[[1,3]],[],[],[],[],[]]
<strong>Output</strong>
[null,1,1,1,1,0]

<strong>Explanation</strong>
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.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= w.length &lt;= 10<sup>4</sup></code></li>
	<li><code>1 &lt;= w[i] &lt;= 10<sup>5</sup></code></li>
	<li><code>pickIndex</code> will be called at most <code>10<sup>4</sup></code> times.</li>
</ul>
Array; Math; Binary Search; Prefix Sum; Randomized
type Solution struct {
	s []int
}

func Constructor(w []int) Solution {
	n := len(w)
	s := make([]int, n+1)
	for i := 0; i < n; i++ {
		s[i+1] = s[i] + w[i]
	}
	return Solution{s}
}

func (this *Solution) PickIndex() int {
	n := len(this.s)
	x := 1 + rand.Intn(this.s[n-1])
	left, right := 1, n-1
	for left < right {
		mid := (left + right) >> 1
		if this.s[mid] >= x {
			right = mid
		} else {
			left = mid + 1
		}
	}
	return left - 1
}

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