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
/**
 * @param {number[]} w
 */
var Solution = function (w) {
    const n = w.length;
    this.s = new Array(n + 1).fill(0);
    for (let i = 0; i < n; ++i) {
        this.s[i + 1] = this.s[i] + w[i];
    }
};

/**
 * @return {number}
 */
Solution.prototype.pickIndex = function () {
    const n = this.s.length;
    const x = 1 + Math.floor(Math.random() * this.s[n - 1]);
    let left = 1,
        right = n - 1;
    while (left < right) {
        const 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:
 * var obj = new Solution(w)
 * var param_1 = obj.pickIndex()
 */
