random-pick-with-weight

Algorithms

Random Pick with Weight

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You are given a 0-indexed array of positive integers <code>w</code> where <code>w[i]</code> describes the weight of the <code>ith</code> index.

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

<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>

&nbsp;
Example 1:

<pre>
Input
[&quot;Solution&quot;,&quot;pickIndex&quot;]
[[[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.
</pre>

Example 2:

<pre>
Input
[&quot;Solution&quot;,&quot;pickIndex&quot;,&quot;pickIndex&quot;,&quot;pickIndex&quot;,&quot;pickIndex&quot;,&quot;pickIndex&quot;]
[[[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.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= w.length &lt;= 104</code></li>
	<li><code>1 &lt;= w[i] &lt;= 105</code></li>
	<li><code>pickIndex</code> will be called at most <code>104</code> times.</li>
</ul>

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