Solution: Random Pick with Weight

Statement

You’re given an array of positive integers, weights, where weights[i] is the weight of the $i^{th}$ index.

Write a function, Pick Index(), which performs weighted random selection to return an index from the weights array. The larger the value of weights[i], the heavier the weight is, and the higher the chances of its index being picked.

Suppose that the array consists of the weights $[12, 84, 35]$. In this case, the probabilities of picking the indexes will be as follows:

• Index 0: $12/(12 + 84 + 35) = 9.2\%$

• Index 1: $84/(12 + 84 + 35) = 64.1\%$

• Index 2: $35/(12 + 84 + 35) = 26.7\%$

Constraints:

• $1 \leq$ weights.length $\leq 10^4$

• $1 \leq$ weights[i] $\leq 10^5$

• Pick Index() will be called at most $10^4$ times.

Note: Since we’re randomly choosing from the options, there is no guarantee that in any specific run of the program, any of the elements will be selected with the exact expected frequency.