Random Pick with Weight

Explore how to create a function for weighted random index selection in arrays by applying modified binary search techniques. Understand how weights influence selection probabilities and practice implementing this algorithm efficiently to handle multiple function calls.

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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: $12 / (12 + 84 + 35$ ...