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Solution: Random Pick with Weight

Understand how to implement a weighted random pick function by transforming weights into running sums and applying a modified binary search. Learn to generate a random target within the cumulative weights and efficiently find the corresponding index. This lesson helps you grasp optimized approaches for weighted selections with improved time complexity.

Statement

You’re given an array of positive integers, weights, where weights[i] is the weight of the ithi^{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][12, 84, 35]. In this case, the probabilities of picking the indexes will be as follows:

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

  • Index 1: 84/(12 ...