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Solution: Random Pick with Weight

Explore how to solve the weighted random pick problem by creating running sums of weights and applying modified binary search. This lesson helps you understand generating biased random picks efficiently using time and space optimized approaches.

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+84+35)=64.1%84/(12 + 84 + 35) = 64.1\%

  • Index 2: ...