You're given an array representing weights. Implement a function to randomly pick an index from the array, where the probability of picking each index is proportional to its weight.

Imagine a map where cities are connected by roads. Given a list of roads, find how many separate groups of connected cities (provinces) there are.

Find the minimum number of operations to reduce a given positive integer to 0. You can either subtract a power of 2 or add a power of 2 in each operation.