This is an interesting question, and I suggest that you find out yourself. You will need a few small fish tanks, the brands of bottled water you want to test, and a few other things to monitor the growth.
You may need to search the web for places that can provide you with a type of algae - such as spirulina - and the required equipment, then test out the bottled water yourself. The algae will likely take a few weeks to truly grow, during which you will want to keep all the tanks under the exact same conditions except for the brands of the bottled water you're using.
You may also want to measure the mass of the algae by scooping a bit and weighing this bit - just be careful that you're always scooping all the tanks with the same scoop, and that you are getting the same ratio of algae to water so that your comparison of how well the algae grows is valid across the different brands of water. After a few weeks of collecting data on how well the algae grows, you should be able to see the differences, if any.
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