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Writing programming interview questions hasn't made me rich yet ... so I might give up and start trading Apple stocks all day instead.

First, I wanna know how much money I could have made yesterday if I'd been trading Apple stocks all day.

So I grabbed Apple's stock prices from yesterday and put them in a list called stock_prices , where:

indices values

So if the stock cost $500 at 10:30am, that means stock_prices[60] = 500 .

Write an efficient function that takes stock_prices and returns the best profit I could have made from one purchase and one sale of one share of Apple stock yesterday.

the best profit I could have made from one purchase and one sale of one share of Apple stock yesterday.

For example:

No "shorting"—you need to buy before you can sell. Also, you can't buy and sell in the same time step—at least 1 minute has to pass.

You can't just take the difference between the highest price and the lowest price , because the highest price might come the lowest price. And you have to buy before you can sell.

What if the price ? In that case, the best profit will be negative .

You can do this in O ( n ) O(n) O ( n ) time and O ( 1 ) O(1) O ( 1 ) space!

However, history does offer options to strategists seeking to maximize geopolitical advantage through economic means. A more illustrative approach to restricted trade is to be found in Napoleon’s “Continental System” or, better yet, the British Navigation Acts from the 1650s onward. While not even the British mercantile system was eternal or foolproof—it was an important cause of the American Revolution and the War of 1812—it was durable and it was hardly the principal motivation for the colonists’ revolt. The imperial system of preferences resurrected itself and survived into the 20th century.

What made the British system work for so long was that it did not balance security and prosperity while affording, by the standards of the day, a high standard of political liberty. What it sacrificed in economic growth it repaid in other ways. It was protectionistic and nationalistic—the English got the best of the deal—but not so narrowly so that it crippled other parts of the empire.

A modern analog to the Navigation Acts might be an American-led “Free Trade Among Free Nations” system, giving preferential economic status to those states with more representative governments or allies. And, in practice, the post-World War II economic order amounted to something like that, and could tolerate mercantilistic behavior even within a mostly-open system. Thus, for example, the Japanese economic policies of the 1980s posed no threat—except eventually to the prosperity of the Japanese themselves—since Tokyo was a strategic client of the United States. China’s current practices may be more economically egregious, but they also serve to enrich an American adversary. Mass-produced goods made, say, in Indonesia—not only a struggling democracy but the world’s largest Muslim state—might cost a bit more than those made in China, but the strategic effect might well be worth the cost.

In such a context, both sanctions and preferences might make geopolitical sense—although the Trump steel and aluminum tariffs would not meet this test. The problem is that the United States and its industrialized allies have come to see sanctions as a replacement for harder tools of power rather than as a supplement. The effects on today’s autocrats won’t be much: you don’t rise to a leadership position in the Quds Force or Chinese Communist Party or the Russian oligarchy without learning how to hide your money or being willing to let your own people suffer the consequences of your actions.

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Thomas Donnelly

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