Top seeds Carlos Alcaraz and Stefanos Tsitsipas sail into Barcelona Open quarter-finals

Top seeds Carlos Alcaraz and Stefanos Tsitsipas both won in straight-sets as they secured quarter-final spots at the Barcelona Open on Thursday.

Spaniard Alcarez was made to battle by countryman Roberto Bautista before coming out on top 6-3, 7-5, while Greece's Tsitsipas eased past Denis Shapovalov of Canada 6-3, 6-2.

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The world No 2 pulled out of the recent Monte Carlo Masters with back and hand problems but brushed aside Nuno Borges with ease in the previous round in Catalonia.

Bautista, though, proved a tougher nut to crack amid windy conditions as top seed Alcaraz continued his title defence on the court named after Rafael Nadal.

“I'm very happy to go through to the next round, it was a very difficult game,” said the 19-year-old, who will now face another Spaniard in 10th seed Alejandro Davidovich Fokina on Friday.

“Everyone knows the capacity Roberto has, how tough he is, and it wasn't easy at all with the wind.

“We say that games like this you have to win with professionalism and hard work. It was very hard to play at the best level, for Roberto too, I'm sure.”

In a heavy-hitting clash, second seed Tsitsipas saved both break points he faced and hit his groundstrokes with weight on the Barcelona clay.

“I tried to stay as aggressive as I could from the baseline,” said Tsitsipas, who also found the conditions tricky. “Against Denis you have to keep up with the pace and be ready to attack when you can.

“It wasn’t easy out here but I did a very good job. I was responsible with my decision making. It was a good day.”

Tsitsipas will now face Australian Alex de Minaur, who advanced after Grigor Dimitrov had to drop out due to illness.

Fourth-seeded Jannik Sinner overcame a second-set stumble to defeat Yoshihito Nishioka 6-1, 4-6, 6-3 as the Italian reached his seventh quarter-final of the season.

The Italian now takes on countryman Lorenzo Musetti, who fought back from a set down to beat seventh seed and British No 1 Cameron Norrie 3-6, 6-4, 6-1. Russian sixth seed Karen Khachanov was beaten 6-3, 6-4 by British No 2 Dan Evans.

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Country-size land deals

US interest in purchasing territory is not as outlandish as it sounds. Here's a look at some big land transactions between nations:

Louisiana Purchase

If Donald Trump is one who aims to broker "a deal of the century", then this was the "deal of the 19th Century". In 1803, the US nearly doubled in size when it bought 2,140,000 square kilometres from France for $15 million.

Florida Purchase Treaty

The US courted Spain for Florida for years. Spain eventually realised its burden in holding on to the territory and in 1819 effectively ceded it to America in a wider border treaty.

Alaska purchase

America's spending spree continued in 1867 when it acquired 1,518,800 km² of Alaskan land from Russia for $7.2m. Critics panned the government for buying "useless land".

The Philippines

At the end of the Spanish-American War, a provision in the 1898 Treaty of Paris saw Spain surrender the Philippines for a payment of $20 million.

US Virgin Islands

It's not like a US president has never reached a deal with Denmark before. In 1917 the US purchased the Danish West Indies for $25m and renamed them the US Virgin Islands.

Gwadar

The most recent sovereign land purchase was in 1958 when Pakistan bought the southwestern port of Gwadar from Oman for 5.5bn Pakistan rupees.