How many times a tennis player became world number one ranking without ever winning a grand slam?

ATP:

• Ivan Lendl was the only player in the list who has won singles grand slams prior to Wozniacki winning her only slam in 2018. He's known as one of the greatest players ever, holding the world #1 for 270 weeks (the 3rd most all time by a male player). He reached #1 seed first time in 1983. In 1984 he won his first grand slam at the French Open after four major finals losses. Lendl has won 8 majors championships, having won all grand slams except for Wimbledon.

• Marcelo Rios was the top seed for only 6 weeks in 1998. In his only grand slam finals appearance he lost to Petr Korda in the 1998 Australian Open.

WTA:

• Caroline Wozniacki finished 2010 and 2011 as the top seed, in total she's been the world #1 for 67 weeks. Despite winning 25 WTA titles, she's never won a grand slam. Her only grand slam finals happened in the US open in 2009 and 2014. EDIT: Before retiring, Wozniacki won the 2018 Australian Open. The championship propelled her to the #1 ranking once more, but this time as a grand slam champion.

• Jelena Jankovic reached the top seed in 2008 and finished the year in that spot, making her the first player in WTA to finish a year as world #1 without wining a grand slam. Her only singles majors finals was the 2008 US open. It is noteworthy that she won a grand slam in mixed doubles of 2007 Wimbledon with Jamie Murray.

• Dinara Safina became world #1 in 2009. She made the most singles grand slam finals without a championship among the players in this list. She was the runner up in 2008 and 2009 French Open as well as the 2009 Australian Open. Similar to Jankovic, Safina's only majors championship came in the doubles. She won the 2007 US open women's doubles with Nathalie Dechy.