Mayor Bill de Blasio won re-election on Tuesday, with one of the biggest achievements of his first term being the creation of universal pre-K for 4-year-olds.

The mayor’s most serious challenger was Nicole Malliotakis, a Republican state assemblywoman from Staten Island who has condemned sanctuary cities and spoken out against plans to make undocumented immigrants eligible for state financial aid for college.

The Times interviewed Ms. Malliotakis and Mr. de Blasio about their approach to management and their visions for New York City.